Subject Code / Name: IC6501/ Control Systems

UNIT-I

SYSTEMS AND THEIR REPRESENTATION

PART-A

1.

Name the basic elements used in control systems. (AU ND 14)-3

Error detector,

Amplifier and controller,

Actuator,

Plant and

Sensor or feedback system

2.

Define transfer function. (AU ND 14)-3

ATransfer Functionis the ratio of the output of a system to the input of a system, in the Laplace domain considering its initial conditions and equilibrium point to be zero. If we have an input function ofX(s), and an output functionY(s), we define the transfer functionH(s)to be:

3.

List the major advantages and disadvantages of open loop control systems. (AU MJ 14)-2

Advantages:

The open loop systems are simple, economical, easy to construct and stable.

Disadvantages:

The open loop systems are inaccurate, unreliable

4.

What are the applications of Synchros? (AU MJ 14)-3

To control the angular position of load from remote place or long distance.

To automatic correction of changes due to disturbances in the angular position of the load.

5.

Name any two dynamic model used to represent control systems. (AU MJ 13)

Block diagram reduction

Signal flow graph representation.

6.

Write the masons gain formula of signal flow graph. (AU MJ 13)-3

Masons Gain formula states that the overall gain of the system is

k - No. of forward paths in the signal flow graph.

Pk - Forward path gain of kth forward path

= 1 - [sum of individual loop gains ] + [sum of gain products of all possible

combinations of two non touching loops] - [sum of gain products of all

possible combinations of three non touching loops]+

k = for that part of the graph which is not touching kth forward path.

7.

Compare open loop and closed loop system. (AU MJ 13)-5

OPEN LOOP SYSTEM CLOSED LOOP SYSTEM

Inaccurate

Accurate

Simple and economical

Complex and costlier

The Changes in output due to external disturbance are not corrected

The Changes in output due to external disturbance are corrected automatically

They are generally stable

Great efforts are needed to design a stable system

8.

List the basic elements for modelling in translational and rotational systems. (AU MJ 13)-2

Translational system: Mass (M), Dash pot (B), Spring (K), Input- Force.

Rotational system: Moment of Inertia (J), Dash pot (B), Spring (K), Input- Torque.

9.

What are the advantages of the closed loop control system? (AU ND 12)-3

It usually performs accurately even in presence of non-linearities. Change of system

Component is automatically taken care of.

Increased bandwidth

Reduced sensitivity of the ratio of output to variation in system characteristics.

10.

Write down the transfer function of the system whose block diagram is shown below.

(AU ND 12)-2

Solution:

11.

What are the properties of signal flow graph? (AU MJ12)

A branch indicates the functional dependence of one signal upon another. A signal

Passes only in the direction specified by the arrow of branch.

A node adds all signals of all incoming branches and transmits this sum to all outgoing branches.

A mixed node which has both incoming and outgoing branches may be treated as an output node by adding an outgoing branch of unity gain.

12.

What is meant by block diagram of a control system? What are the basic components of a block diagram? (AU ND 11)

A block diagram of a system is a pictorial representation of the functions performed by each component of the system and shows the flow of signals. The basic elements of block diagram are block, branch point and summing point.

13.

State the importance of a feedback element in control system. (AU MJ 11)

The feedback element is the control and partial elimination of the effect of disturbance signal in the control system.

14.

Difference between servo motor and dc motor. (AU MJ 09)

Servo motor

DC motor

Servo motors have three wires (power, ground & control)

DC motors have two wire (power & ground)

Servo motors does not have continuous rotation

DC motors have Continuous rotation motors

15.

Define thermal resistance. (AU ND 07)

The resistance for the heat transfer between two substances is defined as the ratio of change in temperature and change in heat flow rate.

Thermal resistance R= (Change in temperature, ( C) / Change in heat flow rate, (kcal/sec))

16.

Define servomechanism.

Servomechanism is the feedback control system in which the controlled variable or the output is a mechanical position (or) its time derivatives such as velocity or acceleration.

17.

