Advanced Control system on MPC controller in MATLAB

Introduction—

MATLABSolutions demonstrate In this task we are going to designModel Predictive Control (MPC) is one of the most popularly use advanced control techniques since it can be used in a multivariable system and also has the ability to handle explicit constraints. The objective of this project is creating, installing, and analyzing an MPC controller in a state-space environment with a given system dynamics. The main target is to carry out the coordination and control with the constraints and achieving the desired performance.

Initially the exercise includes a continuous-time state-space model of four states with definite parameters, which reflects the system's overall dynamic spectrum. The first step in developing the MPC controller is transforming the model of the system which does not include time into a discrete-time format which is more suitable for the practical application of MPC. The steps of the controller design are choosing the control and prediction horizons, defining the value function, and taking into account the constraints for the controls as well as for the process variables.

Problem Statement

This project selects, compose and judge the effectiveness of a four-state system with state-space model containing Model Predictive Control (MPC). MPC is a closed-loop control technique and offers considerable performance in MIMO systems with constraints on both input and output variables over the prediction horizon. By modeling the system's dynamics using mass and spring constants the state-space matrices are described in forms (A), (B), (E), or (C) (Hu et al. 2021). The main goal of the project is to construct the MPC controller that guarantees stability and acts within limits, but simultaneously handles disturbances. The issue is how to design the controller settings for MPC resulting in the best performance with the variable parameters like spring constant (ks). On the other hand, the controller must be robust to respond to disturbances and obey feasibility principle that maximize use of available resources. This project assesses the performance of the MPC approach in terms of ISE and OS under different scenarios to endorse that such a controller performs optimally and identifies possible improvement measures when necessary.

Design

Steps in the development of MPC system comprised of some critical operations to get acceptable control and to stick to constraints during system operation. The model started by mapping the matrices of A, B, E and C. In between, the process was discretized by use of a sampling time of 0.1 seconds to allow the implementation of MPC model.

The MPC controller was constructed with a 2 control and 10 prediction steps horizon, which was enough both for accuracy and for the computational complexity (Rodriguez et al., 2021). Considering constraint handling and the requisite constraints for input and output variables as safety measures were an integral part of the design whose primary objective was to ensure safe operation. Rates of manipulated variables, outputs variables, and constraint relaxation were calculated and evaluated.