identification and control of mechatronic systems · identification and control of mechatronic...

Identification and Control of

Mechatronic Systems

Dr. Tarek A. TutunjiPhiladelphia University, Jordan

NATO - ASI

Advanced All-Terrain Autonomous Systems Workshop

August 15 – 24, 2010

Cesme-Izmir, Turkey

2Dr. Tarek A. Tutunji

Overview

Mechatronics Engineering

System Identification

Control Techniques

Hardware-in-the-Loop (HIL)

Design Procedure

Case Studies


Philadelphia University, Jordan

Philadelphia is the ancient name of Amman

named by Ptolemaeus Philadelphus in the year 285 B.C


Definition: What is Mechatronics?

Mechatronics Engineering is the

Analysis

Design

Manufacturing

Integration

and maintenance

of mechanics with electronics through intelligent computer

control.


Mechatronics Main Components


Mechatronic System Overview

ActuatorsElectrical Motors,

Pneumatic, Hydraulic

Mechanical system

SensorsInductive, Capacitive, Resistive, Ultrasonic,

Photo

Conditioning & Interface

Input:A/D, Filter, Amplifier

Output:D/A, Power

Circuit

Control Architectures

mcontroller, PLC, PC, DSP Control Algorithm

Graphical display

LED, LCD, CRT


Tarek A. Tutunji


Modeling / Identification Communities

Statistics

Econometrics and Time Series Analysis

Machine Learning

Process Control

Data Mining

Artificial Neural Networks



Dynamic Models Classification

SISO vs. MIMO

Linear vs. nonlinear

Parametric vs. nonparametric

Time invariant vs. time variant

Time domain vs. frequency domain

Discrete vs. continuous

Deterministic vs. stochastic



Mathematical models can be constructed using analytical approach, such as physics laws, or using experimental approach.

System identification is the field of approximating dynamic system models from input/output patterns acquired through physical experiments.

The target is to establish a mathematical model that mimics the original system and therefore minimizes the error between the system and model outputs.


Two Main Theories

Realization

Theory of how to realize linear state space models

from impulse responses (Ho-Kalman 1966)

Prediction-Error

Prediction of the output at certain time depends

previous measured input and output (Astrom-Bohlin

1965)


Deterministic Realization Theory

State-space realization problem is stated as follows:

Construct a minimal state-space realization

tt

ttt

Cxy

BuAxx

1

1kktkt uHy

For the input-output model

described by its impulse

response matrices, Hk


Deterministic Realization Theory

The problem is to replace the infinite description

1k

kk zHzH

BAzIC)z(H1

with a finite description so that


Maximum Likelihood Theory

ML notations such as cost criteria and parameter estimate

ttt e)z(Cu)z(By)z(A 111

Algorithmic derivation of ML identification for ARMA

(Auto-Regressive Moving-Average) models.

N

tt.V

1

250 Vminˆ


Maximum Likelihood

to Prediction Error

Maximization of the likelihood function is

equivalent to minimizing the sum of the squared

prediction errors.

under the assumption of white Gaussian noise in the

ARMAX model


Ljung, Stoica, and Soderstrom

Major work: 1980‟s

Two independent concepts:

The choice of a parametric model structure

ttt e,zHu,zGy

N

tt

NN f

NZ,V

1

1

The choice of an identification criterion


Breakthroughs: 1975 - 1985

Multi-Input Multi-Output (MIMO) systems

Identifiability of closed-loop systems


Identification as a Design Problem

Identification can be viewed as an approximation

Estimated models are used for a specific purpose

The model error should be controlled in order not

to penalize the goal for which the model was built

for.

Goal-oriented design problem


Identification for Control

In 1990, identification and control design were

looked as a combined design problem.


System Identification Steps

1. Experiment design. This includes the choice of lab equipment to be used such as computers, DAQ, and interface.

2. Model structure determination. The choice of the model can range from nonparametric models, such as transient and frequency analysis, to parametric methods, such as difference equations and neural networks.

3. Experiment run. This is usually done by exciting the system with an input signal (pulse, sinusoid, or random) and measuring the output signal over a specified time interval.


System Identification Steps

4. Algorithm choice and run. The algorithm used for

convergence can vary from simple one-shot least

squares, recursive least squares to advanced multi-

structures such as back propagation.

5. Validation of results. The output of the identified

model is compared to the original system through

different and „new‟ input signals.



