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
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