Reduction of the ASM 1 model for optimal control of small-size activated sludge treatment plants
In order to meet the stricter wastewater effluent guidelines adopted by the European Union, wastewater treatment plants require better management strategies. Wastewater treatment process models have become a major tool to design closed-loop control schemes. However, the dynamic models that are currently used in the simulation of activated sludge treatment plants (ASM 1, ASM 2 and, more recently, ASM 3 models) are highly dimensional and are not appropriate for on-line implementation (e.g., for model predictive control or optimal control). It is therefore important to develop reduced models that could be used for this purpose. A reduced model was developed to describe the behaviour of alternating activated sludge treatment plants, with the aim of applying it to the optimal control of an aeration system. The reduction scheme was based on appropriate simplifications to the ASM 1 model (which is more appropriate for open-loop control). The objective was to verify if accurate predictions could be made time periods of several hours (about 8 h). The present results are related to an existing small-size wastewater treatment plant. This plant was designed for 15,000 population-equivalents (p.e.) and consists of a primary treatment stage (screening, grit removal, primary sedimentation), followed by a secondary treatment stage (biological treatment). The latter consists of a single aeration tank of about 2,050 m3 equipped with 3 turbines which are operated cyclically to create alternating aerobic and anoxic conditions. Ammonia is converted into nitrate during air-on periods (nitrification step) and nitrate is subsequently removed during air-off periods (denitrification step). It is important to note that a dynamic model, based on the ASM 1 model and calibrated from a set of input/output measurements over a one-day period (Chachuat, 2001), was used here as a reference to perform model reduction. The following two-level simplification procedure was applied : · A homotopy method was first used to establish relationships between the states and the dynamics of the system, via an eigenvalue decomposition. The components that are associated with the slowest dynamics are then assumed constant to reduce the state space dimension. Heterotrophic (XB,H) and autotrophic (XB,A) biomass and inert particulate organic compounds (XI) were detected as the slow state variables. It was found that the short-term predictions of the dynamic model were not affected by assuming that XI, XB,H and XB,A concentrations were constant. Eliminating these 3 state variables, along with the concentrations of soluble inert organic compounds (SI), resulted in a 7-dimensional dynamic model. · However, further simplifications were required to enable the on-line optimisation of the bioreactor aeration profiles with reasonable computational times. These simplifications consisted of taking into account the process specifications in order to reduce the state space dimension to 4 or 5, and were therefore based on more heuristic considerations. Both organic and nitrogenous compounds are under consideration: (i) a single organic compound (denoted as XDCO) is formed by adding soluble and particulate organic compound concentrations, and (ii) the mathematical expression that describes the organic nitrogen hydrolysis process is simplified so that the dynamics with respect to soluble and particulate organic nitrogen are independent. The two previous simplification steps produced a reduced 5-dimensional dynamic model with state variables XDCO, SNO, SNH, SND and SO. It should also be noted that the resulting model involved the parameters YH, iNBM, KS, KNO, KO,H, KNH,A, ηNO,g and ηNO,h that are identical to those defined in the original ASM 1 model by Henze et al. (1987). In addition, 7 specific parameters were defined defined (θ1, θ2, θ3, θ4, θ5, KDCO, KND). These new parameters exhibited rather slow temporal variation, thus agreeing with the general ASM 1 model for short time periods. Afterwards, a two-step procedure was applied to calibrate the model. This procedure first consisted of determining a reduced set of identifiable parameters by the use of both sensitivity and principal component analyses. Note that the inlet concentrations of organic compounds, ammonia nitrogen and soluble organic nitrogen may be considered as additional parameters since they are generally not measured on-line. The selected parameters (θ1, θ2, θ3) and inlet concentrations (XinDCO, SinNH) were then estimated by the application of a local gradient search method (successive quadratic programming, SQP). Comparisons between the dynamic behaviour of both reduced and ASM 1 models show that accurate predictions can be obtained over time periods of several hours (8 h). It was also shown that the reduced model was observable and structurally identifiable under aerobic and anoxic conditions from dissolved oxygen, ammonia and nitrate concentration measurements. These results therefore demonstrate the ability of the reduced model to be embedded into closed-loop control schemes. The conclusions from this work are twofold: (i) The reduced model can be used as a basis to construct an on-line observer to estimate the unmeasured state variables, the unknown (most sensitive) parameters and inlet concentrations; (ii) Non-linear model predictive control (NMPC) schemes can then be implemented to operate the aeration system so that the nitrogen discharge or the energy consumption are minimised (optimal control). The initial results demonstrate that the application of NMPC strategies is likely to give large reductions of nitrogen discharge with respect to usual operating strategies (e.g., oxygen or redox control). Such closed-loop control schemes are particularly efficient in dealing with large influent variations (inlet flow rate, concentration and composition) resulting from both human activities and climatic conditions, and inherent modelling uncertainties. However, an experimental validation of this control strategy on a pilot scale or an industrial scale is required to confirm these results.