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Automatic ControlProf. Giulio Panzani

A.Y. 2011/2012

n ro uc on o mu n

Trento, 762012

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General information

SIMULINK is a MATLAB toolbox for the simulation of dynamicsystems

It has a graphical editing interface that allows system modeling in aoc agrams as on.

, , ,discrete time, multivariable and multirate (different sampling time)systems.

Blocks are included in general/specialized libraries, e.g. signal andcontrol system ones.

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Basic block libraries

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Simulation of a dynamic system

1. Model definition

2. Model codification

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Simulation of a dynamic system

Simulation:Define model parameters

Compute the initial state

Define input time historyCompute time behaviourAnalyze results

Modeling Codification

Iterative

processModify/extend

Modify initial stateNew input

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Simulation of a dynamic system

Matlab and simulink are intgrated one with the other

Parameter

Write arrays

Vout,t

R = 1C = 1

MATLAB SIMULINK MODEL

Simulate

In the simulation

instants

model

Compute o resu s

Plot(t,Vout)

Voutea ,

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Simulation of a dynamic system

Simulation parameters/settings

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Example Model definition

Simple mechanical system

Equation of motion

Compute t e constant input to reac esire ina va ue

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Example codification in Simulink

METHOD N 1 Equation of motion integration

ACCELERATIONSPEED DISPLACEMENT

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Example codification in Simulink

METHOD N 2 Transfer functionCan be a lied onl to linear s stems: transfer function can be defined as polynomial ratio

From equation of motions using the Laplace transform the transfer function is derived

Time domain Laplace domain

.

In Simulink the block Transfer Fcn is devoted to this operation

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Example codification in Simulink

METHOD N 2 Transfer function

To define a transfer function, numerator and denominator polynomial

coefficients are

needed

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Example codification in Simulink

METHOD N 3 State space representationCan be a lied onl to linear s stemsState space matrices are needed

State equation Output equation

n mu n e oc a e pace s evo e o s opera on

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Example codification in Simulink

METHOD N 3 State space representation

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Example proportional control

On the previous example a proportional controller is applied: the control action is proportional to the position error

Using t e irst met o , t e system is ui t in Simu in

REFERENCE

Mechanical system

DISPLACEMENT

force

ACCELERAT. SPEED DISPLACEMENT

displacement