text:
\section{Introduction}

For the description of finite-dimensional systems, due to the illustration
of the underlying physical effects, the port-Hamiltonian (pH) system
representation has proven to be an adequate framework. A major advantage
is the close relation between the total energy of the system and the
corresponding evolution equations, providing an insight into the energy
flows within the system and with the system environment. In particular
the fact that so-called energy-ports appear, makes the pH-system representation
interesting for control-engineering applications, see \cite{Schaft2000,Ortega2001}
for instance. The basic idea of such appropriate control strategies
is to design a closed-loop system exhibiting a desired behaviour.
Therefore, the objective is to shape the total energy of the system
and increase the dissipation rate, or even modify the structure of
the system dynamics.

Some of these well-known control strategies, like the so-called energy-Casimir
method, have already been extended to systems governed by partial
differential equations (PDEs), where for the most parts the occurrence
of boundary-energy ports is exploited. It must be mentioned that the
pH-system representation in the infinite-dimensional scenario is not
unique, see \cite{Schoeberl2013b} for a comparison of the Stokes-Dirac
approach and an approach based on jet-bundle structures by means of
a mechanical example. As a consequence, the generation of the boundary
ports strongly depends on the chosen approach. In \cite{Schaft2002,Macchelli2004a,Gorrec2005},
the boundary-energy flow for infinite-dimensional systems formulated
within the Stokes-Dirac scenario is investigated, while in \cite{Ennsbrunner2005,Schoeberl2014a,Malzer2018}
the generation of boundary ports for the jet-bundle approach is discussed.
With regard to control by interconnection based on structural invariants
(Casimir functionals), these boundary ports shall be used to couple
the infinite-dimensional plant to a dynamic controller. This control
strategy provides the opportunity to inject additional damping into
the closed loop, and moreover, the mentioned Casimir functionals are
used to relate (some) of the controller states to the plant in order
to shape the energy of the system, see, e.g., \cite{Macchelli2004b,Macchelli2004}
for the controller design in the Stokes-Dirac framework and \cite{Siuka2011a,Schoeberl2013a,Rams2017a}
for the jet-bundle approach. From a mathematical point of view, an
essential feature is that a system governed by PDEs is coupled at
(a part of) the boundary with a system that is described by ordinary
differential equations (ODEs).

It is worth stressing that the application of boundary-control schemes
constitutes a restriction with regard to the energy flows. Furthermore,
there are many actuators, like, e.g., piezoelectric actuators, which
do not operate on the boundary but within the spatial domain. In view
of these facts, it seems natural to extend the known boundary-control
schemes to the control of infinite-dimensional systems with in-domain
actuation. There, a distinction needs to be drawn. On the one hand,
we consider systems with lumped inputs that may act on a part of the
spatial domain. For this system class, the interconnection of the
system with a dynamic controller corresponds to a coupling of a PDE
and an ODE-system within the spatial domain of the infinite-dimensional
system. On the other hand, the scenario of systems with distributed
input densities would call for infinite-dimensional controllers, which
represents the coupling of a PDE with a PDE. For stability investigations
of infinite-dimensional systems, usually functional-analytic methods
are used, see e.g. \cite{Jacob2012}. This framework also allows to
investigate the well-posedness of a problem. However, in this contribution
we assume well-posedness and confine ourselves on energy considerations.
Thus, no detailed stability investigations are carried out.

To demonstrate the proposed control strategy, we consider pH-systems
with 2nd-order Hamiltonian on 1-dimensional spatial domains. For such
systems, in \cite{Rams2017a} a dynamic boundary controller has been
derived. Now, we intend to develop an in-domain control strategy for
this system class. Therefore, the main contributions of this paper
are as follows. First, we state a proper pH-system representation
of a piezo-actuated Euler-Bernoulli beam in Section 3. Furthermore,
we derive an appropriate control methodology for infinite-dimensional
pH-systems with lumped inputs that may act on a part of the spatial
domain and show the capability of the approach by means of simulation
results for the piezo-actuated Euler-Bernoulli beam, see Section 4.

\section{Notation and Preliminaries}

Throughout this paper, we make heavy use of differential-geometric
methods, where the notation is similar to that of \cite{Giachetta1997}.
Formulas are kept short and readable by applying tensor notation and
using Einsteins convention on sums. However, the ranges of the used
indices are not indicated when they are clear from the context. We
use the standard symbols $\wedge$, $\rfloor$ and $\mathrm{d}$ denoting
the exterior (wedge) product, the natural contraction between tensor
fields and the exterior derivative, respectively. To avoid exaggerated
notation, the use of pull-back bundles is omitted. Furthermore, the
expression $C^{\infty}(\mathcal{M})$ denotes the set of all smooth
functions on a manifold $\mathcal{M}$.

In this contribution, we investigate systems governed by PDEs in a
pH-setting. Therefore, we introduce some geometrical structures and
begin with defining a so-called bundle $\pi:\mathcal{E}\rightarrow\mathcal{B}$,
which allows a clear distinction between dependent and independent
coordinates. Here, the base manifold $\mathcal{B}$ is equipped with
the independent coordinate $z^{1}$ as we confine ourselves to 1-dimensional
spatial domains. Consequently, the boundary $\partial\mathcal{B}$
is zero-dimensional and the restriction of a mathematical expression
to $\partial\mathcal{B}$ is indicated with $(\cdot)|_{\partial\mathcal{B}}$.
As the total manifold $\mathcal{E}$ comprises the dependent coordinates
$x^{\alpha}$, with $\alpha=1,\ldots,n$, as well, it is equipped
with $(z^{1},x^{\alpha})$. Moreover, $\pi$ is a surjective submersion
from the total manifold $\mathcal{E}$ to the base manifold $\mathcal{B}$
and is called projection. Next, we consider (higher-order) jet manifolds
to be able to introduce derivative coordinates (jet variables). For
instance, the 4th jet manifold $\mathcal{J}^{4}(\mathcal{E})$ possesses
the coordinates $(z^{1},x^{\alpha},x_{1}^{\alpha},x_{11}^{\alpha},x_{111}^{\alpha},x_{1111}^{\alpha})$,
where, exemplarily, $x_{11}^{\alpha}$ denotes the 2nd-order derivative
coordinate, i.e. the 2nd derivative of $x^{\alpha}$ with respect
to the independent coordinate $z^{1}$.

Furthermore, we introduce the so-called tangent bundle $\tau_{\mathcal{E}}:\mathcal{T}(\mathcal{E})\rightarrow\mathcal{E}$
equipped with the coordinates $(z^{1},x^{\alpha},\dot{z}^{1},\dot{x}^{\alpha})$,
where the abbreviations $\partial_{1}=\partial/\partial z^{1}$ and
$\partial_{\alpha}=\partial/\partial x^{\alpha}$ denote the fibre
bases of the bundle. An important subbundle of $\tau_{\mathcal{E}}$
is the vertical tangent bundle $\nu_{\mathcal{E}}:\mathcal{V}(\mathcal{E})\rightarrow\mathcal{E}$,
which possesses the coordinates $(z^{1},x^{\alpha},\dot{x}^{\alpha})$.
Since the relation $\dot{z}^{1}=0$ holds, the vertical vector field
$v=v^{\alpha}\partial_{\alpha}$ is tangent to the fibres of $\mathcal{E}$.
Furthermore, the 2nd prolongation of a vertical vector field $v$
is given by $j^{2}\left(v\right)=v^{\alpha}\partial_{\alpha}+d_{1}(v^{\alpha})\partial_{\alpha}^{1}+d_{1}(d_{1}(v^{\alpha}))\partial_{\alpha}^{11}$
and makes use of the total derivative $d_{1}=\partial_{1}+x_{1}^{\alpha}\partial_{\alpha}+x_{11}^{\alpha}\partial_{\alpha}^{1}+x_{111}^{\alpha}\partial_{\alpha}^{11}+x_{1111}^{\alpha}\partial_{\alpha}^{111}+\ldots$
together with the abbreviations $\partial_{\alpha}^{1}=\partial/\partial x_{1}^{\alpha}$
and $\partial_{\alpha}^{1\ldots1}=\partial/\partial x_{1\ldots1}^{\alpha}$.

Further important bundles are the cotangent bundles $\tau_{\mathcal{B}}^{*}=\mathcal{T}^{*}\left(\mathcal{B}\right)\rightarrow\mathcal{B}$
and $\tau_{\mathcal{E}}^{*}=\mathcal{T}^{*}\left(\mathcal{E}\right)\rightarrow\mathcal{E}$
possessing the coordinates $(z^{1},\dot{z}_{1})$ and $(z^{1},x^{\alpha},\dot{z}_{1},\dot{x}_{\alpha})$,
respectively, where the holonomic bases are denoted by $\mathrm{d}z^{1},\mathrm{d}x^{\alpha}$.
These bundles allow to locally define one-forms according to $\varpi=\varpi_{1}\mathrm{d}z^{1}$
and $\omega=\omega_{1}\mathrm{d}z^{1}+\omega_{\alpha}\mathrm{d}x^{\alpha}$,
with $\varpi_{1}\in C^{\infty}(\mathcal{B})$ and $\omega_{1},\omega_{\alpha}\in C^{\infty}(\mathcal{E})$.
In what follows, we are interested in one-forms with coefficients
depending on derivative variables. More precisely, we focus on (Hamiltonian)
densities $\mathfrak{H}=\mathcal{H}\Omega$ with $\mathcal{H}\in C^{\infty}(\mathcal{J}^{2}(\mathcal{E}))$,
i.e. on densities that may depend on 2nd-order derivative coordinates.
Here, $\Omega=\mathrm{d}z^{1}$ denotes the volume element on $\mathcal{B}$
and $\Omega_{1}=\partial_{1}\rfloor\mathrm{d}z^{1}$ the boundary-volume
form. The integrated quantity of $\mathfrak{H}$, which is given by
$\mathscr{H}=\int_{\mathcal{B}}\mathcal{H}\Omega$, is called the
Hamiltonian functional. The bundle structure $\pi:\mathcal{E}\rightarrow\mathcal{B}$
allows to construct some further geometric objects like the tensor
bundle $\mathcal{W}_{1}^{r}(\mathcal{E})=\mathcal{T}^{*}(\mathcal{E})\wedge\mathcal{T}^{*}(\mathcal{B})$
with a typical element $\omega_{\alpha}\mathrm{d}x^{\alpha}\wedge\mathrm{d}z^{1}$
for $\mathcal{W}_{1}^{r}(\mathcal{E})$, where $\omega_{\alpha}\in C^{\infty}(\mathcal{J}^{r}(\mathcal{E}))$
is met.

