Unconstrained and Constrained Model Predictive Control for a Modified Quadruple Tank System

In this paper, an implementation of Model Predictive Control (MPC) for a Modified Quadruple Tank System (MQTS) is addressed. The MQTS system is a multi-input-multi-output (MIMO) system and has complicated variables interactions. The aim of this work is to demonstrate the implementation of MPC, including the derivations of unconstrained and constrained MPC equations for the particular system.

Besides that, we want to evaluate the performance of the MPCs in terms of the behaviour of the system and to verify should the realisations are physically feasible. For the purpose of the study, a linear discrete-time state space model is employed. The model is from an existing dynamics of the system which comprises deterministic and stochastic components.

As for the controller, the MPC consists of a state estimator and a constrained regulator. A Kalman filter is incorporated to estimate the current state from the filtered part while the predictions part is used by the constrained regulator, which is an Optimal Control Problem (OCP) to predict the future output trajectory.

The objective of the OCP consists of a tracking error term that penalizes deviations of the predicted outputs from the setpoint and a regularization term that penalizes the changes in the inputs (manipulated variables). The resulting OCP is represented as a Quadratic Programming (QP) is solved and the performance of MPC is demonstrated through simulations using MATLAB.