Basics of Control Systems – II | Time-Domain Analysis | First & Second Order Systems | Steady-State Error | Lecture 28

Control systems play a crucial role in electric vehicles, enabling accurate speed regulation, fast dynamic response, and reliable tracking of reference commands. In this lecture, we continue our study of Control Systems for Electric Vehicles by introducing time-domain analysis and studying how a control system responds to different inputs. The concepts of natural response, forced response, transient response, and steady-state response are explained using practical electrical-system examples.

This lecture introduces the commonly used standard test signals—unit impulse, unit step, ramp, parabolic, and sinusoidal signals—and explains why these signals are used to analyse control-system performance. The behaviour of first-order systems is then studied through the concept of time constant, followed by an EV-oriented example comparing the speed response of a sports car and a normal car.

The lecture further covers second-order systems, including natural frequency, damping ratio, poles, underdamped, critically damped, overdamped, and undamped responses. The effect of damping ratio on system performance is demonstrated, including the commonly used ζ=0.707 condition for fast settling with limited overshoot in EV motor control.

Important time-domain specifications such as rise time, peak time, settling time, and percentage overshoot are introduced along with their mathematical expressions. A numerical example is also presented to calculate the natural frequency, damping ratio, peak overshoot, settling time, and peak time of a second-order system.

Finally, the lecture introduces steady-state error and explains how it depends on the type of reference input and the number of integrators in the open-loop transfer function. The concepts of system type, position constant Kp, velocity constant Kv, acceleration constant Ka and their effect on steady-state accuracy are discussed, along with an EV cruise-control example.

Topics Covered

Time-Domain Analysis of Control Systems
Natural and Forced Response
Transient and Steady-State Response
Standard Test Signals
Unit Impulse, Step, Ramp and Parabolic Inputs
First-Order Systems
Time Constant and System Response
Second-Order Systems
Natural Frequency and Damping Ratio
Underdamped, Critically Damped and Overdamped Systems
Rise Time, Peak Time and Settling Time
Percentage Overshoot
Time-Domain Performance Specifications
Steady-State Error
System Type
Kp, Kv and Ka Error Constants
EV Cruise Control Example

Who Should Watch?

B.Tech. and M.Tech. students
Power Electronics and Control Systems learners
Electric Vehicle enthusiasts
GATE and ESE aspirants
Researchers working on EV control and electric drives
Engineers designing EV motor control and closed-loop systems

Recommended References

K. Ogata, Modern Control Engineering, 5th Edition, Pearson.

N. S. Nise, Control Systems Engineering, 6th Edition, Wiley.

R. C. Dorf and R. H. Bishop, Modern Control Systems, Pearson.

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