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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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