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Control Systems Lab SC4070

Lecture 4, February 20, 2012

dr.ir. Alessandro Abate

Delft Center for Systems and Control

Delft University of Technology

The Netherlands

e-mail: [email protected]

tel: 015 27 85606

(slides modified from the original, drafted by Robert Babuska)

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Lecture outline

Mitigating influence of nonlinearity over linearized control.

Real-time software.Simulink and Matlab issues.

Final tips.

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Influence of nonlinearity

Let us assume that a linear controller has stabilized the system

under study

However, some effects of the nonlinearity may still be visible

process nonlinearity

friction, stiction

You may try to improve the linear controller

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Influence of nonlinearity: helicopter example

u

y

10 15 20 25 30 35 40 45 50-0.2

0

0.2

0.4

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Nonlinear feedforward control

ux

Nonlinearfunction

Observer

Process-L

uc

y

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Nonlinear feedforward control: helicopter

0 50 100 1500.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

time [s]

[

rad]

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Effect of stiction in inv. pend.: linear control

0 10 20 30 40 50 600.5

0

0.5

time [s]

c

artposition[m]

0 10 20 30 40 50 600.2

0.1

0

0.1

0.2

time [s]

an

gle[rad]

0 10 20 30 40 50 601

0.5

0

0.5

1

time [s]

controlinput[]

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Real-Time Programming Issues

off-line vs. on-line vs. real-time

single process, multiple parallel processes

single-processor, multi-processor, distributed

time slicing, scheduling (priorities)

synchronization, communication

wait loop vs. interrupt driven

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Wait loop vs. interrupt driven

Interrupt handler

Code:A-D Conversion

Compute control variableD-A conversion

Wait for tick

Clock

Code:A-D Conversion

Compute control variableD-A conversion

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Real-Time Toolbox for MATLAB

PC

MatlabUser

Driver

Real-time toolbox

Real-time kernel(Windows)

Driver

Physical processto be controlled

Driver

Joystick A/D - D/ACard

Port Signal

conditioningPort

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Real-time Simulink templates

Check the version of Matlab installed (and stick to it)

Each setup has a Simulink template:

D:\Opstellingen\Pendulum1D:\Opstellingen\Pendulum2

. . .

D:\Opstellingen\Helicopter

Files:

...template.mdl(Simulink file)hwinit.mdl(Matlab script SW/HW definitions)

Copy all files to your own directory, remove read-only attribute

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More about the templates

Create your own files through menu: File / Save As ...

Scopes are configured to export data to Matlabs workspace

You may change the name through the Parameters icon

Save data in workspace by the command line command:

save filename

(for identification and model validation, presentation and re-

port)

To export data you can also use the To Workspace or To File

blocks

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Procedure

Switch off the setups electronics box

Reboot the computer (not absolutely necessary)

Start Matlab, change to your working directoryOpen your real-time Simulink file

(first time in the lab: open the template)

Switch on the setups electronics box

(with pendulum and wedge: first move the cart by hand to the

rightmost position and hold it there while switching the box on)Define in Matlabs workspace the sampling time, e.g.:

h = 0.1

Start experimenting (small amplitude input signals first)

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Running real-time experiments

Define suitable duration of experiment through the menu:

Simulation / Simulation Parameters / Stop time

Do not change the simulation methodStart simulation by thePlayarrow or pressCtrl-T

Do not click the mouse or drag windows around during experi-

ment

If the computer hangs . . .

first switch off the setups electronics box, then restart computer

If only Matlab terminates . . .

start Matlab again (do not restart the computer)

type: rtclear all; rtunload;

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Common Matlab and Simulink problems

Pole placement:place(A,B,P) . . . P must contain poles (not the polynomial)

do not define poles directly in discrete time

do not mix continuous and discrete time

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Vector dimensions mismatch in Simulink:

check Gain blocks (element-wise vs. vector)not all blocks can be vectorized

show vector dimensions, disconnect loops temporarily

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Vector dimensions mismatch in Simulink:

check Gain blocks (element-wise vs. vector)not all blocks can be vectorized

show vector dimensions, disconnect loops temporarily

Stability problems in RT experiments:check the order of states in RT and simulation model

run model in parallel with the process

make sure equilibrium coordinates properly defined

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Models linearization:

index number of the integrators changes usingtrimandlinmod.

alternative is using operpoint and linearize

1. in a Simulink modelsystem.mdl, set the state-values of the

desired equilibrium point as initial values of the integrators

2.op = operpoint(system) to extract the state informa-

tion linsys = linearize(system, op) to obtain a lin-

ear state-space model of your system

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Tips for presentations

Do not explain mathematical models in detail, do explain whatis measured and actuated.

Compare simulation and real-time results, evaluate critically.

Motivate all choices made (e.g., sampling, design parameters).

Stress own experience, inventions, discoveries, lessons learnt.

Be visual.

Max time to be decided.

Be prepared for questions.

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Tips for reports

Max 10 pages.

Include Table of content, Introduction and Conclusions.

Write concisely, do not include theoretical background.Stress own experience, inventions, lessons learnt. State contri-

butions of each team member.

Motivate all choices made (e.g., sampling, design parameters).

Compare simulation and real-time results, evaluate critically.

Plots:

use colors in presentations, but not in reports (use line types)

use the Matlab function plot, do not paste Simulink scopes

label axes (variables and units), provide figure captions

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Be rigorous with notations.

LaTeX preferred to Office Word.

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Literature, on-line resources

Do not hesitate to lookup articles relevant to your setup

TU Delft library

http://www.library.tudelft.nl/

IEEE Transactions and conference proceedings

http://ieeexplore.ieee.org/

Elsevier journals and conference proceedings

http://www.sciencedirect.com/

Use keyword search

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Questions ?

Documents

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