## Control system- Time response AnalysisThe primary purpose of the time response analysis is to evaluate the system's performance with respect to time. The time-response graph is shown below: It comprises of two parts, After applying an input to the control system, the output takes some time to reach the steady condition. The response during this stage is known as To describe a system, we need to develop the relationship between the inputs and output of the system that are the functions of time. The most common model used to describe such behavior is known as the The common input signal is shown below: A test signal r(t) is applied as the input to the system that results in the response c(t). The input signal of a system can take many forms. ## Note: The input and output are functions that vary with time.Here, we will discuss the ## Transient ResponseIt is a part of the time response that reaches Or Transient response is defined as the change in the response of the system from the equilibrium state. For example,
The characteristics BJT or Bipolar Junction transistor depicts the transient nature. ## Steady-state responseThe response that comes after the transient response is called the steady-state response. In the graph analysis containing poles and zeroes, the poles on the Let's discuss some examples where we will find the transient and steady-state terms of the given equation. ## Examples
Here, the transient part of the equation is 2e^-t because as t approaches to infinity, the term becomes 0. Hence, 2e^-t is the transient term. In the case of the first term 5, it will remain same when t approaches infinity. Hence, 5 is the steady-state term of the equation.
Here, the first term, 10, is the steady-state term of the equation because it will remain the same when t approaches infinity. In the case of the second term, 5e^t, the result is infinity when t approaches infinity. Hence, it is not a transient term. It is because something to the power infinity is always infinity. So, there is only a steady-state term in the equation. ## Standard signals- Step Input signal
- Ramp input signal
- Sinusoidal input signal
- Impulse input signal
## Step Input signalFor the positive value, the step input shows constant values of the time. It has zero value for the negative value of the time signal. The initial value of the signal is and the transition is in the form of step size with a constant value. If the constant value of the signal is 1, it is called The value of the signal is: 0 for t=0 and 1 for t>0 The graph is a function of one variable named t. ## Ramp input signalThe graph of the ramp input signal is in the shape of The ramp function is represented as: The value of the signal is: At for t>0 and 0 for t<0 If the value of A is 1 when t>0. The signal is known as unit ramp signal. ## Sinusoidal input signalA sinusoidal input is one whose oscillations can be described by an equation in the form of The sinusoidal signal in the control system is represented as: The sine wave starts from zero, covers positive value, reach zero, covers negative values, and again reaches zero, as shown above. ## Impulse Input signalThe impulse signal is a type of high amplitude signal and has a very short duration. It means that the magnitude approaches Its integration from -infinity to infinity is 1, as shown above. It is a physical non-existing signal, which is defined based on the area concept. It is not based on the amplitude concept. The impulse input signal is represented as: |

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