Give some examples of servomechanism.

Position control system

Power steering apparatus for an automobile

Missile launchers

Roll stabilization of ships

18.

What is source and sink?

Source is the input node in the signal flow graph and it has only outgoing branches.

Sink is an output node in the signal flow graph and it has only in coming branches.

19.

Define thermal capacitance.

Thermal capacitance is defined as the ratio of change in heat stored and change in temperature.

Thermal capacitance C= (change in heat stored, (kcal)/ change in temperature (C))

20.

Define self-loop.

A path starting from one node and terminating at the same node without crossing any other node even once is called self-loop.

PART-B

1.

Consider the mechanical system shown in figure, write the differential equation describing the dynamics of the system and also draw the electrical analogy for the system.(16)

(AU MJ 13)

2.

The block diagram of a control system is shown in figure, determine the transfer function. (8)

(AU MJ 13)

3.

Give the step by step procedure of determining transfer function using signal flow graph. (8)

(AU MJ 13)

4.

Find the transfer function of the block diagram shown in figure, using masons gain formula. (16) (AU MJ 13)

5.

Construct the equivalent signal flow graph and obtain C/R using Masons formula for the given block diagram. (16) (AU ND 12)

6.

For the block diagram shown below, find the output C due to R and disturbance D. (16)

(AU ND 12)

7.

Write the differential equation governing the mechanical rotational system shown in figure. Draw the torque-voltage and torque-current electrical analogous circuits and verify by writing mesh and node equation. (16) (AU ND 12)

8.

Find C(S) / R(S) for the signal flow graph shown below.(16) (AU ND 12)

9.

Using block diagram reduction technique. Find the closed-loop transfer function C/R of the system. Whose block diagram is shown below. (16) (AU MJ 12)

10.

Construct the signal flow graph for the following set of simultaneous equations obtains the overall transfer function using Masons gain formula.(16) (AU MJ 12)

11.

Consider the mechanical system shown below. Identify the variables and write the differential equation. (16) (AU ND 11)

12.

Draw the torque-voltage electrical analogus circuit for the following mechanical systems shown. (16) (AU ND 11)

13.

Obtain the transfer function of the following electrical network. (16) (AU ND 11)

14.

For the signal flow graph shown in figure. Find C(S) / R(S) by using Masons gain formula. (16) (AU ND 11)

15.

Find the transfer function C(s) / R(S) of block diagram shown below. (8)

(AU ND 11)

16.

Write the differential equation governing the system shown in figure. Draw the electrical circuits based on both (a) Force Voltage (b) Force Current analogies for the translational mechanical system. (16) (AU MJ 11)

17.

Obtain the overall transfer function of the following system by Masons gain formula. (16)

(AU MJ 11)

UNIT II

TIME RESPONSE

PART-A

1.

Write PID controller equation. (AU ND 14)

Transfer function of PID Controller Gc(S)=Kp+(Ki/S)+KdS

2.

What are the standard testing signals used in control system? (AU MJ 14)

The commonly used test input signals are Impulse, Step, Ramp, Acceleration and sinusoidal signals.

3.

The closed loop transfer function of a second order system is given by M(S) = (400/ (S2+2S+400)). Determine the damping ratio and natural frequency of oscillation. (AU MJ 13)

Solution: Natural frequency of oscillation n, (n2 = 400)

n = 20

Damping ratio ,

, = 0.05

4.

Give the steady state errors to a various standard inputs for type-2 system. (AU MJ 13)

ess for step input = 0

ess for ramp input = 0

ess for parabolic input = A/K

5.

What are transient and steady state response of a control system? (AU ND 12)

The transient response is the response of the system when the system changes from one state to another. The steady state response is the response of the system when it approaches infinity.

6.

With reference to time response of a control system, define peak time. (AU ND 12)

It is the time taken for the response to reach the peak value for the very first time (or) it is the time taken for the response to reach peak overshoot, Mp .

7.

List the advantages of generalized error coefficients. (AU MJ 12)

Steady state is function of time.

