Digital Control and Instrumentation

Question 1:
A digital controller is used to control a continuous plant as shown in Figure 1. The parameters of the controller, the plant and sampling time are given below:

• Show all steps for your calculations. Determine the following.
• The Z transform of the continuous system
• Derive the Z-transform for the closed loop system
• Characteristic equation of the closed loop system
• Determine the pole locations, comment on stability
• Check the stability of the system based on the Jury Test

Figure 1 Digital Control System

Question 2:

a) Rank the following FIR filter window methods (1 - best to 3 - worst) in terms of ‘sharpness' (i.e. narrowness of transition band), and ‘stopband performance' (i.e. attenuation)

• Rectangular window
• Hamming window
• Blackman window

b) You are required to design a low-pass FIR filter to remove HF noise from a measurement signal. The desired frequency response of low pass filter is given in Figure 2:

The cut-off frequency is given by, .

Determine the filter co-efficient and frequency response of the FIR filter, if Hamming window is used with M = 7.
Determine the Low-pass filter type coefficients, for n=0,1,2,3
Determine the Hamming window coefficients, for n=0,1,2,3
Determine the filter coefficients, for the FIR filter for n=0,1,2,3
Obtain the magnitude response for designed low-pass digital filter.
where,

Filter order
Low pass filter
Hamming window
Filter coefficients
Magnitude response

Question 3:

a) For applications like audio equalization, biomedical signal processing, and high-speed telecommunications when a sharp frequency response is needed with minimal computational complexity, where memory constraints are present, and linear phase is not critical; would an IIR or FIR filter be more appropriate? Explain your selection. Book your writer now for solution!

b) Demonstrate the design of a first order Butterworth high-pass digital IIR filter, with cut-off frequency =1 rad/sec and sampling frequency Fs = 1Hz

Calculate the equivalent pre-wrapped cut-off frequency.
Determine the high-pass IIR filter transfer function,

c) A discrete-time system has the transfer function;

Determine the stability of the system from the characteristic equation
Determine the final value and steady state offset/error, assuming the input to the discrete time system is a unit step