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Chapter: Control Systems : Time Response Analysis

Typical Input Signals

Typical Input Signals: o Impulse Signal o Step Signal o Ramp Signal o Parabolic Signal

Typical Input Signals


o   Impulse Signal


o   Step Signal


o   Ramp Signal


o   Parabolic Signal



Time Response Analysis & Design


Two types of inputs can be applied to a control system. Command Input or Reference Input yr(t).


Disturbance Input w(t) (External disturbances w(t) are typically uncontrolled variations in the load on a control system).


In systems controlling mechanical motions, load disturbances may represent forces.

In voltage regulating systems, variations in electrical load area major source of disturbances.


Test Signals

Transfer Function


o   One of the types of Modeling a system


o   Using first principle, differential equation is obtained


o   Laplace Transform is applied to the equation assuming zero initial conditions


o   Ratio of LT (output) to LT (input) is expressed as a ratio of polynomial in s in the transfer function.


Order of a system


o   The Order of a system is given by the order of the differential equation governing the system


o   Alternatively, order can be obtained from the transfer function


o   In the transfer function, the maximum power of s in the denominator polynomial gives the order of the system.


Dynamic Order of Systems


o   Order of the system is the order of the differential equation that governs the dynamic behaviour


o   Working interpretation: Number of the dynamic elements / capacitances or holdup elements between a


o   manipulated variable and a controlled variable


o   Higher order system responses are usually very difficult to resolve from one another


o   The response generally becomes sluggish as the order increases.

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Control Systems : Time Response Analysis : Typical Input Signals |

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