# SOLVED PROBLEM IN CONTROL SYSTEM BY JAIRATH PDF

AK JAIRATH ME, FIE, FIETE give the students extra problem-solving practice. cesses/plants and feedback elements of various types of control systems. I am. Problems And Solutions Of Control Systems By A K Jairath Pdf - [Free] . Stratton Manuals File Type Pdf The Innovators Solution By Clayton. Here is the best location to obtain Solution And Problems Of Control Systems A K Jairath Pdf. Free Download by resourceone.info Learning totally free.

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Problems and Solutions of Control Systems by A. K. Jairath. 1. Created by For example, Exa means solved example of this book. Problems And Solutions Of Control Systems By A K Jairath Pdf - [FREE] customer communications project management harold kerzner solution problems . problems and solutions of control systems by a k jairath is available in our book collection Control systr,m with reference input and disturbance input. Solution.

I wish to thank the University of Sussex for the facilities they have provided to me in retirement which have been very helpful in writing all three bookboon books and finally to my wife Constance for her love and support over many years.

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Please approve this email to receive our weekly eBook update. The advantages of closed loop system are: Such systems senses environmental changes, as well as internal disturbances and accordingly modifies the error.

In such system, there is reduced effect of non-linearites and distortions. Highly affected by non-lineariteis Reduced effect of non- linearities. Highly sensitive to the disturbances Less sensitive to disturbances and environmental changes and environmental changes.

Feedback element and error detector Feedback element and error are absent detector are absent Generally stable in nature Stability is the major consideration while designing. Linear system. A system is said to be linear if it obeys the principle of superposition and homogeneity.

The principle of superposition states that the response of the system to a weighted sum of the responses of the system to each individual input signals. The system is said to be linear, if it satisfies the following two properties: Most of the systems are non-linear in nature because of different non-linearities such as saturation, friction, dead zone etc.

Definition of Transfer Function Transfer function of a given system is defined as the ratio of the laplace transform of output variable to laplace transform of input variables at zero input conditions. Properties of transfer functions. The properties of transfer function are as follows: The system stability can be described in terms of the location of the roots of the transfer function.

Advantages of transfer function. Disadvantages of transfer function. The disadvantages of transfer function approach are: From transfer function, physical nature of the system, whether it is electrical, mechanical, thermal or hydraulic cannot be judged. Hence initial conditions loose importance. Important features of feedback. The basic elements used for modeling mechanical translational system: The model of mechanical translational system can be obtained by using three basic elements mass spring and dashpot.

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Translational system Consider a mechanical system in which motion is taking place along a straight line. Such systems are of translational type. These systems are characterized by displacement, linear velocity and linear acceleration. Definition of torque. This is the motion about a fixed axis. In such systems, the force gets replaced by a moment about the fixed axis.

Definition of friction. Whenever there is a motion, there exists a friction. Friction may be between moving element and fixed support or between two moving surfaces. Friction is also non- linear in nature.

The types of friction. Friction can be divided into three types. The two types of analogies for mechanical system are force-voltage analogy and force-current analogy. Analogous systems Systems whose differential equations are identical form are called analogous systems.

The two variables in physical systems are through variables and across variable. Through variables refer to a point, the across variable is measured between two points. The other names for force voltage analogy and force current analogy are Force voltage analogy- Loop analysis.

Force current analogy- nodal analysis. In block diagram, the system consists of so many components. These components are linked together to perform a particular function. Each component can be represented with the help of individual block. Block diagrams of some of the systems turn out to be complex, such that the evaluation of their performance required simplification or reduction of block diagrams which is carried out by block diagram rearrangements.

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 disadvantages of block diagram are: The basic components of block diagram are block, branches, summing point, arrows. It indicates the function of particular system.

R s is the reference or controlling variable. G s is the transfer function of the particular system. C s is output or controlled variable. It is used to add or subtract one or more signals. It is called negative feedback. The signal which is added or subtracted to the reference signal is called feedback signal.

If the blocks are in cascade then Solved by A. Moving summing point after the block, then Rule 6: Moving the summing point ahead before the blockff Rule 7: Eliminating feedback loop, then Solved by A. Fig 1. Eliminating feedback loopI as in fig. Eliminating feedback loop II as in fig 1. Step 5: Using block diagram reduction technique, find the transfer function from each input to the output C s for the system shown in fig.

Step 2: Step 4: Combine the blocks in series.

## A K Jairath

Step 8: Reduce the block diagram shown in fig. Determine the overall transfer function of the block diagram shown in fig. The graphical representation of the variables of a set of linear algebraic equations representing the system is called signal flow graph.

Need for signal flow graph: Block diagrams are very successful for representing control systems, but for complicated systems, the block diagram reduction process is tedious and time consuming. So signal flow graphs are needed which does not require any reduction process because of availability of a flow graph formula, which relates the input and output system variables.

