MATLAB Code Implementation of MPC Example for Flywheel System Control

MATLAB Implementation of MPC Control for Flywheel System Example

Model Predictive Control (MPC) represents an advanced control strategy particularly suitable for dynamic systems like flywheels. The core objective of flywheel systems involves regulating rotational speed through input torque adjustments, while MPC excels at handling system constraints and optimizing control actions over future time horizons.

The fundamental logic of MPC implementation for flywheel control can be divided into three key phases:

System Modeling Flywheel dynamics are typically described using first-order differential equations, correlating angular acceleration with input torque, moment of inertia, and friction coefficients. In MATLAB implementation, engineers can establish prediction models through state-space equations or transfer functions using functions like ss() or tf(), forming the core foundation for MPC controllers. The accuracy of this model directly impacts controller performance.

Prediction and Optimization The MPC controller predicts system behavior over N future steps based on current states, computing optimal control sequences through optimization algorithms like quadratic programming. For flywheel applications, the objective function typically incorporates weighted balances between rotational speed tracking errors and control input variation rates. MATLAB's mpc object and related optimization functions automate the solving of these constrained optimization problems.

Receding Horizon Implementation After executing only the first step of the optimized control sequence, the system advances to the next sampling period for renewed prediction and optimization. This receding horizon mechanism enables MPC to continuously adapt to flywheel dynamic changes while handling physical constraints such as rotational speed limits and torque saturation. The implementation involves iterative calls to MPC's mpcmove function within each control cycle.

Critical implementation details include: sampling time selection affecting real-time performance, prediction horizon length needing to cover primary dynamic processes, and weight parameter tuning requiring balance between response speed and control effort. While MATLAB's MPC Toolbox automates most computational workflows, understanding these underlying principles remains essential for debugging practical systems. Code implementation typically involves configuring MPC objects with model parameters, constraint definitions, and weight matrices before deploying the controller in simulation or real-time environments.