1. The main objective of an optimal control system is to:
(A) Maximize the output
(B) Minimize a performance index
(C) Increase system order
(D) Eliminate transient response
2. The performance index in optimal control is generally expressed as:
(A) Integral of error
(B) Integral of cost function
(C) Laplace transform of output
(D) Root mean square value
3. The most commonly used performance index in optimal control is:
(A) Quadratic performance index
(B) Exponential performance index
(C) Linear performance index
(D) Logarithmic performance index
4. The Linear Quadratic Regulator (LQR) is used to:
(A) Minimize quadratic cost function
(B) Maximize state variable
(C) Increase damping ratio
(D) Improve frequency response
5. The LQR problem results in a control law of the form:
(A) u = Kx
(B) u = −Kx
(C) u = Kx + r
(D) u = r − Kx
6. The optimal feedback gain matrix (K) in LQR is obtained using:
(A) Riccati equation
(B) Ackermann’s formula
(C) Routh-Hurwitz criterion
(D) Nyquist criterion
7. The Riccati equation is a:
(A) Linear matrix equation
(B) Nonlinear matrix equation
(C) Quadratic scalar equation
(D) Frequency-domain equation
8. In LQR design, the weighting matrices are:
(A) Q and R
(B) A and B
(C) B and C
(D) P and Q
9. The matrix Q in the cost function represents:
(A) Weight on control effort
(B) Weight on state variables
(C) Weight on error
(D) Weight on output
10. The matrix R in the cost function represents:
(A) Weight on state variables
(B) Weight on control effort
(C) Weight on error
(D) Weight on system input
11. The solution to the Riccati equation gives:
(A) Optimal feedback gain K
(B) System poles
(C) Transfer function
(D) Controllability matrix
12. An optimal control system provides:
(A) Fastest response only
(B) Least energy consumption
(C) Best compromise between performance and effort
(D) Maximum overshoot
13. The Hamiltonian function in optimal control combines:
(A) State and control variables
(B) Error and gain
(C) Time and frequency
(D) Poles and zeros
14. The Pontryagin’s Minimum Principle is used to:
(A) Find optimal control law
(B) Find poles
(C) Test controllability
(D) Design filters
15. In optimal control, the control effort should be:
(A) As high as possible
(B) As low as possible for given performance
(C) Independent of states
(D) Zero at all times
16. The LQR controller is applicable to:
(A) Linear time-invariant systems
(B) Nonlinear time-varying systems
(C) Frequency-domain systems
(D) Unstable open-loop systems only
17. The solution to the Algebraic Riccati Equation (ARE) must be:
(A) Positive semi-definite
(B) Negative definite
(C) Complex
(D) Arbitrary
18. In optimal control, Q matrix should be:
(A) Positive semi-definite
(B) Negative definite
(C) Zero
(D) Singular
19. In optimal control, R matrix should be:
(A) Positive definite
(B) Negative semi-definite
(C) Zero
(D) Complex
20. The state feedback gain (K) in LQR depends on:
(A) A, B, Q, and R matrices
(B) B, C, and D matrices
(C) Only A and B
(D) Q and R only
21. The optimal control law minimizes:
(A) Integral of quadratic performance index
(B) Integral of steady-state error
(C) Transient response
(D) Phase margin
22. The advantage of LQR over classical control methods is:
(A) It is easier to design
(B) It provides systematic trade-off between performance and control effort
(C) It eliminates need for feedback
(D) It uses frequency domain analysis
23. The LQG controller combines:
(A) LQR and Kalman filter
(B) PID and observer
(C) Nyquist and Bode methods
(D) Root locus and Routh criterion
24. The Kalman filter is used for:
(A) State estimation
(B) Noise generation
(C) Gain computation
(D) Transfer function simplification
25. The optimal estimator minimizes:
(A) Estimation error covariance
(B) State error
(C) Phase lag
(D) Gain margin
26. The LQG control strategy is optimal for:
(A) Linear systems with Gaussian noise
(B) Nonlinear systems
(C) Time-varying systems
(D) Systems without noise
27. In optimal control, the trade-off is between:
(A) Speed and control effort
(B) Damping and overshoot
(C) Gain and phase
(D) Stability and accuracy
28. The optimal control system ensures:
(A) Stability and minimum energy usage
(B) Maximum overshoot
(C) Unbounded output
(D) Delay-free response
29. The optimal control theory is based on:
(A) Calculus of variations
(B) Frequency domain techniques
(C) Laplace transforms
(D) Classical stability analysis
30. The dynamic programming approach to optimal control was introduced by:
(A) Pontryagin
(B) Kalman
(C) Bellman
(D) Bode
31. The Hamilton-Jacobi-Bellman (HJB) equation is used in:
(A) Dynamic programming
(B) Frequency response
(C) Root locus
(D) Classical control
32. The HJB equation provides:
(A) Necessary and sufficient conditions for optimality
(B) Only necessary conditions
(C) Only sufficient conditions
(D) Approximate solution
33. The Kalman filter provides:
(A) Optimal estimate of system states
(B) Exact measurement
(C) Noise amplification
(D) Frequency response
34. The optimal control law in the presence of process and measurement noise is implemented using:
(A) LQG controller
(B) PID controller
(C) Root locus
(D) Nyquist method
35. In LQR, increasing the value of Q results in:
(A) Faster response, more control effort
(B) Slower response, less control effort
(C) No change
(D) Instability
36. In LQR, increasing the value of R results in:
(A) Slower response, less control effort
(B) Faster response, more control effort
(C) Unstable system
(D) Reduced damping
37. The control energy in optimal control is minimized by:
(A) Proper choice of R matrix
(B) Increasing Q matrix
(C) Using derivative control
(D) Reducing observer poles
38. The state feedback in optimal control:
(A) Uses full state vector
(B) Uses output only
(C) Ignores system states
(D) Uses random feedback
39. The Kalman filter is the dual of:
(A) LQR
(B) PID
(C) Root locus
(D) Nyquist plot
40. The optimal control design ensures:
(A) Stability and minimum cost
(B) Instability
(C) Zero steady-state error only
(D) Maximum control energy