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For a feedback control system all the roots of the characteristic equation can be placed at the desired location in the s-plane if and only if the system is 1. Observable 2. Controllable Which of the above statements are correct?

For a feedback control system all the roots of the characteristic equation can be placed at the desired location in the s-plane if and only if the system is 1. Observable 2. Controllable Which of the above statements are correct? Correct Answer Both 1 and 2

Controllability:

A system is said to be controllable if it is possible to transfer the system state from any initial state x(t0) to any desired state x(t) in a specified finite time interval by a control vector u(t)

Kalman’s test for controllability:

ẋ = Ax + Bu

Qc = {B AB A2B … An-1 B]

Qc = controllability matrix

If |Qc| = 0, system is not controllable

If |Qc|≠ 0, system is controllable

Observability:

A system is said to be observable if every state x(t0) can be completely identified by measurement of output y(t) over a finite time interval.

Kalman’s test for observability:

Q0 =

Q0 = observability testing matrix

If |Q0| = 0, system is not observable

If |Q0| ≠ 0, system is observable.

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