Test: The Infinite Time Regulator Problem - Electrical Engineering (EE) MCQ

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.

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.

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.

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

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.

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.

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.

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.

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

Explanation: In infinite state regulators stability is not guaranteed and hence the nonlinear stability is converted into to the linear stability.