Roll No.
Total No. of Questions : 08
Total No. of Pages : 02
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M.Tech (EE) EI-II (2018 Batch) (Sem.-1)
OPTIMAL AND ADAPTIVE CONTROL
Subject Code : MTEE-104D-18
M.Code: 75224
Time: 3 Hrs.
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Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
- Attempt any FIVE questions out of EIGHT questions.
- Each question carries TWELVE marks.
Q1. (a) Define optimal control problem.
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(b) Find the curve with the minimum arc length joining the point (0, 0) and line 0 (t) = 2 - t.
Q2. (a) Discuss the steps in solving optimal control problem using Hamilton-Jacobi method.
(b) Consider the system
? = u
Is to be controlled to minimize the performance index
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J= ? u²dt
Find a set of necessary conditions for optimal control problem.
Q3. (a) Discuss various performance indices used in optimal control.
(b) Find the trajectory in the (t, x) plane that will extremize
J = ? (tx+x²) dt ; x (0) = 1, x (1) = 5
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Q4. What is Hamiltonian? What is the use of Hamiltonian in solving optimal control problem?
Q5. For given plant equation x=-x+u with boundary conditions x (0) = 0, x (1) = 1 and performance index J= ? (3x²+u²)dt find the optimal control using Hamiltonian method.
Q.6. (a) Discuss Dynamic programming and its use in control.
(b) Discuss the model reference adaptive control and draw one scheme.
Q7. (a) Discuss MRAC using Lyapunov method.
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(b) For the process and reference models respectively described by_x=Ax+Bu, Xm = AmXm+Bmr, obtain MRAC with state feedback using Liapunov method.
Q8. (a) The transfer function of a second order plant is
(s+b) / (s²+a1s+ao)
With normal values a1 = 3, ao = 10 and b = 2. Use a suitable control law and determine the response of the MRAC scheme with unit step input r(t) = u (t), if the response is specified by the reference models Gm(s)= 1/(s+1)
(b) Discuss design of variable structure and adaptive model following control.
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NOTE : Disclosure of Identity by writing Mobile No. or making of passing request on any page of Answer sheet will lead to UMC against the Student.
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