Hybrid model predictive control of a nonlinear three-tank system based on the proposed compact form of piecewise affine model

In this paper, a predictive control based on the proposed hybrid model is designed to control the fluid height in a three-tank system with nonlinear dynamics whose operating mode depends on the instantaneous amount of system states. The use of nonlinear hybrid model in predictive control leads to a problem of mixed integer nonlinear programming (MINLP) which is very complex and time consuming to solve. One way to solve this problem is to approximate nonlinear equations with linear or piecewise affine (PWA) expressions. The linear approximation often has a large error in calculating the operating modes and the system states. The PWA approximation produces less error than the linear approximation, but its computational load is much higher. In this study, with the aim of reducing the computational load, a closed form model has been obtained for the equations of the three-tank system in each of the modes. The resulting system is an PWA, each mode being described by an PWA expression. Predictive control of this system is a mixed integer linear programming problem that can be solved by conventional solvers. To evaluate the performance of the proposed method and the possibility of using it online, the optimal control input sequence is calculated using MOSEK commercial solver in MPT toolbox, and at any sampling time only the first member of the sequence is applied to the precise modeled three-tank system in the Simulink/Stateflow environment. The simulation results indicate that the proposed controller performs the tracking efficiently and the constraints on the system states are also satisfied.