# Control Systems Questions and Answers – The Infinite Time Regulator Problem

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This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “The Infinite Time Regulator Problem”.

1. In infinite time regulator for the final time is:
a) t1
b) t0
c) Infinite
d) Zero

Explanation: In infinite time regulator is the extended version of the state regulator and the final time for the infinite time regulator is infinite in this case.

2. When time and the state variables tend to infinity then the system becomes:
a) Unstable
b) Stable
c) Marginally stable
d) Conditionally stable

Explanation: The terminal penalty term has no significance and it does not appear in the performance index and terminal time if tends to infinity then the system becomes stable.

3. In finite time regulator:
a) There is no restriction on the controllability of the plant
b) Performance index is infinite
c) Instability imposes problem in finite-interval control
d) No restriction on controllability and performance index

Explanation: In finite time regulator there is no restriction on the controllability of the plant. This is because is always finite and instability does not impose any problems in finite-time control.

4. Performance index can become infinite if:
a) One or more state are uncontrollable
b) The uncontrollable states are uncontrollable
c) The unstable states are reflected in system performance index
d) All of the mentioned

Explanation: Performance index can become infinite if one or more states are uncontrollable and unstable states are reflected in system performance index.

5. In Infinite regulator the optimal control cannot be differentiated from other controls.
a) True
b) False

Explanation: In infinite regulator the optimal control may have same output for all the controls as the same solution for the infinite regulators will exist.

6. The differential term in the riccati equation in infinite regulator is:
a) Finite
b) Positive
c) Infinite
d) Zero

Explanation: As the final time is not defined hence the differential term of the riccati equation becomes zero and the equation we get is the modified riccati equation.

7. The solution of the modified riccati equation may be:
a) Independent
b) Dependent
c) Unique
d) Non-unique

Explanation: The solution of the modified Riccati equation may not be unique as the solution depends upon the requirement that P must be positive and definite.

8. If Q is positive semi- definite:
a) The optimal closed loop system is asymptotically stable
b) The asymptotic stability is not guaranteed
c) The system is stable
d) The system is unstable

Explanation: If the plant is controllable and bounded and in infinite state regulators the asymptotic stability is not guaranteed even if the Q is positive and semi-definite.

9. Tracking problem can be in:
a) Infinite state regulators
b) Finite state regulator
c) Sub-optimal state regulators
d) Non-linear regulators

Explanation: The application of the optimal regulators is that the minimum time, energy, fuel and tracking problems are designed.

10. The regulators that convert the non-linear stability into linear stability:
a) Linear
b) Sub-optimal
c) Finite
d) Infinite 