ENGR3711 Control Systems : Proportional Compensator

ENGR3711 Control Systems : Proportional Compensator

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ENGR3711 Control Systems

Task:

Motivation

The aim of this practical is to design compensators using the time domain, in particular the root locus technique, in order to achieve the desired system requirements. This practical will demonstrate the usefulness of this approach to the design of control systems. The time-domain design of control systems refers to the utilisation of the time-domain properties and specifications of the system to be designed. Since there is a close relationship between the time-domain properties and the s-plane characteristics of the system transfer function, the time-domain design of linear control systems is carried out by working with the poles and zeros of the system transfer function in the s-plane.

In this practical you will design closed-loop control systems using the root-locus technique. This technique allows designers to place the control system’s closed-loop poles in the desired locations and therefore alter the system’s transient, steady-state and/or stability parameters. The evaluation of the system responses will be conducted using MATLAB. The design principles for proportional, phase-lead, phase-lag, PD and PID compensators are covered in the lecture notes and the topic textbook.

This practical is marked and you will have to submit a report on it. When needed code for sections should be saved and named A, B, C, etc. as appropriate. Copies of these files should be submitted with your report. Remember that while you are able to do the practical in a group, you must maintain your own logbook and write your own report, making sure you name your group partner(s) in your report.

Your written report must be submitted in Word or PDF format and not within a zipped file. Any submitted code should be contained within a zip file. A 10% penalty will apply for disregarding these instructions.

Aims

  • To design a variety of compensators using the root locus technique
  • To use the modelling and simulation capabilities of MATLAB to realise compensator design

A) Proportional Compensator 

A servo motor, depicted in Figure 1, is an example of a closed-loop control system. A desired or reference angle is received, θr(t), and compared to the current angle of the servo horn as measured by a potentiometer, θf(t). The difference between these signals, θe(t) is then used by a control system, C(s), to control a plant, G(s). The signal received by the plant, a(t) controls the velocity of a DC motor which is connected to the servo horn via a gear system that translates the velocity of the motor shaft

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