Design and application of discrete sliding mode controller for TITO process control systems

Abstract

Selection of the proper control system for the multi-variable systems with time delay is a challenging task because of the interacting dynamic behaviour of system variables. Till date most of the multi-variable processes are controlled using proportional-integral-derivative (PID) controllers. The PID controllers for multivariable systems are either having centralized (full structured) or decentralized (diagonal) structure. The design procedure for centralized controllers is very complicated as the loop controllers cannot be designed independently. The decentralized controller design procedure either requires detuning or decoupling of the interactions. The controllers designed with detuning do not perform well for larger interactions. Thus decentralized PID controller with decoupler is the better choice with simple design procedure. In the design procedure for decentralized controllers, initially the decoupler is designed and decoupled subsystems are obtained. Then for each subsystem, the single loop controller is designed and the control signal is applied through decoupler to track the system variables. From the available literature, it can be seen that most of the PID design methods are based on linearized reduced order models. Due to model order reduction, the parametric uncertainty (plant-model mismatch) is introduced, which is not taken into consideration in the design process. Hence the designed PID controller is less robust and even may lead to instability especially in presence of time delay in the system model. Sliding mode control (SMC) is one of the robust control strategy with inherent property of invariance to parametric uncertainty. The continuous time SMC can produce the best response only for very small sampling time in implementation since the implementation sampling time is not taken into account in its design procedure. The discrete time SMC uses the discrete time model of the system and hence considers the sampling time in the design steps. However, it produces chattering in the control signal because of big sampling steps. This limitation can be overcome by designing DSMC with convergent quasi-sliding mode. In this chapter, the discrete convergent quasi-sliding mode is presented for interacting two input two output (TITO) systemswith time delay. The ideal decoupler is designed to determine the non-interacting subsystem models for each loop. Then each subsystem is reduced to all pole third order plus delay time (TOPDT) model using four point fitting of frequency response. The separate DSMCs are designed for each loop using discrete time state model of the corresponding reduced subsystem. The control signals generated by the DSMCs are applied to the system through the decoupler. The stability condition for the presented controller is derived using Lyapunov stability approach. To validate the performance of the presented controller two well studied systems are simulated. To show the effectiveness of the prosed strategy, its performance is compared with the existing decentralized PID controllers.