Control Systems

Course Objectives
To provide information on feedback control Principles and to apply these concepts to typical physical processes. To introduce solution of typical problems.

1.0 Component Modeling, Linearization: (7 hours)
1.1 Differential equation and transfer function notations
1.2 State-space formulation of differential equations, matrix notation
1.3 Mechanical components: mass, spring, damper
1.4 Electrical components: inductance, capacitance, resistance, sources, motors, tachometers, transducers, operational amplifier circuits
1.5 Fluid and fluidic components
1.6 Thermal system components
1.7 Mixed systems
1.8 Linearized approximations of non-linear characteristics

2.0 System Transfer Functions and Responses: (10 hours)
2.1 Combinations of components to physical systems
2.2 Block diagram algebra and system reduction
2.3 Mason’s loop rules
2.4 Laplace transform analysis of systems with standard input functions - steps, ramps, impulses, sinusoids
2.5 Initial and final steady-state equilibria of systems
2.6 Principles and effects of feedback on steady-state gain, bandwidth, error magnitude, dynamic responses

3.0 Stability: (4 hours)
3.1 Heuristic interpretation of the conditions for stability of a feedback system
3.2 Characteristic equation, complex plane interpretation of stability, root locations and stability
3.3 Routh-Hurwitz criterion, eigenvalue criterion
3.4 Setting loop gain using the R-H criterion
3.5 Relative stability from complex plane axis shifting

4.0 Root Locus Method: (6 hours)
4.1 Relationship between root loci and time responses of systems
4.2 Rules for manual calculation and construction of root loci diagrams
4.3 Computer programs for root loci plotting, polynomial root finding and repeated eigenvalue methods
4.5 Derivative feedback compensation design with root locus
4.6 Setting controller parameters using root locus
4.7 Parameter change sensitivity analysis by root locus

5.0 Frequency Response Methods: (4 hours)
5.1 Frequency domain characterization of systems
5.2 Relationship between real and complex frequency response
5.3 Bode amplitude and phase plots
5.4 Effects of gain time constants on Bode diagrams
5.5 Stability from the Bode diagram
5.6 Correlation between Bode diagram plots and real time response: gain and
phase margins, damping ratio
5.7 Polar diagram representation, Nyquist plots
5.8 Correlation between Nyquist diagrams and real time response of systems: stability, relative stability, gain and phase margin, damping ratio

6.0 Simulation Using Microcomputer and Appropriate Software: (4 hours)
6.1 Role of simulation studies
6.2 Linear and non-linear simulations
6.3 TUTSIM as a simulation tool

7.0 Performance Specifications for Control Systems: (2 hours)
7.1 Time domain specifications: steady-state errors, response rates, error criteria,
hard and soft limits on responses, damping ratio, log decrement
7.2 Frequency domain specifications: band width, response amplitude ratio

8.0 Compensation and Design: (8 hours)
8.1 Application of root locus, frequency response and simulation in design
8.2 Meeting steady-state error criteria
8.3 Feedback compensation
8.4 Lead, lag, and lead-lag compensation
8.5 PID controllers

Laboratory:
1.0 Identification of Control System Components
- establish transfer functions and block diagram of electromechanical servo
system for position and velocity control
2.0 Open and Closed Loop Performance of Servo Position Control System
- note effects of loop gain on response
- record step responses and compare with those predicated by theory
3.0 Open and Closed Loop Performance of Servo Velocity Control System
- note effects of loop gain on response
- record step responses and compare with those predicated by theory
4.0 Simulation Study of Feedback System Using TUTSIM
- set up simulation model of servo system using TUTSIM on a microcomputer
and repeat response tests
5.0 Design of a PID Controller
- design of a PID controller for position servo
- check design with TUTSIM
- check design on operating system
6.0 Non-Electrical Control System
- study of a hydraulic or pneumatic servo system

Textbook:
1.0 K. Ogata, “Modern Control Engineering”, 2nd Edition, Prentice Hall, Englewood Cliffs, New Jersey, 1990.