1 SOUTHERN TAIWAN UNIVERSITY ELECTRICAL ENGINEERING DEPARTMENT Gain Scheduler Middleware: A Methodology to Enable 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 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 conditions

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

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 (t s ): t s 0.309s rise time (t r ): t r 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:

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: MSE 0 – nominal mean-squared error P.O. 0 – nominal percentage overshoot t r 0 – nominal rise time e(k) = y(k) – r(k)

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

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

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 - 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

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