Basics of Control Systems – VI | State Space Methods-II | Controllability & Pole Placement | State Feedback Control | Electric Vehicles | Lecture 32

In this lecture, we continue our study of State-Space Methods by introducing the concept of controllability and understanding how control inputs can influence the states of a dynamic system. The concepts are discussed in the context of Electric Vehicles and electric drive systems, including vehicle speed, motor speed, motor current, battery SOC, and DC-link voltage.
The lecture explains the controllability condition, controllability matrix, and the rank test for determining whether a system is completely controllable. Examples of controllable and uncontrollable systems are also discussed.
The lecture then introduces pole-placement control using state feedback, where the feedback gain matrix is designed to achieve desired closed-loop pole locations. A DC motor control example demonstrates controllability analysis and the design of state-feedback gains for desired closed-loop dynamics.

Topics Covered

Control Problems in Electric Vehicles
Controllability of Dynamic Systems
Controllable and Uncontrollable Systems
Controllability Matrix
Rank Condition for Controllability
Pole Locations and System Dynamics
Pole-Zero Cancellation and Uncontrollable Poles
State Feedback Control
Pole Placement Design
Desired Closed-Loop Pole Locations
Calculation of State Feedback Gain Matrix
DC Motor Control Example
Applications in Electric Vehicles and Electric Drives

Who Should Watch?

B.Tech. and M.Tech. students
Control Systems learners
Power Electronics and Electric Drive students
Electric Vehicle enthusiasts
GATE and ESE aspirants
Students learning Modern Control Theory
Researchers and engineers working on EV control and electric drives

Recommended References

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

N. S. Nise, Control Systems Engineering, Wiley.

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

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