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

Outline Abstract Introduction System Description Case Study: GSM for PI DC Motor Speed Controller Simulation Results Conclusions

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 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

III. System Description 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

IV. Case Study: PI DC Motor Speed Controller Problem Formulation Continuous time approach, first assuming IP network delays constant.

IV. Case Study: PI DC Motor Speed Controller 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 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: MSE0 – nominal mean-squared error P.O.0 – nominal percentage overshoot tr0 – nominal rise time e(k) = y(k) – r(k)

IV. Case Study: PI DC Motor Speed Controller 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 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 - median of RTT delays 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

IV. Case Study: PI DC Motor Speed Controller D. Parameterization for Gain Scheduling: Actual IP Network Delay

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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