Download PTU M.Tech. EE 2nd Semester 76107 ROBUST CONTROL Question Paper

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M.Tech. (EE) (2018 Batch) (Sem.-2)

ROBUST CONTROL

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Subject Code : MTEE-204B-18

M.Code: 76107

Time: 3 Hrs.

Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

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1. Attempt any FIVE questions out of EIGHT questions.
2. Each question carries TWELVE marks.

1. Check definiteness of the scalar function applying Sylvester's criterion- V(x)=4x1² +5x2² + x3²-8x1x2+4x1x3-4x2x3.
2. Apply the vectorization method to solve the Lyapunov equation. AP + PA = With
   A = 1 -1 2
   

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   -5 -1 3
   1 -2 1
3. Determine the optimum input using Riccati equation when the performance index is :
   X^T 1 0
   0 1 X+M^T 1 0
   

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   0 1 Mdt
   X = 0 1
   0 0 X+M
4. Given the system with state-space matrices :
   A= 0 1
   

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   3 2 ;B= 0
   1 ;C=[-1 1]
   Design the linear quadratic regulator with Q = CC^T and r = 5.
5. Distinguish between H₂ and H₈ control.
6. Given the system
   

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   x?1=x1+u+2w
   y=x1+w
   z=2x1+2u
   Calculate analytically the compensator C(s) with the H₈ control technique.
7. Using the LMI approach, find the control law that stabilizes simultaneously the two systems:
   

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   A1= -2 0 0
   0 1 0
   0 0 5 ; B1 = 0
   1
   1 A2 = 0 -5 0
   

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   0 -6 0
   0 0 3 ;B2 = 0
   1
   3
8. Give the system with transfer function G(s) = s-3. determine the coprime factorization.
   

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   Then determine the class of stabilizing compensators
   Finally, calculate the energy associated to the impulse response for the closed-loop system.
9. Given the continuous-time system with transfer function G(s) = a / (s³+s²+4s+4) calculate
   for which values of a is the system bounded real.

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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