control system design of lti systems using matlab
TRANSCRIPT
![Page 1: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/1.jpg)
S Wongsa 1
CONTROL SYSTEM DESIGN USING MATLAB
MATLAB provides several tools for control design. These tools include
• Simulink
• Control System Toolbox
• Real-Time Workshop
• Simscape
• Simulink Control Design
• Stateflow
, which can be used to support each stage of the development, from plant modelling to deployment
through automatic code generation. The flexibility of the tools makes them one of the first choices, if
not the first, in control design for control engineers around the world.
This document is purposed to provide you the introduction of what Control System Toolbox
can do in the design of LTI (Linear Time Invariant) systems. In general, there are four steps of
control design: plant modelling and analysis, controller designs, verifying and refining your designs,
and deploying them. Here we focus on the modelling and design parts by simulation.
1. PLANT MODELLING AND ANALYSIS
You can build a linear model of your plant with the use of physical model, or fitting test data
using System Identification Toolbox if the physical model is not available. Either model can be
imported into Control System Toolbox as an object. Once a model is created, you can use the toolbox
to analyse and control it. Some MATLAB command-line functions for modelling and analysis of LTI
systems are listed in Table 1. Using these commands, you can view and compare the time and
frequency responses of several linear models at once. You can also inspect key performance
parameters, such as rise time, settling time, percent overshoot, and stability margins.
Table 1 Examples of MATLAB commands for modelling and analysis of LTI systems
Command Description
Creation of LTI models
tf Create a transfer function model.
ss Create a state-space model.
zpk Create a zero/pole/gain model.
Data extraction
tfdata Extract numerator(s) and denominator(s).
ssdata Extract state-space matrices.
zpkdata Extract zero/pole/gain data.
Conversions
tf Conversion to transfer function.
ss Conversion to state space.
zpk Conversion to zero/pole/gain.
c2d Continuous to discrete conversion.
d2c Discrete to continuous conversion.
Model dynamics
pole, eig System poles
pzmap pole-zero map
dcgain DC gain
damp Natural frequency and damping of system poles
pade Pade approximation of time delays.
Time response
step Step response. Impulse Impulse response.
![Page 2: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/2.jpg)
S Wongsa 2
lsim Response to arbitrary inputs.
Initial Response of state-space system with given initial state.
Frequency response
bode Bode plot of the frequency response.
nyquist Nyquist plot.
nichols Nichols chart.
margin Gain and phase margins.
System interconnections
parallel Generalized parallel connection.
series Generalized series connection.
feedback Feedback connection of two systems.
2. CONTROL DESIGN
For designing SISO control systems, you can use command-line and GUI tools of
Control System Toolbox. Some MATLAB command-line functions for control design are listed in
Table 2. The MATLAB control design GUI, known as the SISO Design Tool, facilitates the design of
compensators for single-input, single output feedback loops. It lets your rapidly perform control
design tasks, such as manipulating closed-loop dynamics using root locus techniques, adding
compensator poles and zeros, and adjusting phase and gain margins.
Table 2 Classical control design tools.
Command Description
rlocus Root locus plot.
rlocfind Interactive root locus gain determination.
zgrid Generate z-plane grid lines for a root locus or pole-zero map.
acker SISO (single-input-single-output) pole placement.
place MIMO (multiple-input-multiple-output) pole placement.
In what follows, examples of digital control designs using MATLAB Control Toolbox are
provided. These examples are obtained and available freely on internet. You are strongly
recommended to try on all examples by yourself and read the references for more details.
Part I: Design using MATLAB command-line tools, taken from [1].
Example I Cruise control
Example II DC motor speed control
Example III DC motor position control
Example IV Ball and Beam problem using PID Control
Part II : Design using SISO Design Tool, taken from [2].
