9a13601 advanced control systems

7/28/2019 9A13601 Advanced Control Systems

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Code: 9A13601

B.Tech III Year II Semester (R09) Regular & Supplementary Examinations, April/May 2013

ADVANCED CONTROL SYSTEMS

(Electronics & Control Engineering)

Time: 3 hours Max. Marks: 70

Answer any FIVE questions

All questions carry equal marks

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1 Obtain the state space representation of the system shown in figure 1 in which x1, x2, x3constitute the state vector. Also find transfer function matrix.

Figure 1

2 Discuss the state controllability and observability of the given system:

3 What are the different types of non-linearities? Explain each of them briefly.

4 Draw the phase trajectory of the system described by the equation . Checkthe stability of the system and write a comment on it.

5 For the system ; find the suitable Lyapunov function V(x) obtain an upper

bound on the response time such that it takes the system to go from a point on theboundary of the closed curve = 100 to a point within the closed curve =0.05.

6 (a) Enumerate the design steps for pole placement.(b) Prove Ackermanns formula for the determination of the state feedback gain matrix K.

7 (a) Discuss the application of Euler-Lagrange equation and derive the equation.(b) The functional given by

is free. Find the extremals.

8 Write short notes on the following for optimal control system design:(a) Minimum fuel problem.(b) Output regulator problem.(c) Tracking problem.

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+- -+

S

S2

U(s) X1(s)X2(s)

X3(s)


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Code: 9A13601







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1 Consider the system

and output . Transform the system into

(a) controllable canonical form and

(b) observable canonical form.

2 A linear time invariant system is described by the following state model. Obtain the canonical

form of the state model:

and .

3 Derive the expression of describing function for dead zone non-linearity.

4 Construct phase trajectory for the system described by the equation, . Comment

on the stability of the system.

5 Determine the stability of the following system using Lyapunov method.

6 (a) Show that the zeros of a scalar system are invariant under state feedback to the input.

(b) For a single input system explain pole placement by state feedback.

7 (a) Find the curve with minimum arc length between the point and the curve

.

(b) Discuss control and state variable inequality constraints.

8 Describe the minimization of functions in the optimal control system design.

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1 Consider the system defined by ;

where

Transform the system equations into the controllable canonical form.

2 Discuss the state controllability and observability of the following system:

3 A system has a nonlinear element, with describing function, in cascade

with, . Determine the limit cycle of the system.

4 Linear second order servo is described by the equation whereand Determine the singular point. Construct

the phase trajectory, using the method of isoclines.

5 (a) Describe the instability theorems of Lyapunov.(b) What are the sufficient conditions of stability of non-linear autonomous system?

6 Consider the system by ;

where

The system uses the observed state feedback such that Design a full order stateobserver, assuming the desired Eigen values of the observer matrix are and

7 Consider a non-linear system described by the equations:

;Find the region in the state plane for which the equilibrium state of the system isasymptotically stable.

8 Write short notes on the following for optimal control system design:(a) Characteristics of the plant.(b) State regulator problem.

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1 Consider the transfer function system . Obtain the state space representation

of the system in:

(a) Controllable canonical form and

(b) Observable canonical form.

2 State the basic theorem for determining the concept of controllability of time varying system

utilizing state transition matrix. Explain the same with proof.

3 What are the common physical non-linearities? Explain saturation and backlash non-

linearities.

4 Determine the type of singularity for each of the following differential equations.

Also locate the singular points on the phase plane

(i)

(ii) Draw the phase trajectories.

5 Check the stability of the system described by

use variable gradient method.

6 (a) Explain the effect of state feedback on controllability and observability.

(b) Describe the full order observer with neat block diagram.

7 Construct the state model for the system characterized by the following differential equation

. Also develop the block diagram.

8 (a) What are the major theoretical approaches for design of optimal control? Explain one of the

approach in detail.

(b) Find the extremals for the functional

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9a13601 advanced control systems

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