Closed-loop

Control design under what conditions can closed-loop poles be placed arbitrarily?

Control design under what conditions can closed-loop poles be placed arbitrarily?
  1. What is the necessary condition for closed loop control?
  2. Can closed-loop poles be placed anywhere in the complex plane?
  3. What is necessary and sufficient condition for arbitrary pole placement?
  4. Can you place the closed-loop poles of the system at arbitrary locations using full state feedback why?

What is the necessary condition for closed loop control?

For a closed-loop feedback system to regulate any control signal, it must first determine the error between the actual output and the desired output. This is achieved using a summing point, also referred to as a comparison element, between the feedback loop and the systems input.

Can closed-loop poles be placed anywhere in the complex plane?

All the closed loop poles of a controllable single input linear time invariant (LTI) system can be assigned arbitrary locations in the complex plane using full state feedback.

What is necessary and sufficient condition for arbitrary pole placement?

Pole Placement Design

A necessary condition for pole placement using state feedback is that pair (A,b) is controllable, i.e., its controllability matrix, MC, is of full rank, where MC=[b,Ab,…,An−1b] . By including control law in the state equations, the closed-loop system is given as: ˙x(t)=(A−bkT)x(t)+br(t)

Can you place the closed-loop poles of the system at arbitrary locations using full state feedback why?

As long as the system is controllable, the plant dynamics don't matter -- with full state feedback, we can always cancel them and place the closed-loop poles arbitrarily.

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