Signals, Control and Communications Study Notes

Introduction to Signals, Control and Communications

Learning Outcomes

• By the end of this part of the module students should be able to:

  • Model Linear Time Invariant Systems.

  • Realise the difference between transient and steady state responses as well as stable, marginally stable, and unstable responses.

  • Understand the concepts of transfer functions, block diagrams, poles and zeros, simple feedback systems.

  • Understand the impact of noise and disturbance as well as the use of standard inputs to evaluate system response.

  • Derive transfer functions and determine the step response for a system having any order.

  • Derive transfer functions for mechatronic and electromechanical systems.

  • Solve simple problems using MATLAB.

Contents

1.0 Introduction to Control/Systems Engineering
1.1 The Translation of Energy
2.0 System Models using Analogous Components
2.1 Effort Accumulation
2.2 Flow Accumulation
2.3 The Scotch Yoke
2.4 D’Allenbert’s Law
2.5 Properties of Mechanical Components
2.5.1 Springs
2.5.2 Dissipators
2.6 Analogous Components
3.0 Linear Time Invariant Systems
3.1 Circuit models and ordinary differential equations (ODEs)
3.2 First order dynamic systems
3.2.1 Response to initial conditions
3.2.2 Response to an input signal
3.3 Second order dynamic systems
3.3.1 Response to initial conditions
3.3.2 Response to an input signal
3.4 Summary
4.0 The Differential Operator
4.1 First order transfer functions and system response
4.2 Second order transfer functions and system response
4.2.1 Damped second order transfer function and system response
4.3 Transfer function poles and system stability
4.4 Summary
5.0 Determining a transfer function from an electric circuit model
5.1 The relationship between transfer function of a system and its frequency response
5.1.1 Simplifying circuit models prior to mesh analysis in the p domain
5.2 Summary
6.0 Convolution and Block Diagram Notation
6.1 Block Diagram Notation
6.1.1 Cascaded blocks
6.1.2 Summed blocks
6.1.3 Feedback Loops
6.2 Closed loop system response
6.3 Multiple input and multiple output (MIMO) systems
6.3.1 Noise and disturbance
6.4 Summary
7.0 The step response of a LTI system of any order
7.1 Step response of 3rd and higher order LTI systems
7.1.1 An additional rule for partial fraction expansion
7.2 Summary
8.0 LTI System response to initial conditions – the closing switch problem
8.1 Switch closing example 1: Determine the current flowing through L after the switch is closed
8.2 Switch closing example 2: Determine the current flowing through R2 after the switch is closed
8.3 Summary
9.0 Mechatronic Systems
9.1 Rotational mechanical systems
9.1.1 Rotational Torque
9.1.2 Moment of Inertia
9.1.3 Rotational Damping
9.1.4 Rotational Spring
9.1.5 Summary of rotational mechanical properties
9.2 A simple dc motor model
10.0 Full model of a servomotor
10.1 Closed loop speed control
10.2 Transducers and transformers
10.3 Complete model of a dc servo with gearbox
10.4 Summary