Steady state can be determined from any type of input

Generalized error series gives error signal as a function of time.

Using generalized error constants the steady state error can be determined for any type of input but static error constants are used to determine m state error when the input is anyone of the standard input.

8.

Why derivative controller is not used in control system? (AU ND 11)

The derivative controller produces a control action based on the rate of change of error signal and it does not produce corrective measures for any constant error.

9.

The damping ratio and natural frequency of oscillation of a second order system is 0.5 and 8 rad/sec respectively. Calculate resonant peak and resonant frequency. (AU MJ 11)

Solution :

Given : = 0.5 and n = 8

Resonant peak Mp

, Mp = 0.163

Resonant frequency d = n d = 6.928

10.

With reference to time response of a control system, define Rise time. (AU MJ 11)

It is the time taken for response to rise from 0 to 100% for the very first time.

For under damped system, the rise time is calculated from 0 to 100% .

For over damped system it is the time taken by the response to rise from 10% to 90%.

For critically damped system, it is the time taken for response to rise from 5% to 95%.

11.

How a control system is classified depending on the value of damping? (AU MJ 11)

Depending on the value of damping, the system can be classified into the following four cases:

Case 1: Undamped system, = 0

Case 2: Under damped system, 0 < < 1

Case 3: Critically damped system, = 1

Case 4: Over damped system, > 1

12.

Define type and order of a control system. (AU MJ 11)

Type number is specified for loop transfer function but order can be specified for any transfer function. (Open loop or closed loop transfer function).

The type number is given by number of poles of loop transfer function lying at origin of s-plane but the order is given by the number of poles of transfer function.

13.

What are error coefficients Kp, Kv, Ka of a Type-0 system? (AU MJ 11)

Positional error coefficient Kp = K

Velocity error coefficient Kv = 0

Acceleration error coefficient Ka = 0

14.

What is meant by peak overshoot? (AU ND 10)

It is defined as the ratio of the maximum peak value measured from final value to final value. Let final value = c(), Maximum Value = c(tp)

Peak Overshoot, Mp = [c(tp) - c() ] / c()

15.

What is meant by steady state error? (AU ND 10)

The steady state error is the value of error signal e(t), when t tends to infinity The steady state error is a measure of system accuracy. These errors arise from the nature of inputs, type of system and from non-linearity of system components.

16.

Define delay time.

Delay time is the time required for the response to reach 50% of the final value.

17.

Define settling time.

Settling time is the time required for the response to reach and stay within a specified tolerance band (2% to 5%) of its final value.

18.

Define pole.

The pole of a function F(S) is the value at which the function F(S) becomes infinite. Poles are the roots of the denominator polynomial.

19.

Define zero.

The zero of a function F(S) is the value at which the function F(S) becomes zero, where F(S) is a function of complex variable S. They are the roots of numerator polynomial.

20.

What is weighting function?

The impulse response of the system is called weighting function. It is given by inverse Laplace transform of system transfer function.

PART-B

1.

Consider a second order model and damping ratio 0 t0 .

3.

Define state variable. (AU MJ 13)

The variables involved in determining the state of a dynamic system X (t), are calked the state variables. X1(t), X2(t)........Xn(t) are nothing but the state variables. These are normally the energy storing elements contained in the system.

4.

What is meant by Sampled-data control systems? (AU ND 12)

When the signal or information at any or some points in a system is in the form of discrete pulses, then the system is called discrete data system or sampled data system.

5.

How the model matrix is determined? (AU MJ 12)

The modal matrix M can be formed from eigenvectors. Let m1, m2, m3mn be the eigenvectors of a nth order system. Now the modal matrix M is obtained by arranging all the eigenvectors column wise as shown below Modal matrix, M=[ m1 m2 m3 ..mn]

6.

What is meant by quantization? (AU MJ 12)

The process of converting a discrete-time continuous valued signal into a discrete time discrete valued signal is called quantization. In quantization the value of each signal sample is represented by a value selected from a finite set of possible values called quantization levels.

