This invention is directed to time delay controlled processes, such as those that may be useful with a servosystem, a robot arm or a magnetically suspended rotor.
A general control strategy consists of at least two levels: a high level controller and a low level controller. The high level controller may perform several functions: (1) observe the state of the system, (2) accept inputs from environment, (3) perform filtering and estimation, (4) decide whether a task is realizable, etc. It then generates a command which is sent to a low level controller. The low level controller, on the other hand, has a few other functions: (1) observe the state of the system, (2) filter and estimate and (3) compute the control action. The control action is generated in order to execute a realizable command issued by the high level controller independent of system dynamic varations. These variations may be due to internal system changes or external disturbances. Internal factors may include parameter changes and/or function changes. A function change could be manifested by the change of the "constituted relation of an element". For example, a spring characteristic could vary from a linear one, where only one constant is used in the model to a hardening spring where two constants may be used. The present invention is directed to the design of low level controllers that guarantee the proper execution of realizable tasks.
The low level control of systems with unknown dynamics and unpredictable disturbances has raised some challenging problems. This is particularly important when high system performance is to be guaranteed at all times. Some classical control methods deal with well known, linear, time-invarient systems. In many applications, however, some relevant part of the system may be unknown, time varying, or nonlinear. Controlled systems are thus often limited to operating in only a small portion of their available range. For example, servo motors must operate in the linear part of their range for accurate control. Robot arms and magnetically controlled rotors, such as those used in a turbo molecular pump, are examples of physical processes which would benefit greatly from improved control systems.
Several types of control strategies have been developed to deal with nonlinear, time-variant systems. One of the first methods to accommodate nonlinear systems was Model Reference Control. This technique employs a model of the system and uses the difference between the model response and the plant response as the input signal to the plant [7]. The model is either a physical model or a simulated system on a computer. Although it has no variable parameters, it is very useful for either specifying desired performance or for the observation of unaccessable states. A drawback in this technique is that it requires knowledge of the full dynamic model and system limitations. When perfect cancellation of the system nonlinearities is not achieved due to imperfect modeling or inaccurate parameter values, the dynamic performance of the plant may be degraded to the point of closed loop instability [8].
Another advanced technique is Adaptive Control. An adaptive system measures a certain index of performance which is a function of the inputs, states or outputs of the system. From the comparison of the measured index of performance with a set of given ones, the adaptation mechanism modifies the parameters of the controller [6]. There are several classes of adaptive control. A very common variation used a model for the system as a basis for comparison and is termed Model Reference Adaptive Control (MRAC). It adjusts the controller parameters while keeping the model parameters constant. In contrast is the `self-tuning` system introduced in reference [1] in which the controller parameters are held fixed while the model parameters are modified. Another approach generates the control action in part by an adaptive feedforward controller which `behaves` as the `inverse` of the plant [8]. All adaptive controllers share the distinguishing feature of system identification followed by variation of parameters to maintain desired performance. A drawback of adaptation is that it is generally slow and computationally intense. Often the environment changes faster than the system, causing performance degradation or even instability.
Other control methods, such as Variable Structure Controllers, take totally different strategies to achieve stability in nonlinear, time-invariant systems. This type of controller utilizes state feedback in a control law which switches the structure of the closed loop system between trajectories which may themselves be unstable or marginally stable but when combined by the control law in a switching technique, result in a system which is stable. A method of switching called `sliding mode`, described in [9,10,11], arranges the switching so that ideally the system remains on one of the switching lines (or surface) as it `slides` stably toward the origin of the phase plane. Real systems, however, take time to switch trajectories, resulting in periods of infinite frequency, or no control, as the system switches from one trajectory to another while attempting to remain on the switching line. This high frequency chattering undesirably excites high frequency dynamics.
During the 1970's, several control algorithms emerged which attempt to force a systems response to track a desired trajectory. Two such algorithms which have received significant attention are Model Algorithmic Control (MAC) and Dynamic Matrix Control (DMC) [2,12]. These two algorithms utilize a discrete model representation of a controlled system to minimize predicted future errors relative to a given reference trajectory over a given preview horizon [5]. These two approaches might be grouped under the two more general topics of preview or predictive control. Predictive and preview control are similar in that they attempt to minimize a predicted error, or cost function, over a given preview horizon. Preview control, however, does require a state-space description of the plant. A predictive controller may be used if a simulation and the system step responses are available. Predictive and preview control algorithms are generally computationally intensive since they involve the minimization of some cost function over a preview horizon. Accordingly, they are suitable for control of systems with relatively large time constants. Many improvements to the general method of predictive control have been made over the years to generalize controller design to multivariable systems and to make possible several types of stability robustness analyses. Increases in computational speeds of commonly available microprocessors continue to allow the application of such a control algorithm to systems with increasingly fast dynamics. However, it should be emphasized that the algorithm is based upon the assumption that the dynamics of the controlled system are known, either in terms of analytical models or step response data.
Another method, Time Delay Control (TDC) was originally formulated by Youcef-Toumi and Ito [12] for a class of nonlinear systems with linear input action. Time delay control introduced in references [13,14,15,16], depends neither on estimation of specific parameters, repetitive actions, infinite switching frequencies, nor discontinuous control. It employs, rather, direct estimation of the effect of the plant dynamics through the use of time delay. The controller uses the gathered information for position, velocity and acceleration to cancel the unknown dynamics and disturbances simultaneously and then inserts the desired dynamics into the plant. The TDC employs past observation of the system response and control inputs to directly modify the control actions rather than adjusting the controller gains. It updates its observation of the system every sampling period, therefore, estimation of the plant is dependent upon the sampling frequency.
There are other systems referred to as time-lag or retarded systems, where time delay exists between the cause and effect. In time delay systems, these delays arise as a result of delays existing in the hardware components or computation [1]. In the present invention, the time forumulation for such time delay systems leads to delayed differential equations. A special class of these equations are referred to as integral-differential equations which were studied by Volterra [10]. Volterra was the first to study such systems and developed the theory to investigate the consequences of time delay. Several other researchers have contributed to the development of the general theory of the Volterra type.
It is an object of the present invention to adapt time delay control for use with magnetically suspended rotors and for robot arms. It is a further object of the present invention to provide an improved formulation of time delay control by using convolutions.