Artificial neural network based model predictive control of a distributed parameter system

Abstract

Enough of literature is available for modelling and control of a lumped parameter system (LPS). Many a times, it is desired to have the final properties well within some predetermined range for which the assumption of the system being lumped may not hold good. While it is easier to model and control a lumped parameter system, it is much difficult to control a distributed parameter systems in which the parameter of interest is a function of both space and time.ii First principles model found in literature closely approximates the real system. Developing such equations for a real system having hundreds of variables is simply not feasible since it requires a lot of time and expertise. In it, the dynamics of each and every component of the system have to be separately studied and modelled. On the other hand, data based models inherently takes care of the dynamics of each entity of the system and we can directly relate the input to the output of the system. Data driven models can be developed in a timely manner and can be readily applied in a real control system environment. The only drawback of such models is that they are sensitive to parameter variations and can be used to operate the system in the neighbourhood of the operating environment in which the open loop (input/output) data was generated for modelling purpose. Hence, updating model from time to time should be considered. For a typical distributed parameter system, an effective data driven modelling technique have been presented in this work. Firstly, a linear state space model has been developed but is found to be ineffective in capturing the system dynamics effectively. Next, an artificial neural network (ANN) based model has been developed. Unlike many other methods, this neural network based approach does not demand any a priori information about the governing equations of the system. Training the network requires open loop (input/output) data that has been generated from an experimental setup developed for this purpose. Since the ANN based model being nonlinear takes significant time for computation at each sampling interval, we finally linearize the ANN based model at every sampling interval for online implementation purpose. Further, a Model Predictive Control (MPC) scheme is proposed and has been applied for two different cases viz. set-point tracking and disturbance rejection using each of the models discussed above. Simulation and experimental results for both the cases have been demonstrated.