Input

Model Output

Error

Actual Output

Real

System

System

Model

+

-


System Identification:

ARMA Models

The standard Auto-Regressive Moving-Average model (ARMA)

is given below

m

iiki

n

jjkjk ubyay

01

where uk is the system input, yk is the system output ^yk is the predicted

output, a and b are the ARMA parameters. The goal is to minimize the error

between the desired and predicted outputs

K

kkk

K

kk yyeE

1

2

1

ˆmin


System Identification:

ARMA Models

Coefficients updates using steepest descent

j)e(k)y(kj)y(ky(k)(k)ya(j)

E(k)

ˆ

i)e(k)u(ki)x(ky(k)(k)yb(i)

E(k)

ˆ

ARMA to Transfer Functions

m

0i

n

1j

i)b(i)u(kZj)a(j)y(ky(k)Zn

N1

10

mM

110

za...zaa

zb...zbb

U(z)

Y(z)H(z)

)()()()( kejkyjaja

)k(e)ik(u)i(b)i(b

Control Techniques

Tarek A. Tutunji


Control Techniques / Strategies

Classical Control

Adaptive Control

Robust Control

Optimal Control

Variable Structure Control

Intelligent Control


Classical Control

Classical control design are used for SISO

systems.

Most popular concepts are:

Bode plots

Nyquist Stability

Root locus.

PID is widely used in feedback systems.


Classical Control: PID

Proportional-Integral-Derivative (PID) is the most

commonly used controller for SISO systems

dt

)t(deKdt)t(eK)t(eK)t(u DIp


Classical vs. Modern Control

In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation.

A mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations.

The variables are expressed as vectors and the differential and algebraic equations are written in matrix form.

The state space representation provides a convenient and compact way to model and analyze systems with multiple inputs and outputs.


Adaptive Control

Adaptive control involves modifying the control law used by a controller to cope with the fact that the parameters of the system being controlled are slowly time-varying or uncertain.

Such controllers use on-line identification of the process parameters.

For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; we need a control law that adapts itself to such changing conditions.


Robust Control

Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design.

Robust control methods are designed to function properly so long as uncertain parameters or disturbances are within some set.

The state-space methods were sometimes found to lack robustness, prompting research to improve them. This was the start of the theory of Robust Control, which took shape in the 1980's and 1990's and is still active today.


Adaptive vs. Robust Control

Adaptive control does not need a priori

information about the bounds on uncertainties

or time-varying parameters.

Robust control guarantees that if the changes are

within given bounds the control law need not be

changed, while adaptive control is precisely

concerned with control law changes.


Optimal Control

Optimal control is a set of differential equations describing the paths of the state and control variables that minimize a “cost function”

For example, the jet thrusts of a satellite needed to bring it to desired trajectory that consume the least amount of fuel.

Two optimal control design methods have been widely used in industrial applications, as it has been shown they can guarantee closed-loop stability.

Model Predictive Control (MPC)

Linear-Quadratic-Gaussian control (LQG).


Variable Structure Control

Variable structure control, or VSC, is a form of discontinuous nonlinear control.

The method alters the dynamics of a nonlinear system by application of a high-frequency switching control.

The main mode of VSC operation is sliding mode control (SMC).


Intelligent Control

Intelligent Control is usually used when the mathematical model

for the plant is unavailable or highly complex.

The most two commonly used intelligent controllers are

Artificial Neural Networks

Fuzzy Logic


Intelligent Control: Fuzzy

Fuzzy set theory provides mathematical tools for carrying out approximate reasoning processes when available information is uncertain, incomplete, imprecise, or vague.

Fuzzy logic controllers manage complex control problems through heuristics (IF … THEN) and mathematical models provided by fuzzy logic, rather than via mathematical models provided by differential equations.

This is particularly useful for controlling systems whose mathematical models are nonlinear or for which standard mathematical models are simply not available


Fuzzy Control


Intelligent Control: ANN

Artificial Neural networks (ANN) are nonlinear mathematical models that are used to mimic the biological neurons in the brain.

ANN are used as black box models to map unknown functions

ANN can be used for: Identification and Control


ANN: Single Neuron

y

w0

w1

wM

x1

x2

xM

f(net)

M

mmmwxfy

1


ANN Architecture

x1

x2

…

xM

1

2

Q

1

2

N

z1

z2

zM

vij wjk

N

nnnk dzE

12

1


ANN: System Identification

In the identification process, the neural network is used to

approximate the nonlinear function. The structure of the

neural network plant model is given below, where the

blocks labelled TDL are tapped delay lines that store previous values of the input and output signals.

TDL

TDL

Weights

Weights

Activation

Function+ Weights +

Activation

Function

Plant

Output

Plant

Input

Net

Output

First Layer Second Layer


ANN: Identification and Control

IdentificationControl


ANN: Identification and Control

Hardware-in-the-Loop

Tarek A. Tutunji

Ashraf Saleem


Hardware-in-the-Loop (HIL)

Classical Mechatronic systems are composed of controllers, actuators, and sensors.

