Typical Input Signals

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.