Transient Response, Steady-State Response and Stability

1. Transient Response

Transient response has a very important role in the system. For example if we apply it to the elevator we can see that with a slow transient response passengers will become impatient whereas when it is very rapid then it can be present very unpleasant and scary situation for them.  A confusing situation may occur in case of elevator's oscillations just before the arrival of the floor.  Some major structural changes can also occur with the transient response: a very fast transient response can result in permanent physical damage. Transient response also contributes for the time that is required for a computer to write to or to read from the computer's disk storage. As we know that it is not possible to read and write until head stops , hence head's read/write movement affects the computer's overall speed.  With the help of this book, we will try to establish the quantitative definitions of the transient response. So that we can analyze the existing transient response of a system. Our primary Analysis and design objective is to get a preferred transient response and for that we can make the adjustments in the design components or parameters.

2. Steady-State Response

The Steady state response is the another goal of the analysis and design. This response seems like input and is something that remains when the transients are decayed to zero. For instance, this is a response seen when the elevator has stopped very close to the fourth floor or when the disk drive's head has stopped moving after the right track. The accuracy of the steady state response is a major concern for us.

For a comfortable exit of passengers it is important that an elevator should stop at a proper level with the floor. When the write or read tack is not placed over the command track then there are chances of getting computer errors. An antenna tracking of a satellite is done in order to maintain the satellite in its beam width so that it don't lose the track. In the text we will define the steady state errors on quantative basis, try to analyze the steady state error of the system and then corrective action are designed to decrease steady state error. This is our second analysis and design objective.
And objective of design.

3. Stability

Without the stability, the discussion made in steady state error and on the transient response is doubtful. To give details about the stability we shall begin with the information that the sum of the forced response and the natural response makes up the system's total the time of studying the linear differential equation, many of you may have referred to such responses as the homogeneous and particular solutions, respectively. The method by which a system acquires and dissipates energy was described by the natural response. The system and not the input is the factor that determines the response's nature or form. Whereas the input is responsible for the nature or form of the forced response. So to describe a linear system we can use:
Total response = Natural response + Forced response (1.1)2

In order to make a control system useful, it is necessary for the natural response to reach zero, and so only the forced response should be left. However there are some cases where the natural response without any bound grows and rather than diminish to zero oscillate. Hence the natural response is so much higher to the forced response that it cannot be controlled and the situation is known as instability. Ultimately, this type of condition can end up with self destruction of the physical device until the device has no limit stops as its part. For instance, there are chances of an elevator to crash down through the ceiling or the floor, an aircraft can take uncontrollable roll, there are chances that the antennae that is supposed to point to the target can rotate, it may line up with the target and then can start oscillating for about the target with the increasing oscillations and velocity they can reach to an output limit till antenna are structurally damaged. One can also see this transient response in an unstable system which increases without any proof of steady state response.

It is very important to design a control system to achieve stability. This can be achieved only when the natural response will decay up to the zero level when the time reaches the infinity or oscillate. In most of the systems we will find that the transient response and the natural response are directly proportional to each other.  So, when the natural response degrades with the time approaching to infinity, transient response is going to die out, and only the forced response is left behind. When the system is stable then proper designing of  steady state characteristics and transient response can be done.  The third objective of analysis and design is stability.

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