\section{Infinite-Dimensional PH-Systems}

This section deals with the pH-system representation based on jet-bundle
structures for systems with 1-dimensional spatial domain and 2nd-order
Hamiltonian, see, e.g. \cite{Rams2017a}. The framework has its origin
in \cite{Ennsbrunner2005,Schoeberl2008a}, and is mainly based on
a certain power-balance relation, which allows us to introduce (power)
ports distributed over the domain as well as on the boundary. In this
paper, we focus on systems with in-domain actuation and hence, as
a classical example we derive a proper pH-system representation of
a piezo-actuated Euler-Bernoulli beam.

Let $\mathfrak{H}$ be a 2nd-order Hamiltonian, i.e. $\mathcal{H}\in C^{\infty}(\mathcal{J}^{2}(\mathcal{E}))$,
then a pH-system formulation including in- and outputs on the domain
is given by
\begin{align}
\dot{x} & =(\mathcal{J}-\mathcal{R})(\delta\mathfrak{H})+u\rfloor\mathcal{G},\label{eq:pH_system_general}\\
y & =\mathcal{G}^{*}\rfloor\delta\mathfrak{H},\nonumber
\end{align}
together with appropriate boundary conditions.\begin{rem}It should
be noted that in \cite{Schoeberl2011,Schoeberl2013a,Rams2017a}, only
systems with boundary in- and outputs have been investigated. In this
contribution, we focus our interests on systems with in-domain actuation,
and, therefore we include the term $u\rfloor\mathcal{G}$ in our system
representation.\end{rem}In (\ref{eq:pH_system_general}), the interconnection
map $\mathcal{J}$, which describes the internal power flow, and the
dissipation map $\mathcal{R}$ take the form of $\mathcal{J},\mathcal{R}:\mathcal{T}^{*}(\mathcal{E})\wedge\mathcal{T}^{*}(\mathcal{B})\rightarrow\mathcal{V}(\mathcal{E})$.
Furthermore, $\mathcal{J}$ is skew-symmetric, i.e. the coefficients
meet $\mathcal{J}^{\alpha\beta}=-\mathcal{J}^{\beta\alpha}\in C^{\infty}(\mathcal{J}^{4}(\mathcal{E}))$,
and $\mathcal{R}$ is symmetric and positive semidefinite, implying
$\mathcal{R}^{\alpha\beta}=\mathcal{R}^{\beta\alpha}\in C^{\infty}(\mathcal{J}^{4}(\mathcal{E}))$
and $\left[\mathcal{R}^{\alpha\beta}\right]\geq0$ for the coefficient
matrix. For 2nd-order Hamiltonian densities, the variational derivative
corresponds to $\delta\mathfrak{H}=\delta_{\alpha}\mathcal{H}\mathrm{d}x^{\alpha}\wedge\Omega$
with $\delta_{\alpha}(\cdot)=\partial_{\alpha}(\cdot)-d_{1}(\partial_{\alpha}^{1}(\cdot))+d_{11}(\partial_{\alpha}^{11}(\cdot))$.
Due to the fact that we intend to develop in-domain control strategies
in this paper, the terms including the external inputs and collocated
outputs  in (\ref{eq:pH_system_general}) are of particular interest.
It is worth stressing that both, the coefficients $\mathcal{G}_{\xi}^{\alpha}$
of the input map $\mathcal{G}:\mathcal{U}\rightarrow\mathcal{V}(\mathcal{X})$
as well as the input coordinates $u^{\xi}\in\mathcal{U}$, may depend
(amongst others) on the spatial variable $z^{1}$. Based on the duality
of the input- and the output-bundle, see \cite[Section IV]{Ennsbrunner2005},
we are able to deduce the important relation
\begin{equation}
(u\rfloor\mathcal{G})\delta\mathfrak{H}=u\rfloor(\mathcal{G}^{*}\rfloor\delta\mathfrak{H})=u\rfloor y.\label{eq:distributed_collocation}
\end{equation}
With regard to the control-engineering purposes of the following section,
it is of particular interest how the Hamiltonian functional $\mathscr{H}$
evolves along solutions of the system (\ref{eq:pH_system_general})
(well-posedness provided). If $\mathscr{H}$ corresponds to the total
energy of the system, the formal change, which can be given as
\begin{equation}
\dot{\mathscr{H}}=-\int_{\mathcal{B}}\mathcal{R}(\delta\mathfrak{H})\rfloor\delta\mathfrak{H}+\int_{\mathcal{B}}u\rfloor y+(\dot{x}\rfloor\delta^{\partial,1}\mathfrak{H}+\dot{x}_{1}\rfloor\delta^{\partial,2}\mathfrak{H})|_{\partial\mathcal{B}}\label{eq:h_p_general}
\end{equation}
by means of (\ref{eq:distributed_collocation}), states a power-balance
relation and comprises dissipation and collocation on the domain.
The collocation term $\int_{\mathcal{B}}u\rfloor y$ can be used to
define power ports distributed over the spatial domain allowing for
a non-zero power flow. Furthermore, (\ref{eq:h_p_general}) enables
us to introduce boundary-power ports, where we basically exploit the
boundary operators $\delta^{\partial,1}\mathfrak{H}=(\partial_{\alpha}^{1}\mathcal{H}-d_{1}(\partial_{\alpha}^{11}\mathcal{H}))\mathrm{d}x^{\alpha}\wedge\Omega_{1}$
and $\delta^{\partial,2}\mathfrak{H}=\partial_{\alpha}^{11}\mathcal{H}\mathrm{d}x_{1}^{\alpha}\wedge\Omega_{1}$,
locally given as
\begin{equation}
\delta_{\alpha}^{\partial,1}\mathcal{H}=\partial_{\alpha}^{1}\mathcal{H}-d_{1}(\partial_{\alpha}^{11}\mathcal{H}),\quad\delta_{\alpha}^{\partial,2}\mathcal{H}=\partial_{\alpha}^{11}\mathcal{H}.\label{eq:boundary_operators}
\end{equation}
Worth stressing is the fact that for the system class under investigation
(1-dimensional spatial domain and 2nd-order Hamiltonian), the formal
change (\ref{eq:h_p_general}) can be determined by integration by
parts. However, for pH-systems with 2nd-order Hamiltonian and higher-dimensional
spatial domain, the calculation of $\dot{\mathscr{H}}$ is a non-trivial
task, which is treated in \cite{Schoeberl2018}.

A local system representation of (\ref{eq:pH_system_general}) can
be given as
\begin{align}
\dot{x}^{\alpha} & =(\mathcal{J}^{\alpha\beta}-\mathcal{R}^{\alpha\beta})\delta_{\beta}\mathcal{H}+\mathcal{G}_{\xi}^{\alpha}u^{\xi},\label{eq:pH_non_differential_operator}\\
y_{\xi} & =\mathcal{G}_{\xi}^{\alpha}\delta_{\alpha}\mathcal{H},\nonumber
\end{align}
with $\alpha,\beta=1,\ldots,n$ and $\xi=1,\ldots,m$. Henceforth,
as we focus on systems actuated solely within the spatial domain,
we suppose that no power exchange takes place through the boundary
$\partial\mathcal{B}=\{0,L\}$, i.e. $(\dot{x}^{\alpha}\delta_{\alpha}^{\partial,1}\mathcal{H})|_{\partial\mathcal{B}}=0$
as well as $(\dot{x}_{1}^{\alpha}\delta_{\alpha}^{\partial,2}\mathcal{H})|_{\partial\mathcal{B}}=0$.
Consequently, the power-balance relation (\ref{eq:h_p_general}) follows
to
\begin{equation}
\dot{\mathscr{H}}=-\int_{\mathcal{B}}\delta_{\alpha}(\mathcal{H})\mathcal{R}^{\alpha\beta}\delta_{\beta}(\mathcal{H})\mathrm{d}z^{1}+\int_{\mathcal{B}}u^{\xi}y_{\xi}\mathrm{d}z^{1}\label{eq:h_p_general_local}
\end{equation}
in local coordinates.

As an example, an Euler-Bernoulli beam actuated by one pair of piezoelectric
macro-fibre composite (MFC) patches is studied. To this end, we summarise
the derivation of the equation of motion for the transversal deflection
$w$ of the beam, which is given in detail in \cite{Schroeck2011}.
Furthermore, we aim to find a pH-system representation being suitable
for the control strategy presented in Section 4.

\begin{exmp}[Piezo-actuated Euler-Bernoulli beam]\label{ex:Euler-Bernoulli_Beam_Piezo_actuated}We
consider an Euler-Bernoulli beam actuated by one pair of piezoelectric
patches with two symmetrically placed actuators on the upper and lower
side of the beam. Furthermore, we assume that the beam is clamped
at the position $z^{1}=0$, i.e. $w(t,0)=0$, $\dot{w}(t,0)=0$ and
$w_{1}(t,0)=0$, while the other end $z^{1}=L$ is free, implying
that the shear force and the bending moment vanish.

First, we derive the equation of motion in a Lagrangian framework
by exploiting the calculus of variations, see \cite{Meirovitch1997}
for instance. In this setting, the time $t$ and the spatial coordinate
$z^{1}$ are used as independent variables. To begin with, we state
the energy densities of the system under investigation, where we first
focus on the part of the energy which is due to the beam. If we use
linear constitutive and linearised geometric relations according to
the Euler-Bernoulli hypothesis, the potential-energy density of the
beam can be given as
\[
\mathcal{V}_{b}=\tfrac{1}{2}EI(w_{11})^{2},
\]
with $E$ and $I$ denoting Young's modulus and the moment of inertia,
respectively. Moreover, the kinetic-energy density of the beam reads
as
\[
\mathcal{T}_{b}=\tfrac{1}{2}\rho_{b}A_{b}(w_{t})^{2},
\]
where $\rho_{b}$ is the mass density and $A_{b}$ the cross section
of the beam. With regard to the MFC patch pair, it is important to
mention that it is attached at a specified position. To mathematically
describe the position of the piezoelectric pair, we introduce the
spatial actuator characteristic
\begin{equation}
\Gamma(z^{1})=h(z^{1}-z_{p}^{1})-h(z^{1}-z_{p}^{1}-L_{p}),\label{eq:piezo_spatial_function}
\end{equation}
with $h(\cdot)$ denoting the Heaviside function and $z_{p}^{1}$
the position where the MFC patches of the length $L_{p}$ are attached
meeting $0<z_{p}^{1}<z_{p}^{1}+L_{p}<L$. Consequently, the kinetic-energy
density of the MFC patches follows to
\[
\mathcal{T}_{p}=\rho_{p}A_{p}\Gamma(z^{1})(w_{t})^{2},
\]
where the corresponding cross section and mass density are denoted
by $A_{p}$ and $\rho_{p}$, respectively. To keep the complexity
as low as possible, we assume the following simplifications regarding
the MFC patches. First, we suppose a perfect compensation of all actuator
nonlinearities as well as an uniaxial state of stress. Furthermore,
we describe the electric field between the electrodes by an exclusive
field component $E_{1}$, i.e. $E_{2}=E_{3}=0$, and additionally
neglect the self-generated electric field stemming from the direct
piezoelectric effect as it is irrelevant compared to $E_{1}$. Consequently,
if we use linear constitutive relations for the MFC patches, see \cite[equ. (7)]{Schroeck2011},
and take the preceding assumptions into account, the potential-energy
density follows to
\[
\mathcal{V}_{p}=\Gamma(z^{1})(\Theta_{p}(w_{11})^{2}+2\Delta_{p}w_{11}u_{in}),
\]
where the (constant) material parameters of the MFC patches are hidden
in the abbreviations $\Theta_{p}$ and $\Delta_{p}$. Furthermore,
$u_{in}$ denotes the input voltage of the piezoelectric actuators.
To derive the equation of motion together with the boundary conditions,
we use the 2nd-order Lagrangian density
\begin{equation}
\mathcal{L}=\mathcal{T}_{b}+\mathcal{T}_{p}-\mathcal{V}_{b}-\mathcal{V}_{p},\label{eq:Langrangian_density}
\end{equation}
which can be given as the difference of the total-kinetic energy
density
\begin{equation}
\mathcal{T}=\tfrac{1}{2}\kappa(z^{1})(w_{t})^{2}\label{eq:total_kinetic_energy_density}
\end{equation}
and the total-potential energy density
\begin{equation}
\mathcal{V}=\tfrac{1}{2}\Theta(z^{1})(w_{11})^{2}+2\Gamma(z^{1})\Delta_{p}w_{11}u_{in}\label{eq:total_potential_energy_density}
\end{equation}
by means of the spatially varying parameters $\kappa(z^{1})=\rho_{b}A_{b}+2\rho_{p}A_{p}\Gamma(z^{1})$
and $\Theta(z^{1})=EI+2\Theta_{p}\Gamma(z^{1})$. For the system under
consideration -- 1st-order derivative variable with respect to $t$
and (solely) 2nd-order derivative variables with respect to $z^{1}$
--, the Euler-Lagrange operator corresponds to
\begin{equation}
\delta_{w}(\cdot)\!=\!\partial_{w}(\cdot)-d_{t}(\partial_{w}^{t}(\cdot))+d_{11}(\partial_{w}^{11}(\cdot)),\label{eq:Euler_Lagrange_Domain}
\end{equation}
and the boundary operators are\begin{subequations}\label{eq:Euler_Lagrange_Boundary}
\begin{align}
\delta_{w}^{\partial,1}(\cdot) & =\partial_{w}^{1}(\cdot)-d_{1}(\partial_{w}^{11}(\cdot)),\\
\delta_{w}^{\partial,2}(\cdot) & =\partial_{w}^{11}(\cdot),
\end{align}
\end{subequations}as in mechanics it is common to allow for no variation
on the time boundary. If we apply the domain operator (\ref{eq:Euler_Lagrange_Domain})
and the boundary operators (\ref{eq:Euler_Lagrange_Boundary}) to
the Lagrangian density (\ref{eq:Langrangian_density}), due to the
requirements $\delta_{w}\mathcal{L}=0$ as well as $(\dot{w}\delta_{w}^{\partial,1}\mathcal{L})|_{\partial\mathcal{B}}=0$,
$(\dot{w}_{1}\delta_{w}^{\partial,2}\mathcal{L})|_{\partial\mathcal{B}}=0$,
we obtain the equation of motion
\begin{equation}
\kappa(z^{1})w_{tt}=-\Theta(z^{1})w_{1111}-4\Theta_{p}\partial_{1}(\Gamma(z^{1}))w_{111}-2\Theta_{p}\partial_{11}(\Gamma(z^{1}))w_{11}-2\Delta_{p}\partial_{11}(\Gamma(z^{1}))u_{in},\label{eq:PDE_beam_piezo}
\end{equation}
together with the boundary conditions\begin{subequations}\label{eq:boundary_cond_Piezo}
\begin{align}
(\dot{w}EIw_{111})|_{\partial\mathcal{B}} & =0,\\
(\dot{w}_{1}EIw_{11})|_{\partial\mathcal{B}} & =0.
\end{align}
\end{subequations}It should be noted that the spatial derivatives
of $\Gamma(z^{1})$ occuring in (\ref{eq:PDE_beam_piezo}) would cause
some problems regarding the formulation of the equation of motion.
To avoid this problem, we approximate the discontinuous characteristic
(\ref{eq:piezo_spatial_function}) by the spatially differentiable
function
\[
\Gamma(z^{1})=\tfrac{1}{2}\tanh(\sigma(z^{1}-z_{p}^{1}))-\tfrac{1}{2}\tanh(\sigma(z^{1}-z_{p}^{1}-L_{p}))
\]
with the scaling factor $\sigma\in\mathbb{R}_{+}$.

Next, we are interested in a proper pH-system representation for the
system under investigation. It should be noted that in the pH-setting
the time $t$ plays the role of an evolution parameter, i.e. $t$
is no coordinate any more and, hence, the exclusive independent variable
is the spatial coordinate $z^{1}$. Consequently, we consider the
bundle $\pi:\mathcal{E}\rightarrow\mathcal{B}$ with the independent
coordinate $(z^{1})$ for $\mathcal{B}$ and coordinates $(z^{1},w,p)$
for $\mathcal{E}$ in the following, where we have introduced the
generalised momenta $p=\kappa(z^{1})\dot{w}=\kappa(z^{1})w_{t}$.
In principle, the Hamiltonian density is chosen as the sum of potential-
and kinetic-energy density according to $\mathcal{H}=\mathcal{T}+\mathcal{V}$.
However, to obtain an appropriate pH-system formulation, we set
\[
\mathcal{H}=\tfrac{1}{2\kappa(z^{1})}p^{2}+\tfrac{1}{2}\Theta(z^{1})(w_{11})^{2},
\]
where we intentionally omit the term $2\Delta_{p}\Gamma(z^{1})w_{11}u_{in}$
of (\ref{eq:total_potential_energy_density}), as by using the calculus
of variations it generates the input part in (\ref{eq:PDE_beam_piezo}),
which is hidden in $g(z^{1})=-2\Delta_{p}\partial_{11}(\Gamma(z^{1}))$
in the pH-system representation

\begin{align}
\left[\begin{array}{c}
\dot{w}\\
\dot{p}
\end{array}\right] & =\left[\begin{array}{cc}
0 & 1\\
-1 & 0
\end{array}\right]\left[\begin{array}{c}
\delta_{w}\mathcal{H}\\
\delta_{p}\mathcal{H}
\end{array}\right]+\left[\begin{array}{c}
0\\
g(z^{1})
\end{array}\right]u_{in},\nonumber \\
y & =\left[\begin{array}{cc}
0 & g(z^{1})\end{array}\right]\left[\begin{array}{c}
\delta_{w}\mathcal{H}\\
\delta_{p}\mathcal{H}
\end{array}\right]=g(z^{1})\dot{w}.\label{eq:Piezo_pH}
\end{align}
Moreover, we are able to deduce the formal change of the Hamiltonian
functional, which follows to
\begin{equation}
\dot{\mathscr{H}}=\int_{\mathcal{B}}g(z^{1})\dot{w}u_{in}\mathrm{d}z^{1}\label{eq:h_p_piezo_beam}
\end{equation}
as the boundary terms vanish due to the boundary conditions (\ref{eq:boundary_cond_Piezo}).
It is worth stressing that (\ref{eq:h_p_piezo_beam}) corresponds
to an electrical power-balance relation as the unit of the distributed
output density (\ref{eq:Piezo_pH}) is $\mathrm{\tfrac{A}{m}}$.\end{exmp}
Ex. (\ref{ex:Euler-Bernoulli_Beam_Piezo_actuated}) highlights that
external inputs together with the collocated outputs generate power
ports which may be distributed over (a part of) the spatial domain.
As distributed ports allow for a non-zero power flow over the domain,
we use them to couple an infinite-dimensional system to a dynamic
pH-controller in the following section.

