Nonattendance educational strategies for nonlinear control

NONATTENDANCE EDUCATIONAL STRATEGIES FOR NONLINEAR CONTROL USING THE INVERTED PENDULUM ACE´06 7th IFAC Symposium on Advances in Control Education SERGIO GARCÍA-NIETO RODRÍGUEZ

1. INTRODUCTION Advances in Control Education 2006 2. Theory Concepts 3. Practice Guide 4. Experiments 5. Conclusions MAIN GOALS

Implementation of Hardware-Software platform for control practice with some characteristics:

Use nonlinear models.

Include real elements in simulation models (communication elements, actuators, sensors, etc).

Study of the real implementation problems.

Use Internet as flexibility tool.

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2. THEORY CONCEPTS 1. Introduction 3. Practice Guide 4. Experiments 5. Conclusions INVERTED PENDULUM I

The nonlinear model used in the virtual model.

Two nonlinear second order differential equations (Euler-Lagrange equations):

,

/20 where Advances in Control Education 2006

2. THEORY CONCEPTS 1. Introduction 3. Practice Guide 4. Experiments 5. Conclusions INVERTED PENDULUM II

The nonlinear second order equations:

with

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2. THEORY CONCEPTS 1. Introduction 3. Practice Guide 4. Experiments 5. Conclusions INVERTED PENDULUM III /20

The state space equations:

where

Advances in Control Education 2006

2. THEORY CONCEPTS Advances in Control Education 2006 1. Introduction 3. Practice Guide 4. Experiments 5. Conclusions INVERTED PENDULUM IV The Simulink model used in the virtual model. /20

3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions EQUIPMENT I

The xPC Mathworks software as Process:

Build Simulink model with basic structures.

Compile the model using Matlab compiler.

Transfer the compilation to the PC target.

Start the model.

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3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions EQUIPMENT II

The PC controller:

Desktop PC, with AMD-K6 400 MHz processor and 128 Mb RAM.

PCI-CAN 7841 ADLINK CARD.

The Linux kernel patched with RTlinux-GPL.

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3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions EQUIPMENT IV

The communication system:

CAN bus-CANOpen Protocol.

2 BK5120 BECKHOFF Industrie Elektronik GMBH CAN modules.

1 CAN-CBM-AI410 Esd electronic system design GMBH CAN module.

1 CANbloc-Mini Esd electronic system design GMBH CAN module.

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3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions SOFTWARE The SCADA developed with Java.

TCP/ IP protocol.

SSH communication.

Multiplatform.

GPL license.

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3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions HOW TO USE IT I

The steps for a correct use:

Starting Up.

Connection via Internet.

Establishes the communication with the controller.

Prepares the visualization elements.

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3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions HOW TO USE IT II

Selecting the controller.

Control Law 1 (a=2).

Control Law 3 (a=2, k=5).

where

/20 Aracil, J. and F. Gordillo (2004). The inverted pendulum: a benchmark in nonlinear control.

3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions HOW TO USE IT III

Selecting the controller.

where

/20 Aracil, J. and F. Gordillo (2004). The inverted pendulum: a benchmark in nonlinear control.

3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions HOW TO USE IT IV

Executing the application.

Starts the control system.

Transfers the data via Internet.

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3. PRACTICE GUIDE Advances in Control Education 2006 1. Introduction 2. Theory Concepts 4. Experiments 5. Conclusions HOW TO USE IT V

Saving dates.

Time.

Power.

Angle.

Angular speed.

Speed of the car.

Sample time.

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4. EXPERIMENTS Advances in Control Education 2006 1. Introduction 2. Theory Concepts 3. Practice Guide 5. Conclusions EXPERIMENTS I Aplication of control law 7:

Fixed oscillation.

Marginal stability.

Border cycle.

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4. EXPERIMENTS Advances in Control Education 2006 1. Introduction 2. Theory Concepts 3. Practice Guide 5. Conclusions EXPERIMENTS II Aplication of control law 8:

Zero speed of car.

Stability.

No border cycle.

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4. EXPERIMENTS Advances in Control Education 2006 1. Introduction 2. Theory Concepts 3. Practice Guide 5. Conclusions EXPERIMENTS CONCLUSIONS

Discrete control. The simulations have been made in the continuous time domain, while the platform works in the discrete time domain, with a fixed sample time.

Presence of signal interferences in the sensors and actuators . Another important problem is the magnetic noise. This component introduces appreciable differences between both signals (simulation and real) .

The resolution of the data acquisition card.The resolution of the variables in the simulations is 264 bits, while that resolution is 210 bits in the platform.

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4. EXPERIMENTS Advances in Control Education 2006 1. Introduction 2. Theory Concepts 3. Practice Guide 5. Conclusions PROPOSED EXPERIMENTS

Uncertainty Model : The students should modify the Simulink model in order to introduce some uncertainty. The students can evaluate the control behavior under model uncertainty.

Noise Signal : The inclusion of white noise plus the intrinsic noise in the real communication elements can described the system behavior in a high noise environment.