Digital Control and Instrumentation

Learning outcome 1: Apply knowledge of mathematics, statistics, natural science and engineering principles to the solution of complex problems. Some of the knowledge will be at the forefront of the particular subject of study.

Learning outcome 2: Analyse complex problems to reach substantiated conclusions using first principles of mathematics, statistics, natural science and engineering principles.

Learning outcome 3: Select and apply appropriate computational and analytical techniques to model complex problems, recognising the limitations of the techniques employed.

Learning outcome 4: Use practical laboratory and workshop skills to investigate complex problems.

Learning outcome 5: Communicate effectively on complex engineering matters with technical and non-technical audiences.

Assignment - ICA

Knowledge & Understanding
Demonstrate a comprehensive and detailed knowledge of key aspects digital control and instrumentation, discrete system design and associated analysis tools

Cognitive & Intellectual Skills
Critically analyse and evaluate discrete system problems with respect to conversion of a signal, from a continuous model and to the response of discrete time systems.

Identify and define complex digital control and instrumentation problems and apply appropriate knowledge and tools to their solution.

Practical & Professional Skills
Operate ethically in situations of varying complexity and predictability requiring the analysis of the digital control and instrumentation system-wide issues.

Key Transferable Skills
Select and apply appropriate numerical methods to Digital control & Instrumentation issues.
Select and apply appropriate software to aid analysis of Digital control systems

The report should adhere to the following guidance:

The report should have a title page, abstract and a contents page, and each page should be numbered. The report should then follow a recognised structure and be a maximum of 20 pages long including equations, figures, illustrations and tables. Hire Tutor Now!
One additional page may be used to list references - which should follow a recognised standard.
Figures and tables should be numbered and should have a caption describing the figure/table. The caption should also indicate the primary feature that should

be observed by viewing the figure/table. Figures should also be neat and of a readable size.
Brevity is commendable. Appendices should be used for additional information such as extracts from data sheets. It is important that the report be readable and understandable without reference to the appendices.
If any parts of the exercise are unclear, please ask the module team for clarification

In most modern engineering systems, it is necessary to control the evolution with time of one or more of the system variables. Controllers are required to ensure satisfactory transient and steady-state behaviour for these engineering systems.

To guarantee satisfactory performance in the presence of disturbances and model uncertainty, most controllers in use today employ some form of negative feedback. A sensor is needed to measure the controlled variable and compare its behaviour to a reference signal. Control action is based on an error signal defined as the difference between the reference and the actual values.

The controller that manipulates the error signal to determine the desired control action has classically been an analog system, which includes electrical, fluid, pneumatic, or mechanical components. These systems all have analog inputs and outputs (i.e., their input and output signals are defined over a continuous time interval and have values that are defined over a continuous range of amplitudes). In the past few decades, analog controllers have often been replaced by digital controllers whose inputs and outputs are defined at discrete time instances. The digital controllers are in the form of digital circuits, digital computers, or microprocessors.

Digital control offers distinct advantages over analog control that explain its popularity. To control a physical system or process using a digital controller, the controller must receive measurements from the system, process them, and then send control signals to the actuator that effects the control action. In almost all applications, both the plant and the actuator are analog systems. This is a situation where the controller and the controlled do not "speak the same language," and some form of translation is required. The translation from controller language (digital) to physical process language (analog) is performed by a digital-to-analog converter, or DAC. The translation from process language to digital controller language is performed by an analog-to-digital converter, or ADC. A sensor is needed to monitor the controlled variable for feedback control.

As Instrumentation and control engineer, you are required to undertake the following activities which aim to explore the control systems where digital implementation is the new norm with data derived from manual calculations and simulation models.

Q1. Figure 1 shows a typical application for a digital controller, having an existing piece of plant which has the transfer function P(s); this operates in the continuous domain. As an engineer, your company wanted to add a controller operating in a microprocessor which will improve the running of the existing plant. The parameters of the system is define as follows

Determine a discrete equivalent of the continuous system P(s).
Determine the Z-transform of the overall feedback system.
Write a program in Matlab which calculates the Z transfer function of the feedback system and determine the response of the system to a unit step input.
Compare the result of (b) to that obtained in Matlab in (c)

Q2. The plant in Fig. 1 is replaced with a continuous system comprising of turbine system and its associated actuator as shown in Figure 2. The transfer function of the sub systems are given below:

Use Matlab to determine the Z transfer function of the control system:
With the aid of Matlab determine the position of the poles and zeros for the transfer function and plot the poles and zeros on the z-plane
Comment on the stability of the system
Construct a Jury Table for the z transfer functions, and test its stability

You are tasked with designing both FIR and IIR filters for measured data using sensors in MATLAB. Your goal is to implement and analyse the performance of each filter using the given specifications.

Part 3a: FIR Filter Design Using the Window Method

Design a low-pass FIR filter using the windowing method. The specifications for the FIR filter are as follows:
Sampling Frequency (Fs): 20 kHz
Cut-off Frequency (Fc): 2 kHz
Filter Order: 60
Window Type: Hamming

Tasks:

Design the FIR filter using the window method with the Hamming window.
Plot the following characteristics of the FIR filter:
Magnitude response and phase response.
Impulse response.
Apply the designed FIR filter to a test signal, which consists of two sinusoids:
A low-frequency component at 1 kHz.
A high-frequency component at 3.5 kHz. The signal should be sampled at the specified sampling rate (20 kHz) for a duration of 1 second.
Plot the following:
The input (noisy) signal.
The output (filtered) signal in both the time domain and frequency domain.

Part 3b: IIR Filter Design Using Bilinear Transformation

Design a high-pass IIR filter using the bilinear transformation method. The specifications for the IIR filter are:

Sampling Frequency (Fs): 20 kHz
Cut-off Frequency (Fc): 1.5 kHz
Filter Order: 4
Prototype Filter: Butterworth

Tasks:

Design the analogue Butterworth filter prototype for the high-pass filter and convert it to a digital filter using the bilinear transformation method in MATLAB.
Plot the following characteristics of the IIR filter:
Magnitude and phase response.
Pole-zero plot.
Test the performance of the designed IIR filter by applying it to the same test signal used in Part 1 (two sinusoids at 1 kHz and 3.5 kHz).
Plot the following:
The input (noisy) signal.
The output (filtered) signal in both the time domain and frequency domain.
Discuss and compare the performance of the FIR and IIR filters in terms of:
Passband and stopband behaviour.
Phase characteristics.
Effectiveness in filtering the test signal.