\section{In-Domain Control by means of Structural Invariants}

This section deals with the extension of the energy-Casimir method
to infinite-dimensional pH-systems with in-domain actuation. Here,
we confine ourselves to systems with lumped inputs that may act distributed
over a part of the spatial domain. This has the consequence that the
collocated outputs can be interpreted as distributed output densities.
However, a certain interconnection allows for the use of a finite-dimensional
dynamic controller. An advantage of the proposed control strategy
is the applicability to piezo-actuated beams, which is presented at
the end of this section.

\subsection{Interconnection (Infinite-Finite)}

In the following, we aim at stabilising pH-systems of the form (\ref{eq:pH_non_differential_operator}),
where the lumped inputs $u^{\xi}$ may act distributed over a part
of the spatial domain due to the input-map components $\mathcal{G}_{\xi}^{\alpha}$,
cf. Ex. \ref{ex:Euler-Bernoulli_Beam_Piezo_actuated}. To this end,
we are interested in a power-conserving interconnection of the infinite-dimensional
plant (\ref{eq:pH_non_differential_operator}) and a finite-dimensional
pH-controller, given in local coordinates as
\begin{align}
\dot{x}_{c}^{\alpha_{c}} & =(J_{c}^{\alpha_{c}\beta_{c}}-R_{c}^{\alpha_{c}\beta_{c}})\partial_{\beta_{c}}H_{c}+G_{c,\xi}^{\alpha_{c}}u_{c}^{\xi},\nonumber \\
y_{c,\xi} & =G_{c,\xi}^{\alpha_{c}}\partial_{\alpha_{c}}H_{c},\label{eq:pH_controller_finite}
\end{align}
with $\alpha_{c},\beta_{c}=1,\ldots,n_{c}$ and $\xi=1,\ldots,m$.
There, one must take account of the fact that the outputs of (\ref{eq:pH_non_differential_operator})
are considered as distributed output densities. Thus, to enable a
coupling with the finite-dimensional controller, the output densities
must be integrated over $\mathcal{B}$ and therefore, we choose a
power-conserving interconnection of the form
\begin{equation}
u^{\xi}\int_{\mathcal{B}}y_{\xi}\mathrm{d}z^{1}+u_{c}^{\xi}y_{c,\xi}=0.\label{eq:PCIS_3}
\end{equation}
To obtain a power-conserving interconnection which meets (\ref{eq:PCIS_3}),
we couple the infinite-dimensional plant and the finite-dimensional
controller according to
\begin{equation}
u_{c}^{\xi}=K^{\xi\eta}\int_{\mathcal{B}}y_{\eta}\mathrm{d}z^{1},\quad u^{\xi}=-K^{\xi\eta}y_{c,\eta},\label{eq:PCIS_3_coupling}
\end{equation}
with $K^{\xi\eta}$ denoting the components of an appropriate map
$K$. It is worth stressing that the closed-loop system, which is
a result of the interconnection (\ref{eq:PCIS_3_coupling}), still
possesses a pH-structure, with the closed-loop Hamiltonian $\mathscr{H}_{cl}=\int_{\mathcal{B}}\mathcal{H}\mathrm{d}z^{1}+H_{c}$.
As we consider systems where no power exchange takes place at the
boundary $\partial\mathcal{B}$, i.e. $(\dot{x}^{\alpha}\delta_{\alpha}^{\partial,1}\mathcal{H}+\dot{x}_{1}^{\alpha}\delta_{\alpha}^{\partial,2}\mathcal{H})|_{\partial\mathcal{B}}=0$
is valid, the formal change of the closed-loop Hamiltonian $\mathscr{H}_{cl}$
can be deduced to
\[
\dot{\mathscr{H}}_{cl}=-\int_{\mathcal{B}}\delta_{\alpha}(\mathcal{H})\mathcal{R}^{\alpha\beta}\delta_{\beta}(\mathcal{H})\mathrm{d}z^{1}-\partial_{\alpha_{c}}(H_{c})R_{c}^{\alpha_{c}\beta_{c}}\partial_{\beta_{c}}(H_{c})
\]
because of the coupling (\ref{eq:PCIS_3_coupling}).

Having defined the coupling of the plant (\ref{eq:pH_non_differential_operator})
and the controller (\ref{eq:pH_controller_finite}) by means of (\ref{eq:PCIS_3_coupling}),
we are interested in structural invariants of the closed-loop system
aiming at relating some of the controller states to the plant. By
means of these controller states, we partially shape $\mathscr{H}_{cl}$,
whereas the controller states that are not related to the plant shall
be used for the damping injection and thus for the purpose of stabilisation.\begin{rem}\label{rem:stability}At
this point, it should be mentioned again that stability investigations
for systems governed by PDEs usually require functional-analytic methods.
In this contribution, the focus is on a formal approach exploiting
geometric system properties and consequently, no detailed stability
investigations will be carried out. However, worth stressing is the
fact that $\mathscr{H}_{cl}>0$ and $\dot{\mathscr{H}}_{cl}\leq0$
can be used for stability investigations in the sense of Lyapunov.\end{rem}

\subsection{Structural Invariants}

Motivated by the form of the plant (distributed) and the controller
(lumped), we consider Casimir-functionals according to
\begin{equation}
\mathscr{C}^{\lambda}=x_{c}^{\lambda}+\int_{\mathcal{B}}\mathcal{C}^{\lambda}\mathrm{d}z^{1},\label{eq:Casimir_Functionals_Piezo}
\end{equation}
with $\lambda=1,\ldots,\bar{n}\leq n_{c}$. The functionals (\ref{eq:Casimir_Functionals_Piezo})
must be constant along solutions of the closed loop, i.e. $\dot{\mathscr{C}}^{\lambda}=0$
is valid independently of $\mathcal{H}$ and $H_{c}$, in order to
serve as structural invariants.

\begin{prop}\label{prop:Casimir_Conditions_Piezo}Consider the closed-loop
system which stems from the coupling of (\ref{eq:pH_non_differential_operator})
and (\ref{eq:pH_controller_finite}) via the interconnection (\ref{eq:PCIS_3_coupling}).
Then, the functionals (\ref{eq:Casimir_Functionals_Piezo}) are structural
invariants of the closed loop, iff the conditions\begin{subequations}\label{eq:Casimir_Conditions_Piezo}
\begin{align}
(J_{c}^{\lambda\beta_{c}}-R_{c}^{\lambda\beta_{c}}) & =0\\
\delta_{\alpha}\mathcal{C}^{\lambda}(\mathcal{J}^{\alpha\beta}-\mathcal{R}^{\alpha\beta})+G_{c,\xi}^{\lambda}K^{\xi\eta}\mathcal{G}_{\eta}^{\beta} & =0\label{eq:domain_cond_prop_Piezo}\\
\delta_{\alpha}\mathcal{C}^{\lambda}\mathcal{G}_{\xi}^{\alpha}K^{\xi\eta}G_{c,\eta}^{\alpha_{c}} & =0\label{eq:Casimir_Input_Obstacle}\\
(\dot{x}^{\alpha}\delta_{\alpha}^{\partial,1}\mathcal{C}^{\lambda}+\dot{x}_{1}^{\alpha}\delta_{\alpha}^{\partial,2}\mathcal{C}^{\lambda})|_{\partial\mathcal{B}} & =0\label{eq:Casimir_Cond_Piezo_Boundary}
\end{align}
\end{subequations}are fulfilled.\end{prop}

