Submitted by: Submitted by mithrandir
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Pages: 8
Category: Other Topics
Date Submitted: 10/23/2014 02:21 AM
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...