## ADVANCED CONTROL SYSTEMS JNTU previous years question papers

2011

ADVANCED CONTROL SYSTEMS

(Electrical & Electronic Engineering)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

1. Suppose if the system equations are known in Jordan form. How do you test the properties of controllability? Explain using a state model. [16]

2. State, prove and explain Lyapunovs stability theorm. Also explain what are the suficient conditions of stability. [16]

3. (a) Explain the dierent methods used to find the state feedback gain matrix and compare them?

(b) Consider a linear system described by the transfer function Y (s)

u(s) = 10s(s+2)(s+1)

Design a feed back controller with a state feedback so that the eigen values of the closed loop system are at -2,-1 ± j1. [6+10]

4. (a) Explain Minimum - Time problem?

(b) Explain State Regulator problem in brief? [8+8]

5. Illustrate with an example the problem with terminal time t1 fixed and x (t1) free.

[16]

6. (a) State and prove optimal control problem based on dynamic programming in discrete time system

(b) Explain the principles of causality and invariant imbedding. [16]

7. (a) Explain the popular inherent nonlinear elements and their functionalities.

(b) Derive the Describe function for an on-o nonlinearity. [6+10]

8. Draw a phase-plane portrait of the system defined by [16]

? x1 = x1 + x2

? x2 = 2x1 + x2