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Course overview
This course takes students through control systems analysis from mathematical modeling of physical systems to practical controller design. The progression moves from transfer functions and block diagram algebra, through time-domain response analysis, into frequency-domain techniques, and finally to stability criteria and compensator design. Students who finish the course can derive transfer functions for electrical and mechanical systems, determine stability using Routh-Hurwitz and Nyquist criteria, read Bode plots, and design lag-lead compensators to meet given specifications.
Details
Target audience: Third-year B.Tech ECE students taking Control Systems as a core subject, and GATE aspirants targeting the control systems section.
Duration: 12 to 15 hours across 5 modules
Prerequisites
- Laplace transforms and partial fractions
- Basic electrical circuit analysis
- Differential equations for first and second-order systems
Learning outcomes
- Derive the transfer function of electrical and mechanical systems from their governing equations
- Reduce block diagrams and signal flow graphs to a single transfer function
- Calculate transient response specifications for second-order systems given damping ratio and natural frequency
- Construct root locus plots and determine the value of K for a specified damping ratio
- Draw Bode magnitude and phase plots for first and second-order systems and read gain and phase margins
- Apply the Routh-Hurwitz criterion to determine stability and find the range of K for a stable system
- Design lag or lead compensators to meet given gain margin, phase margin, or steady-state error specifications
Modules
- Laplace transform review and inverse transforms
- Transfer function derivation for electrical networks
- Mechanical translational and rotational systems
- Block diagram reduction rules
- Signal flow graphs and Mason's gain formula
- First-order and second-order system response
- Damping ratio, natural frequency, and time constant
- Transient response specifications: rise time, settling time, overshoot
- Steady-state error and error constants
- Effect of adding poles and zeros
- Root locus construction rules
- Angle and magnitude conditions
- Breakaway and break-in points
- Effect of gain K on closed-loop poles
- Root locus for systems with complex poles
- Bode magnitude and phase plots
- Gain margin and phase margin from Bode plots
- Polar plot and Nyquist stability criterion
- Closed-loop frequency response and M-N circles
- Gain crossover and phase crossover frequencies
- Routh-Hurwitz stability criterion and special cases
- Absolute and relative stability concepts
- Lag compensator design for steady-state improvement
- Lead compensator design for transient improvement
- PID controller tuning using Ziegler-Nichols method