Time Response Control System

• In previous chapter > mathematical model is developed

• This chapter > analyse the mathematical model > evaluate system’s performance

• Analysis > Analyze time response of the system towards standard input signal

• Standard input signal >>> step input, impulse, ramp, sinusoidal

• Analysis on the changes of output variable when standard input signal is applied

Example of time response for control system (step input)

• Initially – 200°C

• Operator – 250°C (reference value ) –step input

• When the reference value is changed , the current flows to the heater will increase due to signal from the controller.

• The output temperature temperature of the microwave will increase until it reaches steady state value.

Ex 2 (ramp input ) – Tracking System

Tracking System – plane moves in constant velocity hence,input signal always changes with time u(t) = at

Structure of mathematical model

InputOutput

Initial condition

U(t), t >t 0Y (t) , t ≥ t0

Y (t) >output; u(t) > input ( change with time ) >>> variablesMain objective of control > how u is used to control yPrevious chapter > mathematical model is developed based on differential equations.Therefore, time response is the solution for this formulation>> Laplace Transform

Differential equation model

Laplace Transform (used to find the time response)

Property of Laplace Transform

Laplace Transform of derivatives

Laplace Transform of integral

• Notes..

• Ex .. Derive the Laplace Transform of an exponential function f(t) = eat

• Laplace Transform of

• > unit step function

• > ramp function

• > impulse function

• > sinusoidal function

Application of L.T to solve differential equations

Differential equation >>>> Laplace form ( Y (s) ) >>> Inverse Laplace ( to get y(t))

• Ex 3.3

• Ex 3.4

• Exercise 3.4

• Ex 3.5

Classification of dynamic system

• EX 3.6

• Exercise 3.9