\begin{proof}We begin by calculating the formal change of (\ref{eq:Casimir_Functionals_Piezo})
along trajectories of the closed loop, which follows to
\begin{equation}
\dot{\mathscr{C}}^{\lambda}=\dot{x}_{c}^{\lambda}+\int_{\mathcal{B}}\dot{x}^{\alpha}\delta_{\alpha}\mathcal{C}^{\text{\ensuremath{\lambda}}}\mathrm{d}z^{1}+(\dot{x}^{\alpha}\delta_{\alpha}^{\partial,1}\mathcal{C}^{\lambda}+\dot{x}_{1}^{\alpha}\delta_{\alpha}^{\partial,2}\mathcal{C}^{\lambda})|_{\partial\mathcal{B}},\label{eq:Casimir_Conditions_Piezo_C_p}
\end{equation}
and take into account the requirement $\dot{\mathscr{C}}^{\lambda}=0$
independently of $\mathcal{H}$ and $H_{c}$. If we substitute the
system equations of the controller and the plant (\ref{eq:pH_controller_finite})
and (\ref{eq:pH_non_differential_operator}), respectively, as well
as the relations (\ref{eq:PCIS_3_coupling}), then we obtain
\begin{multline*}
\dot{\mathscr{C}}^{\lambda}=(J_{c}^{\lambda\beta_{c}}-R_{c}^{\lambda\beta_{c}})\partial_{\beta_{c}}H_{c}+\int_{\mathcal{B}}(\delta_{\alpha}\mathcal{C}^{\lambda}(\mathcal{J}^{\alpha\beta}-\mathcal{R}^{\alpha\beta})+G_{c,\xi}^{\lambda}K^{\xi\eta}\mathcal{G}_{\eta}^{\beta})\delta_{\beta}\mathcal{H}\mathrm{d}z^{1}+\ldots\\
-\int_{\mathcal{B}}\delta_{\alpha}\mathcal{C}^{\lambda}\mathcal{G}_{\xi}^{\alpha}K^{\xi\eta}G_{c,\eta}^{\alpha_{c}}\partial_{\alpha_{c}}H_{c}\mathrm{d}z^{1}+(\dot{x}^{\alpha}\delta_{\alpha}^{\partial,1}\mathcal{C}^{\lambda}+\dot{x}_{1}^{\alpha}\delta_{\alpha}^{\partial,2}\mathcal{C}^{\lambda})|_{\partial\mathcal{B}}
\end{multline*}
and the proof follows immediately.\end{proof} Now, it is interesting
to interpret the results of Prop. \ref{prop:Casimir_Conditions_Piezo}
and draw some conclusions to the results and findings of \cite[Prop. 1]{Rams2017a}
for the boundary control of 1-dimensional pH-systems with 2nd-order
Hamiltonian. In particular, the condition (\ref{eq:domain_cond_prop_Piezo})
is of special interest as it allows to relate the plant within the
domain to $\lambda=1,\ldots,\bar{n}\leq n_{c}$ controller states,
which is not possible with the Casimir condition \cite[Eq. (17b)]{Rams2017a}.
Unfortunately, we are not able to relate every system state to the
plant, since the condition (\ref{eq:Casimir_Input_Obstacle}) describes
the fact that we cannot find any Casimir functions depending on variables
where the inputs of the plant appear in the corresponding system equations.
In \cite{Rams2017a}, the boundary of the infinite-dimensional system
is divided into an actuated and an unactuated part, where the actuated
boundary is used to relate the plant to the controller, see \cite[Eqs. (17c) and (17d)]{Rams2017a}.
In contrast, as we solely consider a coupling of the plant within
the spatial domain, the impact of the Casimir functionals at the boundary
must vanish, cf. (\ref{eq:Casimir_Cond_Piezo_Boundary}), like in
\cite[Eq. (17e)]{Rams2017a} at the unactuated boundary.

Having the preceding findings at hand, the piezo-actuated beam of
Ex. \ref{ex:Euler-Bernoulli_Beam_Piezo_actuated} serves us to demonstrate
the applicability of the proposed control scheme.

\begin{exmp}[Energy-Casimir controller for Ex. 2]\label{ex:Controler_Beam_Piezo}In
this example, we develop a finite-dimensional pH-controller for the
piezo-actuated Euler-Bernoulli beam of Ex. \ref{ex:Euler-Bernoulli_Beam_Piezo_actuated},
aiming at stabilising the equilibrium
\begin{equation}
w^{d}\!=\!\left\{ \begin{array}{cc}
0 & \mathrm{for}\:0\leq z^{1}<z_{p}^{1},\\
a(z^{1}-z_{p}^{1})^{2} & \mathrm{for}\:z_{p}^{1}\leq z^{1}<z_{p}^{1}+L_{p}\\
b(z^{1}-z_{p}^{1}-L_{p})+a(L_{p})^{2} & \mathrm{for}\:z_{p}^{1}+L_{p}\leq z_{p}^{1}\leq L.
\end{array},\right.\label{eq:equilibrium_piezo_beam}
\end{equation}
To this end, we relate one controller state to the plant, and two
controller states shall be used for the damping injection, i.e., the
dimension of the controller follows to $n_{c}=3$. By means of a proper
choice of the initial controller states, the Casimir function $\mathcal{C}^{1}=-g(z^{1})w$,
which satisfies the conditions (\ref{eq:Casimir_Conditions_Piezo})
if we set $G_{c}^{1}=1$ and $K=1$, yields the important relation
\[
x_{c}^{1}=\int_{\mathcal{B}}g(z^{1})w\mathrm{d}z^{1}.
\]
 It should be noted that $x_{c}^{1}$ corresponds to the weighted,
integrated deflection of the beam, whereas in \cite{Rams2017a} the
deflection and angle at the actuated boundary are used as controller
states. Furthermore, the controller dynamics are constrained to the
maps
\[
J_{c}-R_{c}\!=\!\left[\begin{array}{ccc}
0 & 0 & 0\\
0 & -R_{c}^{22} & J_{c}^{23}-R_{c}^{23}\\
0 & -J_{c}^{23}-R_{c}^{23} & -R_{c}^{33}
\end{array}\right],\:G_{c}\!=\!\left[\begin{array}{c}
1\\
G_{c}^{2}\\
G_{c}^{3}
\end{array}\right]
\]
due to the conditions (\ref{eq:Casimir_Conditions_Piezo}). To be
able to stabilise the equilibrium (\ref{eq:equilibrium_piezo_beam}),
it must become a part of the minimum of the closed-loop Hamiltonian
$\mathscr{H}_{cl}=\mathscr{H}+H_{c}$. For this purpose, we set the
controller Hamiltonian to
\[
H_{c}=\tfrac{c_{1}}{2}(x_{c}^{1}-x_{c}^{1,d}-\tfrac{u_{s}}{c_{1}})^{2}+\tfrac{1}{2}M_{c,\mu_{c}\nu_{c}}x_{c}^{\mu_{c}}x_{c}^{\nu_{c}},
\]
together with the relation $x_{c}^{1,d}=\int_{\mathcal{B}}g(z^{1})w^{d}\mathrm{d}z^{1}$,
the positive definite matrix $[M_{c}]$, $M_{c,\mu_{c}\nu_{c}}\in\mathbb{R}$
for $\mu_{c},\nu_{c}=2,3$, and the positive constant $c_{1}>0$.
Note that the term with $u_{s}$ was incorporated in $H_{c}$ as (\ref{eq:equilibrium_piezo_beam})
is an equilibrium that requires non-zero power, i.e. a stationary
voltage $u_{s}$ inducing a static holding torque. If we consider
the power-conserving interconnection structure $u_{c}=\int_{\mathcal{B}}g(z^{1})\dot{w}\mathrm{d}z^{1}$
and $u=-y_{c}$, the formal change of $\mathscr{H}_{cl}$ follows
to
\begin{equation}
\dot{\mathscr{H}}_{cl}=-x_{c}^{\mu_{c}}M_{c,\mu_{c}\nu_{c}}R_{c}^{\nu_{c}\rho_{c}}M_{c,\rho_{c}\vartheta_{c}}x_{c}^{\vartheta_{c}}\leq0,\label{eq:H_cl_p_Piezo}
\end{equation}
with $\rho_{c},\vartheta_{c}=2,3$. Since in this contribution no
detailed stability investigations are carried out, cf. Rem. \ref{rem:stability},
we are content with the fact that $\dot{\mathscr{H}}_{cl}\leq0$ implies
that $\mathscr{H}_{cl}$ is non-increasing along closed-loop solutions.
Furthermore, Fig. \ref{fig:sim_result} shows that the proposed controller
stabilises the desired equilibrium (\ref{eq:equilibrium_piezo_beam})
with $a=0.3587$ and $b=0.1436$. Here, all system parameters of the
beam are set to 1 and the piezoelectric patches with the length $L_{p}=0.2$
are placed at $z_{p}^{1}=0.2$. The remaining degrees of freedom for
the pH-controller are chosen according to $J_{c}^{23}=1$, $R_{c}^{22}=3$,
$R_{c}^{23}=-1$, $R_{c}^{33}=1.5$, $M_{c,22}=85$, $M_{c,23}=0$,
$M_{c,33}=60$, $G_{c}^{2}=G_{c}^{3}=1.7$ and $c_{1}=0.1$.
\begin{figure}
\center\input{w_Beam.tex}\caption{\label{fig:sim_result}Simulation results for the beam deflection
$w$ against time $t$ and spatial domain $z^{1}$.}
\end{figure}
\end{exmp}

\section{Conclusion and Outlook}

In this article, a control strategy for infinite-dimensional pH-systems
with in-domain actuation yielding a dynamic controller has been developed.
Here, we focused on systems with lumped inputs that act distributed
over a part of the spatial domain and demonstrated the applicability
of the control approach by means of a piezo-actuated Euler-Bernoulli
beam. Since the distributed output density of the system under investigation
cannot be measured, for the implementation of the controller an observer
would be required, which is part of future research. Furthermore,
we aim to extend the proposed control strategy to infinite-dimensional
systems with distributed inputs requiring an infinite-dimensional
controller.

