seminar telematiksysteme für fernwartung und ferndiagnose basic concepts in control theory msc. lei...

Seminar Telematiksysteme für Fernwartung und Ferndiagnose

Basic Concepts in Control Theory

MSc. Lei Ma

22 April, 2004


How a controller works

Introduction


Example: Cruise control

Introduction


Basic principles of control theory

• Modeling of systems• Analysis of system behavior• Controller synthesis

Introduction


What is a dynamic system

• Ein dynamisches System stellt eine Funktionseinheit dar zur Verarbeitung und Übertragung von Signalen (z.B. in form von Energie, Material, Information, Kapital und anderen Größen), wobei die Systemeingangsgrößen als Ursache und die Systemausgangsgröße als deren zeitliche Auswirkung zueinander in Relation gebracht werdem. (H. Unbehauen)

Introduction


Differential equation

vy

ubvvm

)(1

)1(

1

)(

01

)1(

1

)(

0 nmxbxbxbxbyayayaya mm

mm

nn

nn

Modeling of dynamic systems


Transfer function

• The transfer function of a linear, time-invariant, differential equation system is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input under the assumption that all initial conditions are zero.

)()(

1

)(

)()()()(

:

sVsY

bmssU

sYsUsbVsmsV

systemcontrolCruise

nnnn

mmmm

asasasa

bsbsbsb

sX

sYsG

11

10

11

10

)(

)()(



Modeling in state space

• State space model of a system consists of a couple of first-order differential equations.

duxcy

u

u

u

b

x

x

x

A

x

x

x

T

mnn

2

1

2

1

2

1

vy

um

vm

bv

1



State space model



Time response• Transient response

• Steady-state response

Performance of linear, time-invariable systems


Time response of the cruise



Stability

• A linear time-invariant system is stable if the output is bounded and eventually comes back to its equilibrium state if the system is subjected to an initial condition.

• A linear time-invariant system is asymptotic (Lyapunov) stable, if none of the eigen values of the system matrix A has positive real part.



PID controller

• Proportional-Integral-Derivative controller

eKu P

dteKeKu IP

dt

deKeKu dP

s

KsKsKsK

s

KK IPd

dI

P

2

Controller synthesis


PID controller

CL RESPONSE RISE TIME OVERSHOOT SETTLING TIME S-S ERROR

Kp Decrease Increase Small Change Decrease

Ki Decrease Increase Increase Eliminate

Kd Small Change Decrease Decrease Small Change



Cruise with PI controller



State-feedback controller



State observer


Control system with observer



Some kind of controller

• Regulator

• Tracking control

• Force control



A basic teleoperator setup

Basic of teleoperation


Control of teleoperator



Time delay in control system

• introduced by e.g. transportation and communication lags, feedback delays, etc

• Leads to oscillation in the control loop• Even destabilizes the system



Time-delay in teleoperation

• Cause– Transmission in space and undersea

– Communication via Internet

• Variable time-delay– Variable distance and depth

– Bandwidth of comm. channel

– Protocols



Main references

• Lunze, J. Regelungstechnik. Springer1996.• Ogata, K. Modern Control Engineering. 4th Ed.

Prentice Hall 2002.• Munir, S. (2001). Internet-Based Teleoperation.

PhD. Thesis, Georgia Inst. of Tech..


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seminar telematiksysteme für fernwartung und ferndiagnose basic concepts in control theory msc. lei...

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