ECTE442/842/942

Introduction

This assignment provides you with an opportunity to apply the methodologies you are taught in

the lectures and hence to develop a better understanding of them.

Assessment

This is an individual assignment. It has a value 10% of your total mark in this subject.

Your performance will be assessed based on the report you submit. Your report should include:

The procedures and methodologies applied

The results produced including the diagrams and critical analysis of them

The MATLAB program if you use it to assist your design

Due Date: 11:30am Friday week 7, late submit will not be accepted

Please submit your report (with Cover Sheet attached) to the assignments box located at

the EIS Central student enquiries centre in Building 4

In spite of commonality of results, your report should not resemble any other report. In

case of identical reports, your mark will be the mark of one report divided by the number

of identical reports.

2

Part I

(10 marks, covers Lectures 1-4)

Design Task

You are a control engineer who has been assigned the task of developing a digital controller for

the following system, where G(s)=1/s(s+1)

(a) Design a lag compensator D(s)=K(Ts+1)/( αTs+1), α<1, such that the static velocity error

constant Kv is 25 sec-1, phase margin is 45º, and gain margin not less than 8 dB. (2

points) .

If you don’t know how to design the continuous compensator, set K=25 and assume

some values for T and α. The phase margin can then be determined using a Matlab

command, margin. Adjusting T and α by trial and error for the desired phase margin of over

45º the lag compensator can be determined. You can also use Matlab program sisotool for

the design.

Using emulation method to re-design a digital compensator which maintain the phase

margin of the original compensator. (Following the example in the lecture.)

(b) Find the step response, system margin and bandwidth. (1 point)

(c) Choose the sample frequency as 20*bandwidth. (1 point)

(d) Analyze the effects of ZOH and AAF to the system response, redesign D(s) to maintain

the phase margin of continuous time design. (2 points)

(e) Approximate D(s) using bilinear method, find D(z) (1 point)

(f) Compare the discrete system performance with original one with step response, and

bode diagram. (1 point)

(g) Compare the performance of different approximate methods for discretizing continuous

compensator. (2 points)

3

Part II

(10 marks, covers Lectures 5-6)

Design Task

Provide both manual solution and MATLAB code for ALL questions

Satellites often require attitude control for proper orientation of antennas and sensors with

respect to the earth. A simplified model which allows rotation only about one axis is given by

u (double integer)

where u is reference and θ is the output.

Follow the example in lectures 5 and 6 to complete the following tasks

1. Continuous time state space model

2. Discrete time state space model (ZOH) with sample time h=0.2

3. Discrete time controllable canonical form

4. Discrete time transfer function

5. Check the controllability and Observability of the system

6. Using pole placement method to design a controller. Pick the z-plane roots of the closedloop characteristic equation so that the equivalent s-place roots have a damping ratio of

ζ=0.6 and real part of s=-2.4 rad/sec. (Hint: Refer to second order system pole position in s

domain to find the s position, then z position, then controller L)

7. Design the same control using Ackermann’s formula

8. Draw the block diagram of the discrete system with the controller

9. Compare the performance of the system with the deadbeat controller presented in the

lecture. (step response, magnitude of control signal u, bode diagram)

10. Design a full-state estimator, the poles of the estimator satisfies Ae=z2-1.2z+1.2

11. Find the transfer function of the compensator. Draw the block diagram of complete system.

12. Design a reduced order estimator with one pole at z=0.3 for the plant

## ECTE442/842/942

22
Mar