\bibliographystyle{ieeetr}

redpajama_set_name: RedPajamaArXiv


text:
Q: How can I create a function that automatically takes data from Google Sheets and replaces the tags in a Slides template? I am new to Google Apps Script and coding in general and wasn't entirely sure how to do this. I want to create code that allows me to create a new set of Google Slides based on a Slides template using the relevant rows from a Google Sheets document.
function generateNewSlides() {
var wsID = "would insert worksheet URL ID here";
var ws = SpreadsheetApp.openById(wsID).getSheetByName("Data");
var data = ws.getRange(2, 1, ws.getLastRow()-1, 5).getValues();

 >the above should get the relevant table from the sheet

data.forEach(function(info){
if(info[0]){

var firstname = info[0];
var surname = info[1];
var email = info[2];
var phone = info[3];
var image = info[4];
var presName = info[5];

>the above are columns where the different pieces of data would be taken from for the placeholders in the Slides template

var slidesTemplateID = "would insert slides template URL ID here";
var slidesTemplate = SlidesApp.openById(slidesTemplateID);
var template = slidesTemplate.getSlides();
var folderID = "would insert desired folder ID for saving in here";

>the above should get me the Slides template

template.makeCopy(presName,DriveApp.getFolderById(folderID)); **>line where error occurred**
var newPresentation = DriveApp.getFilesByName(presName).next().getUrl();
var Presentation = SlidesApp.openByUrl(newPresentation);

>the above should create a copy and then open it

var shapes = (Presentation.getShapes());
 shapes.forEach(function(shape){
   shape.getText().replaceAllText('{{firstname}}',firstname);
   shape.getText().replaceAllText('{{surname}}',surname);
   shape.getText().replaceAllText('{{email}}',email);
   shape.getText().replaceAllText('{{phone}}',phone);
   shape.getText().replaceAllText('{{presname}}', presName)

});
 >the above should replace all the placeholder tags in the template with the row data

}
});

}

Above is the code I have so far. The worksheet I am extracting data from has columns: first name, surname, email address, phone number, image (URL), and presentation name. When I try to run it I encounter an error on line 37 where it says template.makeCopy is not a function, however I am certain .makeCopy should be able to create a copy for it, no?
My main questions are:
1) What should I change to make it work, generating a new set slides for each row in the worksheet?
2) How can I add images to it replacing placeholder tags I've added in squares (not textboxes) in the template?
Thanks in advance!

A: Issue 1. makeCopy:
makeCopy(name, destination) is a method of the class File, which belongs to the Drive Service, not to the Slides Service. In your code, template is a list of Slides (you retrieve it by calling the method getSlides() from a Presentation). makeCopy cannot work here.
In order to make a copy of a Presentation, you should be using the Drive Service instead. You should replace these lines:
var slidesTemplate = SlidesApp.openById(slidesTemplateID);
var template = slidesTemplate.getSlides();

With this one:
var template = DriveApp.getFileById(slidesTemplateID);

Issue 2. Iterating through all shapes:
Next, you want to iterate through all shapes in your Presentation, and replace all placeholder tags with your desired text. In order to do that, you are using Presentation.getShapes(), which cannot work, since getShapes() is not a method of Presentation, but of Slide.
You should first iterate through all Slides in the Presentation, and for each Slide, iterate through all Shapes. You should replace these lines:
var shapes = (Presentation.getShapes());
 shapes.forEach(function(shape){
   // Replacing text lines
});

With these ones:
Presentation.getSlides().forEach(function(slide) {
  slide.getShapes().forEach(function(shape) {
    // Replacing text lines
  })
});

Note:
In order to retrieve the copied presentation, you are currently doing this:
template.makeCopy(presName,DriveApp.getFolderById(folderID));
var newPresentation = DriveApp.getFilesByName(presName).next().getUrl();
var Presentation = SlidesApp.openByUrl(newPresentation);

There is no need to do this, you can just retrieve the ID of the created template, and open by ID, like this:
var copiedTemplate = template.makeCopy(presName,DriveApp.getFolderById(folderID));
var Presentation = SlidesApp.openById(copiedTemplate.getId());

Reference:

*

*Slides Service

*Drive Service

redpajama_set_name: RedPajamaStackExchange


text:
Robert Kunzig
senior environment editor National Geographic
Robert Kunzig is senior environment editor at National Geographic magazine, where he focuses on global environmental issues such as climate change. Kunzig has been a science journalist for more than 30 years, and his magazine articles have appeared many times in the Best American Science and Nature Writing. He has also written two books: Fixing Climate (with Wallace Broecker) and Mapping the Deep, a book about oceanography, which won the Aventis/Royal Society prize as science book of the year in 2001.

redpajama_set_name: RedPajamaCommonCrawl


text:
Education 31 Community Engagement and Outreach 10 Strategy and Planning 4 Other 4 Executive Leadership 3 Operations and Facilities 3
Development and Fundraising 3 Administrative 3 Product and Program Management 3 Database Administration 2 Data Evaluation and Analysis 2 Accounting and Finance 2 Human Resources 1 Sales 1 Remote/Virtual Role 1
$75,000 - $100,000 1
Curriculum Business Development Los Angeles
Chief Financial Officer - Ednovate Network Support Team Featured
Ednovate Background Ednovate launched its first school, USC Hybrid High, a personalized learning high school, in 2012. Since then, Ednovate has grown to five schools in Los Angeles County and Orange County. Ednovate is committed to serving in areas where students traditionally lack access to a quality college prep education by building tuition-free, safe and high-performing public schools to neighborhoods that need it the most. Ednovate is currently planning for our next growth phase as we continue to fulfill our mission to make a positive multigenerational change within the communities we serve and in our profession. Position Description As a key member of the Leadership Team, the CFO will report directly to the CEO and play a critical role in the overall strategic management of the organization. The CFO will set the financial strategy for Ednovate's $30M operating budget and $50M real estate portfolio, while also designing and delivering effective financial systems across the organization. Additionally, the CFO will steward the organization as it embarks upon its next phase of growth, growing to 11 schools, serving nearly 6,000 students, with a $100M operating budget, and $200M in real estate assets. The CFO will serve as a strategic partner to organizational leaders, providing financial guidance to inform decisions, as well as leading long-term financial strategy, forecasting, and budgeting. The CFO is committed to Ednovate's mission, has deep financial planning and analysis expertise, and is an excellent communicator capable of distilling complex concepts into clear narratives for diverse internal and external audiences, including executives, board members, public officials, funders, and lenders. In carrying out his/her responsibilities, the CFO must be able to manage a complex long-term financial model to support strategic decision-making across the organization. This person will also manage Ednovate's external budgeting and accounting team, ExED, to lead the organization's budgeting process and financial reporting. This position will be based out of the Ednovate Support Team office in Downtown Los Angeles, though time spent in schools will be expected. Duties for this position include, but are not limited to: Organizational Leadership - the CFO will serve as a thought partner to and member of the Ednovate Leadership Team as staff financial lead, setting organizational vision and strategy, mentoring staff, and providing oversight. They will also work closely with the Board of Directors as well as key external stakeholders, including funders, lenders, and authorizers. Strategic & Annual Planning - the CFO will set the financial strategy and lead long-term financial forecasting & budgeting for Ednovate's $30M operating budget. They will review financial systems and processes and drive improvements that will enable leaders at every level of the organization to understand financial impact of decisions and consistently operate favorable to budget. Most importantly, the CFO will see around corners - recognize and anticipate opportunities and challenges as they relate to organizational plans; generate ideas, strategies, and solutions to drive impact. Capital Finance - the CFO will manage the financing strategy for $50M real estate portfolio, and $150M in new campus construction over the next five to ten years. They will also manage relationships with funding partners and lead project financing efforts to ensure timely acquisition of new permanent facilities. Financial Planning and Analysis - the CFO will manage a complex long-term financial model to support strategic decision-making and long-term sustainability across the organization including the development of alternative long-range and short-range scenarios. They will also define metrics to monitor and predict the financial performance of entities across the organization, develop systems to track performance metrics and make decisions around resource allocation. Budgeting, Forecasting, and Reporting - the CFO will lead the annual budgeting process, partnering with stakeholders across the organization, culminating with financially healthy budgets. They will oversee the budget implementation during the fiscal year, managing ExEd to ensure budgets are accurate and support solid decision-making. Key financial metrics will be presented on a monthly basis to ensure all key stakeholders routinely review performance to budget. Management and Oversight - the CFO will oversee all fiscal and fiduciary responsibilities for the organization, in conjunction with the Board of Directors, the Audit Committee, and the Finance/Business Advisory Group. They will also manage and inspire the 4+ person ExEd external budgeting and accounting team. Candidate Qualifications MBA or other advanced degree, or comparable experience of a minimum of 12 years Minimum of 5+ years of progressive senior responsibility in developing and building out FP&A function with a major company or division of a large corporation. Experience in a not-for-profit/school environment is preferred but not required. Knowledge of capital and debt markets landscape, including facilities financing options, is a plus but not required Track record of building, leading, and inspiring effective teams; evidence of building an outcomes/data-driven team culture and coaching/developing others to maximize their potential Budget development and implementation experience in a complex organization Highly effective communicator, capable of distilling complex concepts Highly systems and process-oriented Strong project management skills and ability to work collaboratively with a wide range of constituents A multi-tasker with the ability to wear many hats in a fast-paced and hard-working environment Ednovate Non-Negotiables A history of high achievement and results Impressive work ethic ("good isn't good enough") Clear passion for Ednovate's Mission Obsessive attention to detail Service-focused mentality A belief that all Ednovate students will succeed in college and make a Positive Multigenerational Change Application Process Interested candidates should begin the process by submitting an application through Ednovate's website at http://www.ednovate.org/careers Compensation Compensation will be commensurate with experience and qualifications. A comprehensive compensation plan will include a competitive benefits package. Statement of Non-Discrimination Ednovate does not discriminate on the basis of race, color, gender, handicap, age, religion, sexual orientation, or national or ethnic origin.
Ednovate Charter Schools Los Angeles, CA, USA Full-time
Operations Support Associate - Ednovate Network Support Team Featured
Ednovate Background Ednovate launched its first school, USC Hybrid High, a personalized learning high school, in 2012. Since then, Ednovate has grown to five schools and is on a trajectory to continue to grow over the next several years. Ednovate is committed to serving in areas where students traditionally lack access to a quality college prep education by building tuition-free, safe, and high-performing public schools to serve neighborhoods that need it the most. Ednovate is currently planning for our next growth phase as we continue to fulfill our mission to make a positive multigenerational change within the communities we serve and in our profession. Position Description We are seeking an Operations Support Associate whose primary role will be to provide high-quality customer service and support for all operational matters at our schools and network office. This will primarily entail managing and expanding the network help desk ticketing system. Additionally, this member of the Operations team will support the creation and tracking of project plans for each team quarterly goal in order to optimize resources and clearly identify a path to achieving each goal. The ideal candidate for this position is process driven, detail oriented and an excellent communicator who enjoys working with school-based leaders, staff and students. The candidate needs to possess strong organization, attention to detail and self-management skills. This position will be a critical part of the Ednovate Support Operations Team, working closely with school leaders, school operations staff and teachers. This position will report to the COO and will be based out of the Ednovate Support Team offices in South LA and Downtown, though some time spent in schools will be expected. The Operation Support Associate's duties include, but are not limited to: Help Desk Management Manage a help desk system for all network operations related concerns with a response rate within 48 hours or less for all tickets. Manage/supervise the day-to-day operations of the Help Desk including setting standards and proper expectations to ensure our customers are receiving responsive and complete operational support services. Ensure that tickets are properly assigned, documented, updated and closed daily. Collect real-time data to track trends and facilitate constant improvement in response to support where schools need it most. Train network and school staff members to standardize ticket submission and optimize their use of the help desk features. B2B / B2C, Experience "communicating" with 2nd & 3rd level support Help Desk Expansion Expand the existing help desk to be able to receive tickets in multiple operational and compliance categories, to include: SIS, school nutrition, facilities, finance & budgeting, procurement, and attendance. Expansion to include leveraging Zen Desk features for customer support and data analytics. Collect and analyze new help desk data to drive Ops team resource planning and school support focus for next school year. Operations Project Management Support Work closely with the COO and Network Operations team to identify quarterly projects/priorities aligned to the strategic plan goals. Ensure all quarterly priorities have clear project plans that map resources and timelines to each project ensuring on-time achievement of each priority. Support network-wide events and initiatives to ensure cross team projects have clear plans, owners, mapped resources and lead times. Candidate Qualifications A proactive self-starter with the ability to multitask, establish and rearrange priorities, and maintain focus in a fast-paced environment Project management experience Basic help desk system administration experience Strong analytical skills Relentless results-orientation Ability to work collaboratively with a wide range of constituents Excellent interpersonal, verbal and written communication skills Strong organizational skills and attention to detail Knowledge of public education and charter schools preferred, but not required Belief that all Ednovate students will succeed in college and make a Positive Multigenerational Change Unwavering determination to do whatever it takes to help our students succeed Ednovate Non-Negotiables A history of high achievement and results Impressive work ethic ("good isn't good enough") Clear passion for Ednovate's Mission Obsessive attention to detail Serviced-focused mentality Application Process Interested candidates should begin the process by submitting an application through Ednovate's website at http://www.ednovate.org/careers Compensation Compensation will be commensurate with experience and qualifications. A comprehensive compensation plan will include a bonus incentive and a competitive benefits package. Statement of Non-Discrimination Ednovate does not discriminate on the basis of race, color, gender, handicap, age, religion, sexual orientation, or national or ethnic origin.
Ednovate Charter Schools 3939 South Vermont Avenue, Los Angeles, CA, USA Full-time