Some components can be substituted by its model and simulated in real time.

The simulated components can be run in conjunction with real components under the same environment.

This environment is regarded as HIL


HIL

Three-Stage Design

Procedure

Tarek A. Tutunji

Ashraf Saleem


Three-Stage Design Procedure

Stage 1 online identification

The system-under-test is identified online using ARMA models

Stage 2 controller design

Models are used in simulation runs to design the controller

Stage 3 online control

The designed controllers are tuned and applied to the system-

under-test in Hardware-In-The-Loop (HIL) environment


Three-Stage Design Procedure

Start

Connect

PC/DAQ to

the system

Approximate

Transfer

Function

using

ARMA / RLS

Design

Controller using

software

simulation

Tune and

Optimize

Controller

Apply

Impulse and

Measure

Response

Disconnect

system

Re-connect

PC/DAQ to

the system

Apply

Computer as

Controller

Fine-Tune the

Controller

End


Stage 1: Online Identification

Impulse

PC / DAQ

System

Identification

Simulink

ARMA ModelRLS Algorithm

Electro-mechanical

system under test

Drive

Circuit Sensor

A/D

System Response


Stage 2: Controller Design

Computer Simulation (using Simulink/Matlab)

Control SignalError Controller

Design

Identified

Transfer

Function

Reference

Model Response


Stage 3: Online Control

PC / DAQ

Designed

Controller

Simulink

Electro-mechanical

system under test

Drive

Circuit Sensor

A/DSystem Response

Control

Signal

Case Studies

Tarek A. Tutunji

Ashraf Saleem


Experimental Setup

Computer P4, 3GHz desktop MATLAB / Simulink

National Instruments DAQ card 6036E Sampling rate of 200 kS/s

Input voltage range of ± 10 V

Input signal to the system-under-test (PC output) was a voltage pulse.

The system response is the output (PC input)


Experimental Setup


Case Study: Induction Motor


Induction Motors

Due to their simple structure, reliability of operation and modest cost, the squirrel cage induction motors are the most widely used electrical drive motors.

Induction motors exhibit nonlinear dynamic behavior and therefore it is a challenge to establish an adequate mathematical model for controller design purposes.

The parameters of the induction motor may change during the operation of the drive system, causing deviations between the corresponding signals of the model and the motor.



22nd order model

6th order model


Testing of Open-loop Responses


Stage 2: Controller Design


Stage 2: Control Design

Online Control



Advantages of the Proposed Procedure

Accuracy in the identification model.

Flexibility in the controller design.

Optimizing time resources and minimizing the cost

The induction motor to be controlled will not be used during

the experimentation of the controller design and parameter

tuning and therefore the down time of the induction motor

will be minimized.

This might be a crucial time saving issue when the motor is

used production line. Equally important, damage to the

motor due to inappropriate parameter values is avoided.


Case Study: Pneumatic System


Pneumatic Systems

Pneumatic servo-drives play an important role in industrial mechatronic systems.

This is due to their cost effectiveness, easy maintenance, and clean operating conditions.

However, pneumatic actuators are characterized by high order time variant dynamics, nonlinearities due to compressibility of air, internal and external disturbances and payload variation


Experiment Setup


Online Control

0 100 200 300 400 500 600 700 800 900 10000

1

2

3

4

5

6

7

8

9

10

Time (ms)

Dis

pla

cem

ent

(cm

)

Real System Respnse with Kp=14, Ki=6, Kd=0.2

Real System Disp

Demand Position

Steady State Error


Particle Swarm


Cascade Control

0 500 1000 1500 2000 2500 30000

1

2

3

4

5

6

7

8

Time(ms)

Positio

n

Real PositionSimulated Position


Conclusions Identification and control play an essential role in the design of

mechatronic systems

System identification methods that use linear models, such as Auto-Regressive Moving-Average (ARMA), as well as nonlinear models, such as Artificial Neural Networks (ANN), were presented and compared.

Control methods that range from PID to intelligent controllers, such as fuzzy controllers, were presented and compared.


Conclusions

A three-stage procedure for the identification and control of mechatronic systems was presented.1. The system-under-test is identified online using ARMA models.

2. These models are used in simulation runs to design the controller.

3. The designed controllers are applied to the system using HIL.

Experimental results for two case studies were presented in order to demonstrate the advantages of the procedure.

Finally, an UAV project that used a similar procedure was presented to illustrate the procedure‟s practicality.

identification and control of mechatronic systems · identification and control of mechatronic...

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