Example V Bode diagram design (DC motor)
Example VI Root-locus design (Electrohydraulic servomechanism)
![Page 3: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/3.jpg)
S Wongsa 3
REFERENCES
1. Carnegie Mellon, Digital Control Tutorial, Control Tutorials for Matlab.
Available: http://www.engin.umich.edu/group/ctm/digital/digital.html
2. Control System Toolbox 8.5, Mathworks, Inc.
Available: http://www.mathworks.com/access/helpdesk/help/toolbox/control/
3. F. Haugen, Tutorial for Control System Toolbox for MATLAB, October 11, 2003.
Available: http://techteach.no/publications/control_system_toolbox/
![Page 4: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/4.jpg)
����������� ������������
�������������� ������������������ ����� ��� �������� ������ �����������
![Page 5: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/5.jpg)
![Page 6: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/6.jpg)
![Page 7: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/7.jpg)
![Page 8: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/8.jpg)
![Page 9: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/9.jpg)
![Page 10: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/10.jpg)
![Page 11: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/11.jpg)
![Page 12: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/12.jpg)
��������������������������������
�������������� ������������������ ����� ��� �������� ����� �����������
![Page 13: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/13.jpg)
![Page 14: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/14.jpg)
![Page 15: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/15.jpg)
![Page 16: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/16.jpg)
![Page 17: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/17.jpg)
![Page 18: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/18.jpg)
![Page 19: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/19.jpg)
![Page 20: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/20.jpg)
![Page 21: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/21.jpg)
�������������������� � ������������
�������������� ������������������ ����� ��� �������� ������ �����������
![Page 22: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/22.jpg)
![Page 23: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/23.jpg)
![Page 24: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/24.jpg)
![Page 25: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/25.jpg)
![Page 26: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/26.jpg)
![Page 27: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/27.jpg)
![Page 28: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/28.jpg)
![Page 29: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/29.jpg)
���������������������������������
�� �������������
�������������� ������������������ ����� ��� �������� ���� ������ !����
![Page 30: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/30.jpg)
![Page 31: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/31.jpg)
![Page 32: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/32.jpg)
![Page 33: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/33.jpg)
![Page 34: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/34.jpg)
![Page 35: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/35.jpg)
![Page 36: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/36.jpg)
![Page 37: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/37.jpg)
![Page 38: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/38.jpg)
![Page 39: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/39.jpg)
���������������� ��������� �������������
�������������� ����������"����� ������ ������" ��� ������� ������� �������� #�$%&'()%'����
![Page 40: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/40.jpg)
![Page 41: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/41.jpg)
![Page 42: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/42.jpg)
![Page 43: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/43.jpg)
![Page 44: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/44.jpg)
![Page 45: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/45.jpg)
![Page 46: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/46.jpg)
![Page 47: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/47.jpg)
![Page 48: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/48.jpg)
![Page 49: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/49.jpg)
![Page 50: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/50.jpg)
![Page 51: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/51.jpg)
![Page 52: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/52.jpg)
![Page 53: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/53.jpg)
![Page 54: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/54.jpg)
![Page 55: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/55.jpg)
![Page 56: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/56.jpg)
![Page 57: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/57.jpg)
![Page 58: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/58.jpg)
![Page 59: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/59.jpg)
������������������������ ����
��������������� ����� ������� ������������������ ����������"����� ������ ������" ��� ������� ������� �������� #�$%&'(*�'����
![Page 60: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/60.jpg)
![Page 61: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/61.jpg)
![Page 62: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/62.jpg)
![Page 63: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/63.jpg)
![Page 64: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/64.jpg)
![Page 65: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/65.jpg)
![Page 66: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/66.jpg)
![Page 67: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/67.jpg)
![Page 68: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/68.jpg)
![Page 69: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/69.jpg)
![Page 70: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/70.jpg)
![Page 71: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/71.jpg)
![Page 72: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/72.jpg)
![Page 73: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/73.jpg)
![Page 74: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/74.jpg)
![Page 75: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/75.jpg)
![Page 76: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/76.jpg)
![Page 77: Control System Design of LTI Systems Using MATLAB](https://reader034.vdocuments.us/reader034/viewer/2022042607/55200480497959932f8b4638/html5/thumbnails/77.jpg)