Advanced Control Systems Engineering

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ENGIN5405: Advanced Control Systems Engineering Assignment 2

Total Marks: 100

Weighting: 15%

Submission Deadline: Week 13 - Sunday 8 November 2020 23:59 Hours

Submission Format: Formal - Softcopy (using the Report Template provided under Resources in Moodle)

Submission Location: Moodle Submission Link under Assessment section in course’s Moodle page.

Required Software: MATLAB & SIMULINK

MATLAB and Simulink Information

Helpful MATLAB codes

zpk poly zpk Rlocus exp dcgain

sgrid rlocfind input Abs title pause

real imag sqrt Tf feedback step

whitebg while conv clf clc clear all

axis syms syms hold on

You can also view the Appendix B: MATLAB Tutorial of the following textbook.

Control systems engineering, Nise, Norman S ProQuest (Firm), 2015

An ebook is available for online access through Federation University Australia Library.

Simulink Tutorial

Simulink tutorial can be viewed from Appendix C: Simulink Tutorial of the following textbook.

Control systems engineering, Nise, Norman S ProQuest (Firm), 2015

An ebook is available for online access through Federation University Australia Library.

In particular, please refer to Example C.1 (Simulation of Linear Systems) and Example C.3 (Simulating Feedback Systems).

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Problem 1 (25 Marks)

A unity feedback system is given below.

The system is operating with a dominant pole damping ratio of 0.707.

The aim is to design a PD controller so that the settling time is reduced by a factor of 2.

In order to achieve this, perform the following tasks in MATLAB.

a) MATLAB will generate the root locus for the uncompensated system along with the 0.707 damping- ratio line. You will interactively select the operating point. MATLAB will then inform you of the coordinates of the operating point, the gain at the operating point, as well as the estimated %OS, TS, Tp, ζ, ωn and Kp represented by a second-order approximation at the operating point.

b) MATLAB will display the step response of the uncompensated system.

c) Without further input, MATLAB will calculate the compensated design point and will then ask you to input a value for the PD compensator zero from the keyboard. MATLAB will respond with a plot of the root locus showing the compensated design point. MATLAB will then allow you to keep changing the PD compensator value from the keyboard until a root locus is plotted that goes through the design point.

d) For the compensated system, MATLAB will inform you of the coordinates of the operating point, the gain at the operating point, as well as the estimated %OS, TS, Tp, ζ, ωn and Kp represented by a second-order approximation at the operating point.

e) MATLAB will then display the step response of the compensated system.

In your report, include all your MATLAB codes, results and figures.

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Problem 2 (25 Marks)

Steam-driven power generators rotate at a constant speed via a governor that maintains constant steam

pressure in the turbine. In addition, automatic generation control (AGC) or load frequency control (LFC)

is added to ensure reliability and consistency despite load variations or other disturbances that can

affect the distribution line frequency output. A specific turbine governor system can be described only

using the block diagram.

The governor’s transfer function:

The turbine transfer function:

The machine and load transfer function:

Gc(s) is the LFC compensation to be designed a) Assuming Gc(s) = K, find the value of “K” that will result in a dominant pole with ζ = 0.7. Obtain the

corresponding Ts. b) Design a PID controller to obtain the same damping factor as in Part (a), but with a settling time of

2 seconds and zero steady-state error to step input commands. c) Use a lag-lead compensator instead of a PID controller. Design for a steady state error of 1% for a

step input command. d) Verify your results using MATLAB.

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Problem 3 (25 Marks)

Figure 3(a) shows a heat-exchanger process whose purpose is to maintain the temperature of a liquid

at a prescribed temperature. The temperature is measured using a sensor and a transmitter, TT 22,

which sends the measurement to a corresponding controller, TC 22, which compares the actual

temperature with a desired temperature set point, SP. The controller automatically opens or closes a

valve to allow or prevent the flow of steam to change the temperature in the tank. The corresponding

block diagram for this system is shown in Figure 3(b). Assume the following transfer functions:

Figure 3: a. Heat-exchanger process; b. block diagram.

a) Assuming Gc(s) = K, find the value of K that will result in a dominant pole with ζ = 0.7. Obtain the corresponding Ts.

b) Design a PD controller to obtain the same damping factor as Part (a) but with a settling time 20% smaller.

c) Verify your results through MATLAB simulation.

d) Repeat Parts (b) and (c) using a lead compensator.

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Problem 4 (25 Marks)

An X-4 quadrotor flyer is designed as a small-sized unmanned autonomous vehicle (UAV) that flies

mainly indoors and can help in search and recognizance missions. To minimize mechanical problems

and for simplicity, this aircraft uses fixed pitch rotors with specially designed blades. Therefore, for thrust

it is necessary to add a fifth propeller. A simplified design of the thrust control design can be modelled

as in the Figure below.

The transfer function, P(s) represents the dynamics of the thruster rotor gain, the motor, and the battery

dynamics. Initially, the system is designed using a proportional compensator given by 𝐺𝐺𝐶𝐶(𝑠𝑠) = 3

(Pounds, 2009).

a) Calculate the resulting steady-state error for a unit step input.

b) Design a lag compensator to yield half the steady-state error of the proportional compensator,

without appreciably affecting the system’s transient response.

c) Use SIMULINK to simulate the unit step response of the original design (with proportional

compensator) and the lag compensated design. Verify the lag compensator achieved its

objective.

Pounds, P. E. I., Mahony, R. E., and Corke, P. I. Design of a Static Thruster for Microair Vehicle

Rotorcraft. Journal of Aerospace Engineering, vol. 22, no. 1, 2009, pp. 85–94.