Transcript D. Parameterization for Gain Scheduling: Actual IP Network Delay

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:
Dr. Chi-Jo Wang
Student:
Edith-Alisa Putanu, 普愛麗
M972B205
Authors: Yodyium Tipsuwan, Mo-Yuen Chow
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL 51, NO 6, DEC 2004
1
Outline
I.
Abstract
II.
Introduction
III.
System Description
IV.
Case Study: GSM for PI DC Motor Speed
Controller
V.
Simulation Results
VI.
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
A. External Gain Scheduling

System dynamics of a remote system to be controlled:

Controller rule: u  g ( y, pu )
x  R n - state variable of the remote system
y  R m - remote system output
u  R z - controller output
p x  R w- remote systems parameters
pu  R r - controller parameters
  R r - a variable gain used to adjust
q  R d - network variable representing network traffic conditions
III. System Description
A. External Gain Scheduling

A method to compensate network delay effects is to adapt pu externally
by finding   R z

A relation between

We will obtain simulation or experimental data, then apply a lookup table
 and  is complicated to find
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
A. Problem Formulation

Continuous time approach, first assuming IP network delays constant.
IV. Case Study: PI DC Motor
Speed Controller
B. DC Motor Model

The dc motor transfer function used:


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 ( K P , K I )  ( K 0 P , K 0 I )  (0.1701,0.378)
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)
 1 J  0
IV. Case Study: PI DC Motor
Speed Controller
C. Parameterization for Gain Scheduling: Constant Network Delay
 With network delays   1 may no longer be optimal
 A feasible set of  is estimated by the root locus analysis
   CP   PC
n4
  0.1,0.2,0.5
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
w1  1.64902
w2  0.00833
w3  0.01395
  0.1,0.2,0.6 sec
t f  10 sec
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
E[ ]    
q    
T

- median of RTT delays
 The controller used in the real IP network environment has to be a discretetime 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
Thank You for Your Attention!