Model predictive control

Model predictive control (MPC) refers to a family control method which applies to discrete and continuous-time process models. The future states are predicted at each time instance using the known state and system model, up to a specific time instance. The future control inputs are calculated by optimizing a determined criterion to keep the process as close as possible to the reference trajectory. An explicit solution can be obtained if the criterion is quadratic, the model is linear, and there are no constraints. Comparing to the proportional–integral–derivative (PID) feedback control, feedforward control, and inverse dynamic control that is learned in other courses, MPC has its advantages and is widely used in industry. This thesis is done under the supervision of professor Belabbas, and the main progress is to read academic papers, books, and rederived the mathematical equations of MPC using knowledge of control and linear algebra. Derivations were implemented into MATLAB functions and the control algorithm is simulated on several different models, as well as the reaction wheel pendulum in the control lab. The state-space model is obtained in continuous time domain by LaGrange formalism, and then the equations of motion were transformed into the discrete time domain. A goal is to compare the qualitative performance of PID and MPC controller on this particular system setup.U of I Onlyundergraduate senior thesis not recommended for open acces