Lectures of Linear Control Systems (Spring 2011)

Lecture 1    [pdf]    [ppt]
  1. A brief history of control..
  2. Introducing of some advanced control system.
  3. Important parts of a control system.
    • Inputs and outputs.
    • Measurements and actuators.
    • Disturbances and noises.

Lecture 2    [pdf]    [ppt]

1.        Modeling of systems.

2.        Systems with time delay.

Lecture 3    [pdf]    [ppt]
  1. Different representation of control systems (modeling).
    • High order differential equation.
    • State space model.
    • Transfer function.
    • State diagram.

Lecture 4    [pdf]    [ppt]
  1. General gain formula for state diagram.
  2. Realization.
  3. Relation between different representations. 

Lecture 5    [pdf]    [ppt]
  1. Nonlinear systems.
  2. Linearization of nonlinear system.
  3. Transfer function representation.
    •  Property.
    • Poles and zeros and their physical meaning.
    • SISO and MIMO.
    • Open loop and closed loop system.
    • Effect of feedback

Lecture 6    [pdf]    [ppt]           Quiz#1 and assignment#1
  1.  State space representation. 
    • State transition matrix.
    • Significance of state transition matrix and its property.
    • Calculation of state transition matrix for time varying system.
  2. State transition equation.
  3. State transition equation determined by state diagram.

4.        Eigenvalues of A matrix in state space form and poles of transfer function

  1. Similarity transformation.

Lecture 7    [pdf]    [ppt]
  1. Controllability and Observability
    • Definition of controllability and observability.

·         Controllability and observability of different modes. 

  1. Canonical forms.
    • Controllable and observable canonical forms. 
    • Controllability and observability in Jordan forms.
  1. Transfer function of controllable and observable systems.
  2. Controllability and observability from block diagram.

Lecture 8    [pdf]    [ppt]
  1. Pole placement with state feedback.
  2. State estimation. 

Lecture 9    [pdf]    [ppt]
  1. Stability of linear control systems.
    • Bounded input bounded output stability (BIBO).
    • Zero input stability.
  2. Stability of linear control systems through Routh Hurwitz criterion.

Lecture 10    [pdf]    [ppt]     Quiz#2 and assignment#2
  1. Time domain analysis.

·           Test signals.

·           Steady state error and error coefficient.

·           Error series.

·           Introducing some performance criteria's (ISE, ITSE, IAE and ITAE).

Lecture 11    [pdf]    [ppt]
  1. Time domain analysis (Continue).
    • Introducing a prototype second order system.

2.        Transient response of a prototype second order system

    • Damping ratio and damping factor.
    • Natural undamped frequency and damped frequency.
    • Percent overshoot.
    • Delay time, rise time and settling time.

Lecture 12    [pdf]    [ppt]
  1. Different regions  of  S plane.
    • Constant natural frequency loci.
    • Constant natural damped frequency loci.
    • Constant damping factor loci.

·         Constant damping ratio loci.

  1. Transient response of a position control system.

Lecture 13    [pdf]    [ppt]
  1. Effect of adding poles and zeros to:
    • Open-loop transfer function.
    • Closed-loop transfer function.
  2. Importance of zeros in transfer functions.
  3. Dominant poles of transfer function.
  4. Approximation of high-order systems by low-order systems.

Lecture 14    [pdf]    [ppt]
  1. Root locus criteria.
    • Root loci (RL).
    • Complement root loci (CRL).
    • Complete root loci.

Lecture 15    [pdf]    [ppt]         Quiz#3 and assignment#3
  1. Property and construction of complete root loci.
  2. Effect of adding poles and zeros on root locus.
  3. Effect of movement of poles and zeros.
  4. Root contour.

Lecture 16    [pdf]    [ppt]
  1. Design of controller in time domain.
    • Various controller configurations.
    • Different kind of controllers.
    • Controller realization.

2.        Time domain design of the PID controllers. 

·         Design of PID controllers.

·         Design of PD controllers.

·         Design of PI controllers.

Lecture 17    [pdf]    [ppt]
  1. Time domain design of the lead and lag controllers. 

·          Design of lag controllers.

·          Design of lead controllers.

Midterm . ( All lectures till here.)

Lecture 18    [pdf]    [ppt]
  1. Frequency domain analysis of control systems.
  2. Frequency domain specification.
    • Peak of resonance and resonance frequency.
    • Bandwidth.

3.        Nyquist stability criterion.

Lecture 19    [pdf]    [ppt]
  1. Nyquist stability criterion.(Continue)
  2. Minimum phase systems.
  3. Simplified Nyquist stability criterion.

Lecture 20    [pdf]    [ppt]

1.        Relative stability measures for minimum phase systems.

    • Gain margin.
    • Phase margin.

2.        Nichols chart or gain-phase plot.

    • Stability analysis with gain phase plot.
  1. Bode plot.
    • Stability analysis with gain phase plot.
  1. Step by step Bode plot construction.

Lecture 21    [pdf]    [ppt]
  1. Nyquist chart.

·          Constant M loci.

·          Constant N loci.

  1. Nichols chart.

·          Constant gain loci.

·          Constant phase loci.

·          Frequency domain specification from Nichols chart.

  1. Effect of adding poles and zeros on loop transfer function.

Lecture 22    [pdf]    [ppt]      Quiz#4 and assignment#4
  1. Controller design in frequency domain.
    • Design of lag controllers.

Lecture 23    [pdf]    [ppt]
  1. Controller design in frequency domain (Continue).
    • Design of lead controllers.

Lecture 24    [pdf]    [ppt]

1.        Relation between phase margin and the damping ratio.

2.                                Frequency domain design of control system.

·          Design of PD controllers.

·          Design of PI controllers.

Final Exam All  Lectures. ( 50 points)