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Negative Feedback in a Control System has following Characteristics
Reduction in the gain at the expense of better stability of the system
Rejection of disturbance signals in the system
Low Sensitivity to parameter variations
Accuracy in tracking the steady state value
Basic components of the feedback control system are process system (open loop system), feedback path element, error detector, and controller.
Transfer Function of a control system is defined as:
Ratio of Laplace transform of Output to the Laplace transform of the Input with zero initial conditions
Transfer function is defined as the Laplace transform of Impulse response of the system with zero initial conditions
Time Invariant System is one in which the input and output characteristics of the system does not change with time.
The rules of the Block Diagram reduction Techniques are designed in such a manner that any modifications made in the diagram will not alter the input and output relation of the system.
Servomechanism is used in control system where the output is pertained to vary the mechanical position of a device.
Servo Mechanism is widely used in Governor value position control mechanism used in the power plants where speed of the turbine is taken and processed using the transducers and final control element is brought as mechanical movement of the value. Now a days Governor value control is done with Electronic controls using power Thyristors. Servomechanism is also widely used in the robotic hand movements.
Resonant peak is defined as the maximum value of the closed loop transfer function.A large resonant peak corresponds to large overshoot in the transient respose
The frequency at which resonant peak occurs is called the resonant frequency. Resonance frequency explains about the speed of the transient response.
The slope of the log-magnitude curve near the cut-off frequency is called the cut-off rate. The cut-off rate indicates the ability of the system to distinguish between the signal and the noise.
The frequency at which the phase of the open loop transfer function is 180o is called the phase cross over frequency.
The Gain Margin is defined as the reciprocal of the magnitude of open loop transfer function at phase cross over frequency. The gain margin indicates the amount by which the gain of the system can be increased without affecting the stability of the system
The phase margin is the amount of additional phase lag at the gain cross over frequency required to bring the system to the verge of instability.
A Signal Flow Graph is a diagram that represents a set of simultaneous linear algebraic equations. By taking Laplace transform the time domain differential equations governing a control system can be transferred to a set of algebraic equations in s-domain. The signal Flow graph of the system can be constructed using these equations.
By taking Laplace transform for differential equation in the time domain equations in S-domain can be obtained.
S domain is used for solving the time domain differential equations easily by applying the Laplace for the differential equations.
The basic properties of the signal flow graph are:
Signal Flow Graphs are applicable to linear systems
It consists of nodes and branches. A node is a point representing a variable or signal. A branch indicates the functional dependence of one signal on another
A node adds the signals of all incoming branches and transmits this sum to all outgoing branches
Signals travel along branches only in a marked direction and is multiplied by the gain of the branch
The algebraic equations must be in the form of cause and effect relationship
Control system is a collection of physical elements connected together to serve an objective. The output and input relations of various physical system are governed by differential equations. Mathematical model of a control system constitutes set of differential equations. The response of the output of the system can be studied by solving the differential equations for various input conditions.
Model of mechanical translational system can be obtained by using three basic elements Mass, Spring and Dash-pot.
Weight the mechanical system is represented by mass and is assumed to be concentrated at the center of body.
The elastic deformation of the body can be represented by the spring
Friction existing in a mechanical system can be represented by dash-pot.
Order of the system is defined as the order of the differential equation governing the system. Order of the system can be determined from the transfer function of the system. Also the order of the system helps in understanding the number of poles of the transfer function. For nth order system for a particular transfer function contains 'n' number of poles.
Time response of the control system is defined as the output of the closed loop system as a function of time. Time response of the system can be obtained by solving the differential equations governing the system or time response of the system can also be obtained by transfer function of the system.
Time response of the system consists of two parts:
1.Transient state response
2. Steady state response.
Transient response of the system explains about the response of the system when the input changes from one state to the other. Steady state response of the system shows the response as the time t, approaches infinity.
The knowledge of the input signal is required to predict the response of the system. In most of the systems input signals are not known ahead of the time and it is also difficult to express the input signals mathematically by simple equations. In such cases determining the performance of the system is not possible.Test signals helps in predicting the performance of the system as the input signals which we give are known hence we can see the output response of the system for a given input and can understand the behavior of the control system. The commonly used test signals are impulse, ramp, step signals and sinusoidal signals.
Pole of a function F(s) is the value at which the function F(s) becomes infinite, where F(s) is a function of the complex variable s.
Zero of a function F(s) is a value at which the function F(s) becomes zero, where F(s) is a function of complex variables.
When a number of elements or components are connected in a sequence to perform a specific function, the group of elements that all constitute a System.
In a System the output and inputs are interrelated in such a manner that the output quantity or variable is controlled by input quantity, then such a system is called Control System.
The output quantity is called controlled variable or response and the input quantity is called command signal or excitation.
Two major types of Control Systems are:
Open loop Control Systems: The Open loop Control System is one in which the Output Quantity has no effect on the Input Quantity. No feedback is present from the output quantity to the input quantity for correction.
Closed Loop Control System: The Closed loop Control System is one in which the feedback is provided from the Output quantity to the input quantity for the correction so as to maintain the desired output of the system.
The Feedback in Control System in one in which the output is sampled and proportional signal is fed back to the input for automatic correction of the error ( any change in desired output) for futher processing to get back the desired output.
The role of Feedback in control system is to take the sampled output back to the input and compare output signal with input signal for error ( deviation from the desired result).
Negative Feedback results in the better stability of the system and rejects any disturbance signals and is less sensitive to the parameter variations. Hence in control systems negative feedback is considered.
Positive feedback is not used generally in the control system because it increases the error signal and drives the system to instability. But positive feedbacks are used in minor loop control systems to amplify certain internal signals and parameters.
In the process plant Control room built considering the non-hazardous area. So in case if fire/Explosion takes place in the plant than that has to be restricted from entering Into the control room. So MCT(Multiple cable transient) blocks are used.