##### Control Systems - I

- Introduction to control system
- Examples of control systems
- Engineering design
- Control system design
- Mechatronic systems
- Open loop systems
- Closed loop systems
- Closed-loop control versus open-loop control
- Complex variable & Complex function
- Differential equations of physical systems
- Mathematical Modeling of Dynamic Systems
- Nonlinear systems
- The transfer function of linear systems
- Concept of Transfer function
- Impulse response function
- Transfer function of a field controlled DC motor
- Transfer function of an armature controlled DC motor
- Transfer function of a hydraulic actuator
- Transfer Functions of Dynamic Elements and Networks
- Block diagrams
- Block diagram of a closed-loop system
- Open-loop feedforward and closed loop transfer function
- Closed-loop system subjected to a disturbance
- Procedures for drawing a block diagram
- Block Diagram Transformations
- Block diagram reduction
- Modeling in state space
- State-space equations
- Correlation between transfer functions and state-space equations
- State-space representation of dynamic systems ( forcing function does not involve derivative terms)
- State-space representation of dynamic systems ( forcing function does involving derivative terms)
- Signal-flow graph models
- Transfer function of an interacting system
- Transfer function of a multiple-loop system
- Transfer function of an armature-controlled motor
- Transfer function of a complex system
- State-space model of mechanical systems
- State-space model of Electrical systems
- Transfer functions of cascaded elements
- Transfer functions of nonloading cascaded elements
- Mason's gain formula

- Introduction to Time domain analysis
- Unit-step response of first-order systems
- Unit-ramp response of first-order systems
- Unit-impulse response of first-order systems
- DC servomotors
- A servo system
- Effect of load on servomotor dynamics
- Step response of second-order systems
- Underdamped systems
- Critically damped system
- Overdamped system
- Definitions of transient-response specifications
- Second-order systems Rise Time
- Second-order systems Peak Time
- Second-order systems Maximum overshoot
- Second-order systems settling Time
- Servo system with velocity feedback.
- Impulse response of second-order systems
- Steady-state errors
- Static position error constant
- Static acceleration error constant
- Comparison of steady-state errors in open-loop control system and closed loop control system

- Concept of stability
- Transient response of higher-order systems
- Stability analysis in the complex plane
- Dominant closed-loop poles
- Rouths stability criterion
- The relative stability of feedback control systems
- Axis shift
- The stability of state variable systems
- Stability of a second-order system
- Application of Rouths stability criterion to control system analysis
- Comparison between pneumatic systems and hydraulic systems
- Introduction to Root-locus method
- Root-locus plots
- General rules for constructing roots loci
- Comments on the root-locus plots
- Cancellation of poles G(s) with zeros of H(s)
- Typical pole-zero configurations and corresponding root loci
- Root loci for positive-feedback systems
- Root-Locus Plots of Negative-Feedback and Positive Feedback Systems
- Parameter design by the root locus method
- Sensitivity and the root locus
- Root sensitivity of a control system
- Orthogonality of root loci and constant-gain loci
- Conditionally stable systems
- Nonminimum-phase systems
- Root loci for systems with transport lag
- Approximation of transport lag or dead time
- Root-contour plots - Effects of parameter variations on closed-loop poles

- Introduction to Frequency-Response Analysis
- Bode diagrams or logarithmic plots
- The Gain in Bode diagrams
- Integral and derivative factors in Bode diagrams
- First-order factors in Bode diagrams
- Error in the First-order factors in Bode diagrams
- Transfer function of a first order factor in Bode diagram
- Quadratic factors in Bode diagram
- Phase angle of quadratic factor
- The resonant frequency & the resonant peak value
- General procedure for plotting Bode diagrams
- Minimum-phase systems and nonminimum-phase systems
- Transport lag in Bode Diagrams
- Determination of static position error constants
- Determination of static velocity error constants
- Determination of static acceleration error constants
- Polar Plot
- First-order factors of polar plots
- Quadratic factors of polar plots
- Transport lag of polar plot
- General shapes of polar plots
- Polar Plots of Simple Transfer Functions
- Log-magnitude versus phase plots
- Nyquist stability criterion
- Mapping theorem and application
- Remarks on the Nyquist stability criterion
- Special case when G(s)H(s) involves poles and/or zeros on the jw axis
- stability analysis using Nyquist stability criterion
- Conditionally stable systems of a polar plot
- Multiple-loop system of a polar plot
- Nyquist stability criterion applied to inverse polar plots
- Relative stability analysis through modified Nyquist plots
- Relative stability analysis by conformal mapping
- Phase and gain margins
- Comments on phase and gain margins
- Resonant peak magnitude and resonant peak frequency
- Cut off frequency and bandwidth
- Closed-loop frequency response of unity-feedback systems
- M circles
- N circles
- Nichols chart
- Closed-loop frequency response for nonunity-feedback systems
- Gain adjustments
- Jury's stability test

- System compensation and Cascade compensation
- Compensators and Design Procedures
- Root-locus approach to control system design
- PI controllers
- PD controllers
- Proportional-plus-derivative control of second-order systems
- PID controllers
- Tuning of PID controllers
- Ziegler-Nichols first method for tuning PID controllers
- Ziegler-Nichols second method for tuning PID controllers
- Lead compensators
- Lead compensation techniques based on the root-locus approach and design
- Lag compensator using operational amplifiers
- Lag compensation techniques based on the root-locus approach
- Design procedures for lag compensation by the root-locus method
- Lag-lead compensator using operational amplifiers
- Lag-lead compensation techniques based on the root-locus approach and design