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SOUTHERN TAIWAN UNIVERSITYELECTRICAL ENGINEERING DEPARTMENT

Gain Scheduler Middleware: A Methodology toEnable Existing Controllers for Networked Control

and Teleoperation—Part I: Networked Control

Professor: Student: Dr. Chi-Jo Wang Edith-Alisa Putanu, 普愛麗 M972B205 Authors: Yodyium Tipsuwan, Mo-Yuen Chow IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL 51, NO 6, DEC 2004

I. Abstract

II. Introduction

III. System Description

IV. Case Study: GSM for PI DC Motor Speed

Controller

V. Simulation Results

VI. Conclusions

Outline

I. Abstract

Control over a network implies the need of an algorithm to compensate network delays effects

Usually the existing controller has to be replaced, which is costly, inconvenient and time consuming

A novel methodology is proposed to enable existing controllers for networked control

A gain scheduling algorithm modifies the output of the controller with respect to the current network traffic conditions

II. Introduction

Rapid advancement in communication networks, especially Internet and therefore, in control applications such as teleoperation or remote mobile robots

Network delays can degrade performance and even make systems become unstable

Middleware is a implementation that links applications or function calls together

In the proposed methodology the middleware modifies the controller output based on gain scheduling

III. System Description

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A. External Gain Scheduling

System dynamics of a remote system to be controlled:

Controller rule:

- state variable of the remote system

- remote system output

- controller output

- remote systems parameters

- controller parameters

- a variable gain used to adjust

- network variable representing network traffic conditionsd

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n

Rq

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Ry

Rx

A. External Gain Scheduling

A method to compensate network delay effects is to adapt externally by finding

A relation between and is complicated to find

We will obtain simulation or experimental data, then apply a lookup table

B. Gain Scheduler Middleware (GSM)

Basic Components:

• Network Traffic Estimator

• Feedback Preprocessor

• Gain Scheduler

III. System Description

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B. Gain Scheduler Middleware (GSM)

Network Traffic Estimator – monitors and estimates current network traffic conditions q, used by feedback preprocessor or/and gain scheduler

Feedback Preprocessor – preprocesses data such as motor speed and current (filters noises, predicts remote system states).

Gain Scheduler – modifies the controller output, with respect to current network conditions, q

III. System Description

IV. Case Study: PI DC Motor Speed Controller

A. Problem Formulation

Continuous time approach, first assuming IP network delays constant.

Assumptions regarding the PI controller, with step response:

• percentage overshoot (P.O.): P.O. 5%

• settling time (ts): ts 0.309s

• rise time (tr): tr 0.117s

Using root locus design approach, without considering network delays, feasible choice of

IV. Case Study: PI DC Motor Speed Controller

B. DC Motor Model

The dc motor transfer function used:

)378.0,1701.0(),(),( 00 IPIP KKKK

IV. Case Study: PI DC Motor Speed Controller

C. Parameterization for Gain Scheduling: Constant Network Delay

In order to evaluate the best system performance with respect to under different IP network conditions, the next cost function has to be minimized:

MSE0 – nominal mean-squared error

P.O.0 – nominal percentage overshoot

tr0 – nominal rise time

e(k) = y(k) – r(k)

01 J

C. Parameterization for Gain Scheduling: Constant Network Delay

With network delays may no longer be optimal

A feasible set of is estimated by the root locus analysis

IV. Case Study: PI DC Motor Speed Controller

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C. Parameterization for Gain Scheduling: Constant Network Delay

Result: a longer delay gives a smaller feasible set of

Optimal for a specific delay will be found by iteratively running simulations with various in the feasible region, and comparing the cost of J

IV. Case Study: PI DC Motor Speed Controller

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D. Parameterization for Gain Scheduling: Actual IP Network Delay

Actual IP network delays are not constant, but stochastic and not necessarily continuous in nature

Round Trip Time (RTT) are measured from an Ethernet network in Advance Diagnosis And Control (ADAC) Laboratory for 24h as follows:

IV. Case Study: PI DC Motor Speed Controller

D. Parameterization for Gain Scheduling: Actual IP Network Delay

IV. Case Study: PI DC Motor Speed Controller

The controller used in the real IP network environment has to be a discrete-time PI controller

The optimal has to be established again for the discrete PI controller, but it can be searched in the same feasible set as in continuous time

The sampling time is defined T = 1 ms, so that the behavior is close to the one in continuous time

D. Parameterization for Gain Scheduling: Actual IP Network Delay

The histograms skew to the left, indicating also probability

To investigate how the stochastic behavior affects the optimality of , RTT

is modeled by the generalized exponential distribution

IV. Case Study: PI DC Motor Speed Controller

Tq

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][ - median of RTT delays

D. Parameterization for Gain Scheduling: Actual IP Network Delay

IV. Case Study: PI DC Motor Speed Controller

V. Simulation Results

The performance of the proposed GSM is verified by simulations in Matlab/ Simulink 6.1

Environment:

• steady state reference value c=1

• final simulation time 10s

• sampling time of the PI controller, GSM and plant T=1ms

• number of packets to evaluate the characteristic of RTT delays N=100

Three scenarios are simulated, and the following costs J are obtained:

V. Simulation Results

VI. Conclusions

The paper proposed the concept of external gain scheduling via the GSM

The GSM changes the controller output with respect to the current network traffic conditions

The PI control system is initially formulated with constant network delays, approximated by rational function

The concept is extended for actual IP delays based on RTT measurements and the generalized exponential distribution model

Under reasonably long random IP delays, the GSM can adapt the controller gain suitably and maintain the system performance in a satisfactory level

Thank You for Your Attention!