Two major types of Control Systems are
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.
Basic components of the feedback control system are process system (open loop system), feedback path element, error detector, and controller.
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 trient) blocks are used.
Resonant peak is defined as the maximum value of the closed loop trfer function.A large resonant peak corresponds to large overshoot in the trient respose
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.
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 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.
Model of mechanical trlational 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.
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.
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.
Negative Feedback in a Control System has following Characteristics
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.
By taking Laplace trform for differential equation in the time domain equations in S-domain can be obtained. L{F(t)}=F(s)
S domain is used for solving the time domain differential equations easily by applying the Laplace for the differential equations.
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.
Time response of the system consists of two parts: 1.Trient state response @Steady state response. Trient 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.
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 trducers 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.
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 trfer function of the system.
The Gain Margin is defined as the reciprocal of the magnitude of open loop trfer 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.
The frequency at which resonant peak occurs is called the resonant frequency. Resonance frequency explains about the speed of the trient response.
Trfer Function of a control system is defined as:
The frequency at which the phase of the open loop trfer function is 180o is called the phase cross over frequency.
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.
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.
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 trfer function of the system. Also the order of the system helps in understanding the number of poles of the trfer function. For nth order system for a particular trfer function contains 'n' number of poles.
Time Invariant System is one in which the input and output characteristics of the system does not change with time.
A Signal Flow Graph is a diagram that represents a set of simultaneous linear algebraic equations. By taking Laplace trform the time domain differential equations governing a control system can be trferred to a set of algebraic equations in s-domain. The signal Flow graph of the system can be constructed using these equations.
The basic properties of the signal flow graph are: