Model Predictive Control Example: Gravity Drained Water Tank System with Dynamic Modeling

Model Predictive Control (MPC) represents an advanced control strategy widely adopted in industrial process control. The gravity drained water tank system serves as an excellent case study to illustrate MPC's fundamental principles and implementation methodology.

The gravity drained water tank constitutes a typical nonlinear system where dynamic relationships exist between liquid level height and flow velocity. MPC operates by constructing a mathematical model of the system to predict future behavior, then computes optimal control inputs through optimization algorithms to achieve precise liquid level regulation. In code implementation, this typically involves discretizing the system dynamics using difference equations and solving quadratic programming problems at each control interval.

In this example, establishing the tank's dynamic model forms the foundation, typically employing mass balance equations to describe liquid level variations. The MPC controller utilizes current level measurements and setpoints to predict level trajectories over a predefined horizon, then determines optimal control actions (such as adjusting inlet valve openings) through real-time optimization calculations. A key implementation aspect involves designing prediction horizons and control horizons in the MPC algorithm, often implemented using MATLAB's Control System Toolbox or Python's CVXPY for optimization. Thanks to MPC's receding horizon characteristics, the controller can adapt strategies in real-time despite disturbances or model uncertainties, maintaining robust performance.

Compared to conventional PID control, MPC demonstrates superior capability in handling constraints (such as level limits and valve opening restrictions). It explicitly incorporates these constraints into the optimization problem formulation, ensuring system safety and stability. Code implementation typically involves adding inequality constraints to the optimization solver, where active-set methods or interior-point algorithms efficiently handle constrained optimization problems.