A Small Example of Model Predictive Control: Gravity Drained Water Tank

This is a small example illustrating model predictive control using a water tank system. We can control the water level inside the tank by adjusting the water inflow. The outflow rate depends on the size and position of the orifice at the bottom of the tank. The control objective is to maintain the water level within a desired range by manipulating the flow through the bottom orifice. Model predictive control (MPC) is suitable for this application as it involves future predictions based on a system model. A mathematical model must be developed to describe the tank's physical dynamics and the relationship between orifice flow and water level. The MPC algorithm typically involves solving an optimization problem at each time step to determine control actions that minimize future errors while satisfying constraints. In code implementation, this would require discretizing the system equations and using quadratic programming solvers. Controller parameters can be tuned to minimize prediction errors and improve control performance. Key implementation aspects include: - System identification to determine model parameters - Design of cost functions weighing tracking performance and control effort - Implementation of constraints handling for realistic operation - Real-time optimization using algorithms like interior-point methods The MATLAB MPC toolbox provides built-in functions for creating MPC objects, specifying constraints, and simulating closed-loop performance, making it suitable for such applications.