7.

What are the advantages of state- space approach? (AU ND 11)

The method takes into account the effect of all initial conditions.

It can be applied to nonlinear as well as time varying systems.

It can be conveniently applied to multiple input multiple output systems.

Any type of the input can be considered for designing the system.

8.

What is 'alis' in sampling process? (AU ND 11)

The improper sampling process produces an erroneous signal which is called an alias.

9.

Name the methods of state space representation for phase variables. (AU MJ 11)

state model from differential equation

state model from Transfer function

10.

What is meant by sampling theorem? (AU ND 10)

Sampling theorem states that a band limited continuous-time signal with highest frequency fm, Hertz can be uniquely recovered from its samples provided that the sampling rate Fs is greater than or equal to 2fm samples per second.

11.

Define Acquisition time.

In analog-to-digital conversion process, the Acquisition time is defined as the total time

required for obtaining a signal sample and the time for quantizing and coding .It is also called conversion time.

12.

Define state vector.

If there are n variables x1,x2,.xn to describe the state, then the vector X of n components is called state vector.

13.

Define state space.

The n dimensional space defined by the state variables as coordinate is called the state space.

14.

What is state diagram?

The pictorial representation of the state model of the system is called state diagram. The state diagram of the system can be either in block diagram or in signal flow graph form.

15.

What are the basic elements used to construct the state diagram?

Scalar, Adder and Integrator.

16.

Define characteristic equation of a matrix.

The characteristic equation of a nXn matrix A is the nth degree polynomial of equation, [I-A]=0, where I is the unit matrix.

17.

Define controllability.

A system is said to be completely state controllable if it is possible to transfer the system state from any initial state X(t0) at any other desired state X(t), in specified finite time by a control vector U(t).

18.

Define observability.

A system is said to be completely observable if every state X(t)can be completely identified by measurements of the output Y(t)over a finite time interval.

19.

What is the need for controllability test?

The controllability test is necessary to find the usefulness of a state variable. If the state variables are controllable then by controlling (i.e., varying) the state variables the desired outputs of the system are achieved.

20.

What is the need for observability test?

The observability test is necessary to find whether the state variables are measurable or not. If the state variables are measurable then the state of the system can be determined by practical measurements of the state variables.

21.

List the methods to find Observability and Controllability.

Kalmans method and Gilberts method

PART-B

1.

The state space representation of a system is given below. Obtain the transfer function. (16)

(AU ND 12)

2.

Determine the controllability and observability of the following system. (16)

(AU ND 12)

3.

Obtain the state space representation of armature controlled D.C. motor with load, shown

below. (16)

Choose the armature current ia, the angular displacement of the shaft , and the speed d/dt as state variables and as output variables. (AU MJ 12)

4.

The state model matrices of a system are given below. (AU MJ 12)

Evaluate the observability of the system using Gilberts test. (16)

5.

Find the controllability of the system described by the following equation: (16) (AU MJ 12)

6.

Determine the transfer function from the data given below and also check controllability : (16) (AU MJ 10)

7.

Determine the state controllability and observability of the system described by (16)

(AU ND 10)

8.

Using cascade method decomposes the transfer function and obtains the state model. (16) (AU MJ 10)

9.

Obtain the state space representation for the blow diagram shown in figure below and also check controllability and observability.

(16) (AU MJ 10)

10.

Write the state equations for the system shown below in which x1, x2 and x3 constitute the

state vector. (16) (AU MJ 10)

11.

Determine whether the system is completely controllable and observable. (16) (AU MJ 10)

12.

Explain in detail the state space representation for continuous time systems. (16) (AU ND 10)

13.

Explain in detail the state space representation for discrete time systems. (16) (AU ND 10)

14.

A sampled data control systems is shown in the figure below. (16)

Find the open loop transfer function, if the controller gain is unity with sampling time 0.5 seconds. (AU ND 10)

15.

Compare conventional control method and state space analysis method. (16)

CS 7 KCE/EEE/QB/IIIYr/CS

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