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" The Lovers is card VI of the Tarot, and it is said to represent the sign of Gemini, and all matters of duality, love, and choices. The card usually is depicted with two lovers who, while holding each other, appear to have inward gazes. This is a cosmic truth of creation mythology: The Goddess is born of the Abyss with just her own imagination, and, examining herself in the mirror of empty space, she beholds her reflection, which becomes her Lover, the Other, by which me may discover ourSelves.
The Lovers oil is androgynous, pleasing and unusual. Wear it to discover your Other Self, another Lover, or to help make choices."


Earl Schaffer PBS Special is what first opened my eyes and mind to the trail.....I was 44 , When I first hit the AT in spring 03 ,I had broken my foot the night before horsing around with my nephew but after planning for 6 mos. I was determined to carry on (was hoping it was just sprained) but after struggling 51 miles I knew I had to quit when I got to Helen Ga.(only 17 miles of Ga left...damn),but something happened on my way ....and its changed my life ever since .On my second night out at Long Creek Falls I met the first true long distance hiker of my life and we sat around a small campfire for a few hrs and this guy told me more in a few hrs than I had learned from reading for 6 months ...how to fall (if that happens) where to stay away from and where to go and such but most important was that if I had to quit the trail it would still be there for another try later....as he also had to quit the year before after he was all the way to Pa. and his father had passed away ...well he went back and he made it in 03,but what has changed my life ever since that meeting at the Falls was he saw a pic of some sign stuff I had with me (i had a few pics that I had brought down to show my cousin in Tn.) and he said "wow this is nice stuff....can you make ...like Hiker stuff"? Then he told me about Trail Days and that if I had to quit cause my foot that I should make some Hiker Plaques and come back for the festivities in Damascus....seems that ever since that day I have had nothing but the Trail and "Hiker Stuff" on my brain 24/7 and since that meeting at Long Creek Falls I have been making (just about) nothing but Hiker Stuff and I love it ...I feel it was my destiny and life has been so much better for me since (not financially,just from all the neat folks I have met ).I will be attempting another Thru Hike this march 1st and I have alot of Hiker Stuff to sell before I meet the financial goals I need for making this dream come true .Check out my "stuff" on the Hiker Page at Fishinfreds.com or bid on something on Ebay (search Fishinfred2)....and if you run into a guy called "Greenman" tell him thanks ,for he loves the trail and somehow instilled a passion for it in me ....Thanks for looking ..Happy Trails !
I guess you are talking about Earl Shaffer (not Schaffer), from York Springs,PA, a true "Appalachian Trail Legend".
OOPs on the spelling ....sorry Earl ,thanks ,Ridge!


Retirement for Miriam Bronstein, Sandi Malamud and Harriet Zimmer is fueled each month by helping to make 90 to 120 litres of fresh soup for Willow Place. "We are not retired, we are re-fired," says Miriam Bronstein.
Women and their children who live at Willow Place need to be in this safe and supportive environment because they have experienced domestic violence.
Three years ago, these three dynamos came together to form the Winnipeg chapter of Soup Sisters and Broth Brothers. Individuals, couples and interest groups meet once a month at the Fairmont Hotel to make soup for Willow Place. This hands-on evening is about doing for others, showing that people care and a take home message: "It is not OK to be in an abusive relationship," says Sandi.
At each event someone who lived at the shelter speaks. Jen (not her actual name) is one of those individuals. When Jen resided at Willow Place (formerly Osborne House) she enjoyed the daily soup and jumped at the opportunity to attend a Soup Sisters event. Jen felt strongly that she wanted to give back. "I received the chance to thank the women who helped me in a time of need," she said. "I became one of the women speaking out and standing up to domestic violence." Hearing Jen is a very powerful experience for the participants. "There is usually not a dry eye after she speaks," says Harriet.
The evening is part cooking show, part opportunity to experience the over the top commercial kitchen graciously donated by the Fairmont Hotel and part just a fun evening out.
Chef Tim Palmer from the Fairmont always has something new and exciting to share. Sandi has changed how she cooks, experimenting with different spices and techniques. The participants get to experience a whole new cooking experience such as using an "immersion blender that could double as an outboard motor," said Harriet.
The evening begins on a Sunday at 5:30 and ends at 8:15, when the participants enjoy the fruits of their labour by sitting down to a nice meal at the hotel. Over the past three years, word has spread and the event attracts people from different places such as workplaces, book clubs, church groups or coming to celebrate a special occasion. Sandi, Miriam and Harriet love the people they have met and have built up relationships with the regular attendees. Jen feels that these three women have become part of her family. "They have given me strength, even when they did not know who I was," she said.
It was Miriam, a former teacher, who first attended a Soup Sisters event in Ottawa with her daughter and quickly recruited her colleague, Sandi. Harriet heard about the cause from a relative and joined the group after she retired as a social worker. Sandi said, "I just loved the whole idea." These three retired women have melded together and even adopted nicknames for each other: Miss Bossy, Miss Patient and Miss Lovely are the trifecta for any great fundraiser to be built on. "We balance each other nicely," says Harriet.
Domestic violence continues to be hidden. There is a constant demand for people to live at Willow Place, particularly among the immigrant population, says Harriet. People can become lost while living with their pain, silenced because of their fear. Children can be caught in the crossfire. Perhaps one of the more powerful moments is when Harriet, Sandi or Miriam go to Willow Place to deliver the soup. "I am reminded how lucky I am, but that the world is very difficult", says Miriam. All three women know that Soup Sisters is making a difference and feel strongly about the cause. "We need to eradicate domestic abuse," says Harriet.
Soup Sisters would love to have you come out and join an evening of making soup for Willow Place. You can visit their website at www. soupsisters.org/winnipeg.php for further information and to register for the next event.


