Module I: Introduction to Control Systems
Class PPT Introduction to Linear Control Systems
Introduction
Classification of control systems
Feed-Back Characteristics, Effects of feedback
Feed-Back Characteristics, Effects of feedback (copy)
Mathematical modeling of Electrical systems
Mathematical modeling of Mechanical systems
Transfer function
Transfer function of Potentiometer
Transfer function of Synchro
Transfer function of AC servo motor
Transfer function of DC servo motor
Block diagram reduction technique
Mason’s gain formula
Module 2: Time Domain Analysis
Standard test signals
Time response of first order systems
Transient response of second order system for unit step input
Time domain specifications
Steady state response
Steady state errors and error constants
Effects of P, PD, Pl and PID controllers
Module 3: Stability Analysis in S-Domain
The concept of stability
Routh’s stability Criterion
Absolute stability and relative stability
Limitations of Routh’s stability
Root Locus Technique
The root locus concept – construction of root loci
Effects of adding poles and zeros on the root loci
Module 4: Frequency Response Analysis
Introduction to frequency response
Frequency domain specifications
Bode plot
Stability analysis from Bode plots
Determination of transfer function from the Bode Diagram
Polar Plots
Nyquist Plots
Stability Analysis
Gain margin and phase margin
Control System Design: Introduction
Lag Compensator design in frequency Domain
Lead Compensator design in frequency Domain
Lag-Lead Compensator design in frequency Domain
Module 5: State Space Analysis
Derivation of state models of linear time invariant systems
Controllable state models
Observable state models
Diagonal state models
State transition matrix
Solution of state equation
Concepts of Controllability
Concepts of Observability
Signal flow graph (SGF)
Signal Flow Graph (SFG)
A Signal Flow Graph (SFG) is a graphical representation of a set of linear equations or a linear dynamic system. It shows how signals (variables) interact with each other through gains and dependencies.
Components of SFG
- Nodes: Represent system variables (inputs, outputs, states)
- Branches: Directed edges with gains that show how one variable affects another
- Input Node: Only outgoing branches
- Output Node: Only incoming branches
Mason’s Gain Formula
This formula helps compute the overall transfer function from input to output:
T = Y(s)/R(s) = [∑ Pₖ Δₖ] / Δ
- Pâ‚–: Gain of the k-th forward path
- Δ: 1 – (sum of loop gains) + (sum of products of non-touching loops) – …
- Δₖ: Determinant of the graph excluding loops touching path Pₖ
Advantages of Using SFG
- Simplifies analysis of complex systems
- More structured than block diagrams for linear systems
- Efficient in solving large systems using algorithms
Example Use Case
Consider a system with two loops and one forward path. Using Mason’s Gain Formula, we can easily compute its transfer function without converting everything into equations.
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