TIME RESPONSE ANALYSIS

SUBMITTED TO: SUBMITTED BY:Somesh Chaturvedi Hariom (10655)Asst. Proff. EE dept. B.tech (ME)Career Point university 6TH SEM.

TOPICSimulation between the transient part and steady state part of the time response in terms of time constant.

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Time Response Analysis

– Time Response– Transient Response– Steady state response– Standard input signals– First order system response– Second order system response– Time response analysis

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Time-Response Analysis

Since time is used as an independent variable in most control systems, it is usually of interest to evaluate the state and the output responses with respect to time or simply, the Time-Response.

In control system design analysis, a reference input signal is applied to a system and the performance of the system is evaluated by studying the system response in the time-domain.

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Time-Response

The time-response of a control system is usually divided into two parts namely; the Steady-State Response and the Transient Response.

In other words, the output response of a system is the sum of two responses: the forced response (steady-state response) and the natural response (zero-input response).

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Time-Response of an Elevator

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Transient Response

Defined as the part of the time response that goes to zero as time goes to infinity.

It does mot depend on input signal It gives information about the nature of

response and also give indication about speed.

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Steady-State Response

Defined as the part of the total response that remains after the transient has died out.

It depends on input signal. It gives the information about the accuracy of

the system.

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Standard Input Signals

There are a number of standard inputs that are considered simple enough and universal enough that they are considered when designing a control system.

These inputs are known as a unit step, a ramp, and a parabolic input functions.

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Unit Step Function

A unit step function is defined piecewise as such:

The unit step function is a highly important function, not only in control systems engineering, but also in signal processing, systems analysis, and all branches of engineering.

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Unit Step Function

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Ramp Input Function

A unit ramp is defined in terms of the unit step function, as such: r(t) = tu(t).

It is important to note that the ramp function is simply the integral of the unit step function:

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Ramp Input Function

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Parabolic Input Function

A unit parabolic input is similar to a ramp input:

Notice also that, the unit parabolic input is equal to the integral of the ramp function:

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Parabolic Input Function

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First-Order Systems

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Initial Conditions are zero

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First-Order Systems Response

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System Response

K (1 − e−t /τ ) System response. K = gain

Response to initial condition

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Second-Order Systems Response

ζ = 0

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System Response

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Time Response Specifications

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Rise Time

Is the amount of time that it takes for the system response to reach the target value from an initial state of zero.

Rise time is defined as the time for the waveform to go from 0.1 to 0.9 of its final value.

Rise time is typically denoted tr, or trise. This is because some systems never rise to

100% of the expected, target value and therefore, they would have an infinite rise-time.

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Settling Time After the initial rise time of the system, some systems

will oscillate and vibrate for an amount of time before the system output settles on the final value.

The amount of time it takes to reach steady state after the initial rise time is known as the settling time

Which is defined as the time for the response to reach and stay within, 2% (or 5%) of its final value.

Damped oscillating systems may never settle completely.

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Settling time

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Peak Time

The time required to reach the first or maximum peak. 21

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Percent Overshoot

The amount that the waveform overshoots the steady-state or final value at the peak time, expressed as a percentage of the steady-state value.

100% max

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