## CBS Problems and Solution

The transmittance is the gain acquired by the signal when travels from one node to another node in the signal flow graph. Node represents a system variable, which is equal to the sum of all incoming signals at the node, outgoing signals from the node do not affect the value of the node variable. A signal travels along a branch from one node to another in the direction indicated by the branch arrow and in the process gets multiplied by the gain or transmittance of the branch.

A node having incoming and outgoing branches is known as chain node. A feedback loop consisting of only one node is called self loop. The product of all the gains of the branches forming a loop is called loop gain. A path from the input to output node is defined as forward path.

Find the transfer function for the signal flow graph as shown in fig 1. For the signal flow graph given in fig. Valuate the closed loop transfer function of the system.

Obtain the analogous electrical network for the system shown in fig. The friction B1 is responsible to change the displacement from x1 t to x2 t The Mass M2 is under the displacement x2 t.

The friction B2 and spring K1 are responsible to change the displacement from x2 t to x3 t The Mass M3 and spring K2 are under the influence of displacement x3 t. The equivalent Mechanical system is shown in fig. Rate of change of displacement is replaced by current, force is replaced by voltage.

Draw the equivalent mechanical system of the system shown in fig. May- As shown in fig. M1,K1,and B1 are under the displacement x1 as K1 and B1 are with respect to rigid support. K2 is between x1 and x2 as it is responsible for the change in displacement. While M2 , K3 and B2 are under the displacement x2. Hence the equivalent mechanical system is as shown in fig.

Rate of change of displacement is replaced by voltage, force is replaced by current. The analogous system for force current analogy is shown in fig. Write the equations for mechanical system shown in figure 7.

April , Dec Due to force f t applied to M1, it will displace by the displacement x1 t. As K1 and B1 are between M1 and fixed support, both are under same displacement x1 t Due to friction B3, the force transferred to M2 is different than f t , hence M2 will displace by the displacement x2 t. As K2 and B2are between M2 and fixed support, both are under same displacement x2 t The equivalent system is shown in fig.

Obtain the mathematical model of the following mechanical system shown in figure 8.

April The displacement is x t as shown if fig. Both B1 and B2 are between mass M and fixed support.

Hence under the influence of x t. The equivalent mechanical model is shown in fig.

## Control Engineering Problems with Solutions

Obtain the differential equations of the following mechanical systems as shown in fig. The equivalent nodal diagram for the given mechanical system is shown in fig. For the spring, damper and mass system shown in fig. Obtain the differential equations governing the system. F t is the force applied Au: Show that the systems shown in fig. April There are three displacements xi t xo t and xy t. The input is xi t and output is xo t. Steady state error is an important measure of the accuracy of a control systems.

Basically these errors occur from the nature of inputs, non-lineraities present in the system Etc. Effect of input on steady state error: The open loop transfer function G S of a unity feed back system can be written in two standard forms namely the time constant form and polr zero form. In both respresentatiom, the terms Sn in the denominator represent the n poles at the origin, which represent the type number of the system.

The type number of a system is defined as the number of poles of G S at the origin or number of integrators present in the systems. Where ko, k1,k2…… are called dynamic error coeff To calculate these values co efficient use the following method According to the definition of laplace transform Solved by A. A controller is a device which when introduced in feed back or forward path of system, controls the steady state and transient response as per the requirement.

This controller converts the applied input to some other form of error which is proportional to the error due to which steady state and transient response gets improved. The output of the controller is proportional to the amount of error generated by that device. The performance of this controlling phenomena may be done by means of electrical, mechanical, pneumatic or hydraulic medium.

Classification of controllers: ON-OFF controller 2. This type of controller is the simplest and cheapest typehere the actuating device controller Is the capable of assuming only one two positions, with either zero or maximum input to the process. Proportional controller: It is defined as the action of a controller in which the output signal m t is proportional to the measured actuating error signal e t.

Integral controller: In a controller with integral action, the value of the output m t is propprtional to the measured actuating error signal e t. This integral control overcomes the drawback of proportional control by reducing the steady state error to zero without the use of excessive large control gain.

The integral control action is also called as reset control action. Derivative controller: Derivative controller do not affect state error but effect transient response. The output of derivative controller depends on the rat e of change of error signal. Obtain the mathematical model of the following mechanical system shown in figure 8.

Both B1 and B2 are between mass M and fixed support. Hence under the influence of x t.

The equivalent mechanical model is shown in fig. Obtain the differential equations of the following mechanical systems as shown in fig. The equivalent nodal diagram for the given mechanical system is shown in fig. For the spring, damper and mass system shown in fig. Obtain the differential equations governing the system.

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F t is the force applied AuIn addition, at the end of each chapter a large number of short and long questions with answers are given as exercise. Consider P4. Implies feedback with positive sign B. The output of synchro error detector is a: Whenever there is a motion, there exists a friction.