Real Time Control Assignment 2 Report

University of

School of Electrical Engineering and Telecommunications

Real-Time Computing and Control

Report

Name: Student ID:

Content

1. Introduction 3

2. Part 1 3

3. Part 2 10

4. Conclusion 15

5. Reference 16

6. Appendix 16

MPC design code 16

LQR design code 19

1. Introduction

This report will focus on the building of Non-Minimal State-Space (NMSS) model, the design of Model Predictive Controller (MPC) and Linear Quadratic Regulator(LQR) with given set point signal and filter. In this report, a certain process is given, a MPC controller and a LQR controller for the process is designed and simulated. To do this, in the beginning of each part, the system will be reformed to a NMSS model.

After designing the MPC and LQR, simulation will be ran to show the effect of the cost function on close-loop response and make a compare of set point and the output to see the different with different conditions.

2.Part 1

2.1Non-minimal State Space expression

System black diagram is:

The nominal process P is:

The set point filter M is :

Then, we have:

Which is the error equation.

By multiplying filter to both side of the equation, and let: , we have:

The system’s state space model is:

Through calculation set:

We can get that:

ε=[ 0 0 0 0 1 0 0 0 0 0 0]

Then with the relevant MPC design MATLAB code in the Appendix, we can get:

Feedback gain (When )

Then we have:

Change the value of λ, we can get different results.

2.2Closed loop behavior simulation with differentλ

When λ=1,N=200.

Where red line is s(t), green is y(t) in the upper figure, blue line is filtered s(t), u(t) in the lower figure.

When λ=0.1,N=200.

Where red line is s(t), green is y(t) in the upper figure, blue line is filtered s(t), u(t) in the lower figure.

When λ=0.01,N=200.

Where red line is s(t), green is y(t) in the upper figure, blue line is filtered s(t), u(t) in the lower figure.

When λ=4,N=200.

Where...