(a) For the closed-loop control system with unity feedback, as shown in Figure Q5, (i) Develop an expression for the Closed Loop Transfer Function (CLTF) in discrete form. (5 marks) (ii) From the CLEF...

(a) For the closed-loop control system with unity feedback, as shown in Figure Q5, (i) Develop an expression for the Closed Loop Transfer Function (CLTF) in discrete form. (5 marks)
(ii) From the CLEF derived in (i) above, show how you can design a controller for a desired closed-loop response. (5 marks) Controller Process
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p
m - manipulated process input Gp - process gain c - process output Ga- controller gain r - reference input n - sample number e - error signal Figure Q5. Block diagram for a control system
(b) You are a design engineer and your task is to implement a controller in discrete form to control the position of a satellite dish. The satellite dish is driven to a desired position by supplying the appropriate control voltage to a d.c. servo motor. The application requires that a closed-loop control system be used.
Suggest the type of controller that you would recommend and explain the reasons behind your choice. (5 marks) For the controller that you suggested in (i) above, provide a detailed PDL (Program Design Language) code, which can be based on any programming language such as for example, assembly, C, Java etc, to show how you would implement your control algorithm in software. (10 marks)
State any assumptions that you deem necessary.

Solution

David answered on Dec 20 2021
5 (a)
(i) The transfer function can be given as :
Cn =
Where Gc(z) = ʓ [Gc(s)], Gp = ʓ[Gp (s)]
(ii)Step 1. Convert the basic sampled-data control system to transform the basic system into the z plane.
Step 2. By means of a root-locus analysis, determine Dc(s) = Ksc Dc(s); where Dc(s) is the transfer function and Ksc is the gain.
Step 3. Obtain the control ratio of the compensated systemand the co
espondingtime response for the desired forcing function. If thedesired Figure of Merit are not achieved, repeat step 2 by selecting a differentvalue of damping factor, natural frequency of oscillation, damping frequency etc., or a different desired control ratio.
Step 4.When an acceptable Dc(s) has been achieved, transform the compensator into the z domain.
Step 5. Obtain the z-domain control ratio of the compensated systemand the...
SOLUTION.PDF