Discrete time Linear Quadratic (LQ) optimal control Vs MPC: Integral action and handling constraints

Abstract

Studies on optimal control strategy have been discussed for long years by academic institutions and by industrial persons. This thesis contributes to this wide range of study and compares the Linear quadratic optimal control and Model Predictive control based on constraints handling. MPC is much more popular and used controller than LQ optimal controller and comparison between these controllers are done based on their performance to reach the set point and constraints handling. Theoretical study and literature overview of LQ and MPC is provided and also theoretical description on how constraints are handled. A non linear process like quadruple tank system is selected to compare the performance of these controllers. Quadruple tank system is a multiple input multiple output, contains unknown slowly varying process and measurement disturbance. Minimum phase and Non-minimum phase of the quadruple tank also discussed based on placement of zero. LQ optimal controller is implemented in the quadruple tank system, in two forms such that constrained using if else loops and unconstrained. MPC controller is implemented in three forms such that algorithm based constraints, if else loop constraints and unconstrained form. Comparisons are performed within LQ control, within MPC controller and also between constraints handling of LQ and MPC. PI control was also implemented using RGA analysis for comparison. Kalman filter was used to predict the state of unmeasured tank level. It is observed that MPC unconstrained reaches the set point much quicker, but it violates the constraint limits. MPC algorithm based constraint handling reaches the set point much faster than other controller, it is stable, and robust. MPC if else constraint also reaches the set point at the same time, but it has some overshoot. LQ optimal controller reaches the set point later than MPC but earlier than PI. Finally PI takes a long time to reach the set point.