Modelling and control by Anthony Rossiter

# BLOCK DIAGRAMS

This is a section in the chapter on introduction to the importance and impact of feedback. Use the left hand toolbar to access the other chapters and themes. It is implicit in several of these chapters that students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials and Laplace. More information on these can be found in the Mathematics theme on the left hand toobar.

This section contains the following topics. Under each topic there are hardcopy (pdf) notes, a video talk through of key derivations with example problems and also a tutorial sheet for users to test themselves.

## Block diagrams 1 - Transfer functions

Lectures aimed at giving an introduction to the definitions and meanings of simple block diagrams and easy to understand methods for computing relationships between loop inputs and outputs. Lecture 1 focuses on what is a transfer function?

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

A transfer function represents what?
A. The Laplace transform of the output signal of a system,
B. The relationship between a system input and system output.
C. The system input divided by the system output.
D. None of the above.

## Block diagrams 2 – Series systems

Lectures aimed at giving an introduction to the definitions and meanings of simple block diagrams and easy to understand methods for computing relationships between loop inputs and outputs. Lecture 2 focuses on what is a transfer functions in series.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

To determine the transfer function of two systems in series.
A. Multiply the respective transfer functions.
B. Add the respective transfer functions.
C. Divide the respective transfer functions.
D. None of the above.

## Block diagrams 3 – parallel systems

Lectures aimed at giving an introduction to the definitions and meanings of simple block diagrams and easy to understand methods for computing relationships between loop inputs and outputs. Lecture 3 focuses on what is a transfer functions in parallel.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Block diagrams 4 – summing junctions

Lectures aimed at giving an introduction to the definitions and meanings of simple block diagrams and easy to understand methods for computing relationships between loop inputs and outputs. Lecture 4 focuses on the role and interpretation of a summing junction.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Block diagrams 5 – short cuts

Lectures aimed at giving an introduction to the definitions and meanings of simple block diagrams and easy to understand methods for computing relationships between loop inputs and outputs. Lecture 5 focuses on short cut methods for closed-loop transfer functions.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

## Block diagrams 6 – multiple inputs

Lectures aimed at giving an introduction to the definitions and meanings of simple block diagrams and easy to understand methods for computing relationships between loop inputs and outputs. Lecture 6 considers loops which have multiple inputs.

• A summary of key facts and derivations is given in the pdf file.
• A talk through video is on youtube.

#### Quick test question

For systems with multiple inputs, the overall output is determined by:
A. Multiplying the Laplace transforms for each input.
B. Adding the transfer functions for each input..
C. Using superposition.
D. None of the above.

## Block diagrams 7 – nested loops

Lectures aimed at giving an introduction to the definitions and meanings of simple block diagrams and easy to understand methods for computing relationships between loop inputs and outputs. Lecture 7 demonstrates one method for analysing nested loops.

#### Quick test question

Nested loops are:
A. Quite common in practice.
B. Often refered to as cascade loops.
C. Simple to analyse using short-cut methods of video 5.
D. All of the above.

## Block diagrams 8 – video tutorial sheet on closed-loop transfer functions and use of MATLAB

Tutorial sheet on block diagrams and computation of closed-loop transfer functions for determining the different signals in a loop. Also shows how MATLAB could be used to compute and illustrate overall behaviour of signals in the loop.

• A talk through video is on youtube.

## Block diagrams 9 - video tutorial sheet on multi-input loops and use of MATLAB

Tutorial sheet on block diagrams with several inputs such as a target, a disturbance and sensor noise. Also shows how MATLAB could be used to compute and illustrate overall behaviour of signals in the loop.

• A summary of key facts and derivations is given in the pdf file.
• Talk through video 1 is on youtube.

## Block diagrams 10 - video utorial sheet on nested loops and use of MATLAB

Tutorial sheet on block diagrams with nested loops. Also shows how MATLAB could be used to compute and illustrate overall behaviour of signals in the diagram.

• A summary of key facts and derivations is given in the pdf file.
• Talk through video 1 is on youtube.  