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Next Magic Trackpad May Charge iPhone
May 5, 2020 at 1:52 p.m. PT
The Magic Trackpad is Apple's external pointing device, designed for macOS.
2015 saw the refreshed Magic Trackpad 2, adding Force Touch haptic feedback technology.
Patents show that Apple may be adding wireless charging and Apple Pencil support to the next Magic Trackpad.
Apple's Magic Trackpad Fuses Hardware with Software
Although the first mouse was developed in 1964 by Douglas Engelbart, technology firms ignored the device for almost two decades. Despite popular belief, the Macintosh was not the first computer with a mouse. The Xerox Alto, a machine that never found its way to market, was one of the first computers coupled with the ubiquitous pointing device.
The Xero Alto inspired the Macintosh — a detail often lost in history. In fact, Steve Jobs hired some of the Alto engineers to spearhead Macintosh development. Most of the Mac's user interface advancements stemmed from the Alto, including its iconic mouse.
Flash forward a few decades, and the mouse became a fixture on virtually every computer. The ubiquitous pointing device became stale, and as laptop computers emerged, cumbersome.
Laptop computers posed a significant problem for the mouse. Designed to operate in the field, laptop users might not always have a desk or flat surface to maneuver a mouse. The first solution, the trackpad, was obvious yet cumbersome. While the controller may work well for a game of Centipede, it's not the best way to navigate a user interface.
Apple, even during their less glorious days, pushed design forward unlike any other company. In May of 1994, the Cupertino tech company unveiled the first laptop computer with a trackpad — the PowerBook 500. The laptop embraced many new technologies; however, the trackpad was the most obvious and enticing. It proved to be a massive hit with customers.
For a long time, only laptop and notebook computers used trackpads. Some PC makers developed standalone trackpads for Windows machines. These devices operated exactly like a mouse, with no capability for advanced gestures.
Apple has always enjoyed the advantage of making tightly-coupled hardware and software. Unlike the Windows world, Apple can fully realize hardware capabilities. In 2010, Apple launched the first Magic Trackpad, alongside new gestures for OS X. The combination created a unique and powerful user experience, unlike anything on the market.
Reliable rumors suggest that Apple's next Magic Trackpad will be a great leap forward. A slew of patents indicate that Apple will bring wireless charging and Apple Pencil support to the next Magic Trackpad.
Patent illustrations seem to indicate that the next Magic Trackpad will attach directly to the Magic Keyboard. Using a magnetic fastener, the new trackpad can serve as a wireless charger for the iPhone. It will also function as an active drawing surface for the Apple Pencil.
Apple Pencil support is a bit surprising. Such a move could cannibalize sales from the iPad. For now, the iPad is the only way to use the Apple Pencil, and it may drive graphics professionals to adopt the popular tablet.
No one knows what Apple will unveil next. The company is known to patent features that never see the light of day. It's entirely possible that the Magic Trackpad may serve as a wireless charging device. It could also offer Apple Pencil support. Apple takes the Magic Trackpad seriously, and the device is overdue for a refresh. It may just be the wireless charging solution that iPhone users have been anticipating.


Have you ever thought about what you would do differently if you were given the chance? What advice do you wish you had received when you were 18?
So where was I 10 years ago? Here I am in the middle with my good friends James and Chris, slugging orange VK's, spending far too much time in the local bars and pubs in my home town of Beverley in East Yorkshire.
This time 10 years ago I was about to leave 6th form with three pretty poor A-level results. I received two E's and a C. Back then these equated to 160 UCAS points. Not good enough to be considered for selection for my dream job as an Army Officer. I needed 180 points as a MINIMUM.
I also didn't have enough UCAS points to go to my first choice University.
Damn it! Why didn't I work harder!
The advice I would give a young 18-year-old Adam here looks pretty obvious.
Work harder at your studies. Don't party so much and don't be lazy.
This sounds like sound advice but would I have listened? Not a chance. I was having a great time!
From a very young age, I have always done what I enjoyed.
It started with the Air Cadets. From the age of 13, I fully emersed myself into life as a cadet. Countless weekends, drill nights and weeks away on camps were spent leading my fellow cadets.
At 17 years old in the Reserves. A mortarman from day one.
At 17 years old, whilst I was at 6th from, I joined the Army Reserves or the Territorial Army as it was known back then. Most weekends I was on a field exercise. Digging shell scrapes and getting no more than a couple of hours sleep. I took two weeks off from my studies (without letting the head of 6th form know) to go on the Combat Infantryman's Course in Catterick. This would explain the poor grades. I also worked in a bar when I wasn't playing soldiers and played a lot of rugby.
I generally did what made me happy. Isn't that what life is about?
It's not a coincidence that I have excelled at the things that I have enjoyed. When I've felt valued, useful and happy my performance increases.
Many 18-year-olds have a lot of pressure to get the top grades and go onto a top class University. I had little of that pressure. My parents supported me but let me make my own choices. I was an adult after all.
Even though I had terrible A level results, I was adamant that I would be successful at Army Officer selection. The week before attending the selection in the sleepy town of Westbury in Wiltshire, I received the news that my first choice University had accepted me. I was a whole 120 UCAS points away from achieving the 280 points that Hull University required but for some strange reason, they wanted me to study there. They must have been short of applications in 2007!
With the wind in my sails from this good news, I headed down to the Army Officer Selection Board full of confidence and belief in my ability. I received a pass by the Army Officer Selection Board on the condition that I prove my academic ability by getting an honours degree.
To some people, getting the terrible A-level grades I did would be an absolute failure but I didn't see it this way. I wasn't particularly interested in the subjects I was studying. I selected them as the best of what was available as I had no other idea of what to do after school.
Looking back now, going through this experience has made this even clearer in my mind; that my talent, skills and ability are not defined by an exam grade. There are so many other skills that I feel I have developed over the years that are, in my opinion, more important than being able to recite statute laws for an A level law exam.
My friends in the first picture are also the type of people that do what they love.
James, the tall one on the left with stupid hair was a phenomenal rugby player and a biology whizz kid. So he focused mainly on his rugby and slightly on his biology. He now makes a living playing rugby in the English Premiership with Northampton Saints. He is still a phenomenal rugby player and was called up to the England Saxons team last summer.
Chris (on the right) absolutely lives for what he loves. He has worked multiple ski seasons in the Alps, travelled and worked in Australia and deployed on an Operational tour to Afghanistan in 2011. Chris scuba dives, parachutes and has even recently taken up cycle touring. He is now working for the London Ambulance service. Here his best qualities are best put to good use; his calmness under pressure, leadership, bravery and getting stuck in there where most would look away.
James, myself and Chris. 10 years on, we still have time for a drink. The orange VK's are best avoided nowadays.
It has not been an intentional thought process but I realise that I have surrounded myself with many other people that live with the same values as me.
So what advice would I give a younger Adam? None. Simple as that.
Sure, I've made mistakes. We all have. But from these mistakes, I have grown stronger as a person.
Success is individual to us all. For me, success is truly doing what I love, making a positive difference and impact to other people's lives and ending the day knowing that you have accomplished something, no matter how small.


Marley & Lola's Border Terrier Life: Phew, it be a scorcher.....!
Very good blog again and very entertaining as alway Marley pal and Clapton's advice is spot on. I wear factor 50 sun tan lotion on my nose and pink bits cos mum doesn't want me to burn.
Summer is here at last yeppee but stay cool doglets.
I is glad that you does be taking it easy in this ot weather! I fink extra noms are required to elp us cope wiv the eat!!
Stays in the shade and be cool!!!!
It was super hot here this weekend, too! Mom's a total wimp when it comes to weather, though, so I didn't have to worry about getting overheated.
Oh Marley, I think you need a cool creek to cool your furs off in. You dussn't has to swim or do anything exhausting or nuttin, you just plop down in the water, kind of like you were doing afore Lola woke you up.
Loving the blog as always and good advice der Marley ma pal.
only fing is Clapton dus only av factor 15 sun loshun, you needs to tell him to get higher one for dis hot weather!
Good skills with the slumpin Marley, can you send me some of your furs cos I do be needing some global warming down here by Antarctica.


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News › OBrien to CNIO
UCI Health promotes O'Brien to chief nursing informatics officer
UCI Health is pleased to announce the promotion of Margaret O'Brien RN, BSN, to chief nursing informatics officer (CNIO). This position, along with the chief medical informatics officer, will guide the continuing integration of progressive technology with UCI Health's leading patient care.
"Margaret has worked tirelessly for UCI Health and our IT organization over many years, and has been an unceasing advocate for nursing and for the patient," said Charles Podesta, chief information officer for UCI Health.
In her new role, O'Brien will lead the integration of clinical information systems. This includes the adoption of tech-related change that maximizes patient safety, quality of care and operational efficiency.
O'Brien has been with UCI Health for more than 30 years, starting as a clinical care nurse. As a member of the health system's informatics team, O'Brien played a key role in last year's successful implementation of the Epic electronic medical record initiative. She has worked in patient care settings, including in several intensive care units and was a founding member of the American Nursing Informatics Association in Southern California. She recently partnered with the CNIO at UC San Diego, along with UCI Health nursing leaders to develop a robust partnership to collaborate on nursing governance issues at UCI and UCSD.
UCI Health comprises the clinical enterprise of the University of California, Irvine. Patients can access UCI Health at primary and specialty care offices across Orange County and at its main campus, UCI Medical Center in Orange, California. The 417-bed acute care hospital provides tertiary and quaternary care, ambulatory and specialty medical clinics, and behavioral health and rehabilitation services. UCI Medical Center features Orange County's only National Cancer Institute-designated comprehensive cancer center, high-risk perinatal/neonatal program and American College of Surgeons-verified Level I adult and Level II pediatric trauma center and regional burn center. UCI Health serves a region of nearly 4 million people in Orange County, western Riverside County and southeast Los Angeles County. Follow us on Facebook and Twitter.