QUALITY OF CONTROL --------- Guy Juanole LAAS-CNRS Universit de - - PowerPoint PPT Presentation

QUALITY OF SERVICE and QUALITY OF CONTROL

Guy Juanole LAAS-CNRS Université de Toulouse

TECHNOLOGICAL CONTEXT OF TODAY

• Distributed Computing Systems

 Computers, Communication network(s)  Many Kinds of Distributed Applications  Remote tasks sharing and using ressources ( CPUs, Memories, Links, Buffers)

• Process Control Distributed Applications

(Control over networks  Networked Control Systems) Closed loop structure Stability Requirement  Time constraints . Need of Real Time Distributed Computing Systems  Quality of Service (QoS)

Quality of Service (QoS)

• QoS mechanisms
• Computers: Task Scheduling
• Networks: Message (Routing, Buffering,

Scheduling,Transfer)

• QoS parameters
• Delays (Tasks, Messages): Access and

Use of ressources ( CPUs, Links)

• Losses (Messages): Use of ressources (Buffers,

Links)

Study 1

. Influence of the link layer of a local area network which is used in the feedback loop of a NCS  MAC sublayer (Frame scheduling based on static priorities)  three networks (CAN,FIP,ARINC)  LLC sublayer (Frame transfer protocol)  two protocols ( no loss control, loss control)

Regulation Application

+ _

Input Output Controller Process to control Local Area Network (LAN) Output Samples (period T0, Shannon Th.) Delay Losses Samples Received Producer task Consumer task

+ _

Input Output Controller Process to control Control signal

 Implementation through a distributed system

(Period T)

Distributed System and Process Control Architecture

Tranfer Function considering the Implementation

+ _

Input Output Delay τD Zero order hold Sampler (T0)

Phase Margin : for ω such that

Stability versus Frame Scheduling

Stability versus Frame Tranfer Protocol

Study 2

• Fundamental considerations for

implementing Regulation Applications on a Network Example of the network CAN (Frame Scheduling Problem)  Scheduling based on Static priorities * Two studies:Dedicated CAN; Shared CAN

Reference: a continuous regulation type

• Open loop transfer function G(s) = K/s(1+τ s)
• Closed loop transfer function
• Stability Criteria (Phase margin Фm) Фm = π + arg{G(jω)}

= π - π/2 – arctan (ωτ) for ω0 such that | G(jω)| = 1 Фm defines Damping ξ and Overshoot D%

• Sub class of this type which is considered

Фm = 65°  ω0τ = 0.47 , K τ = 0.51 , ξ = 0.7 , D% = 5% Process to control Controller

1 s(1+τ s) K

input+

• utput

Implementation on a Network Sensor task (T-T) ; Controller task ( E-T)

• External flows (3)
• Internal flows (sensor flow(1), controller flow(2))
• Delays for the internal flows
• Minimal Sampling Period

 Dedicated network: Intrinsic delay

•  Shared network: Intrinsic delay + Extrinsic delay

Controlle r

+ _

Network

T

C2 C1 C3 A D D A Z O H Process to Control (3) (3) (3) (3) (2) (1) Sampling

Considering the Network CAN (1Mbit/s)*

• Internal flows (periodic) of the regulation application

– Sensor flow frame : 72 µs – Controller flow frame : 72 µs – Sampling period Te : > (72 µs + 72 µs) 150 µs => Use Request ( UR) rate: (144/150 <1)

• One external flow (ef) : periodic

– One frame : 128 µs – Variable period >= 128 µs => to make to vary the global UR rate  to saturate the network

• Shared Network: To define Priority Schemes

– (Psf, Pcf) > Pef case 1: Psf > Pcf – Pef > (Psf, Pcf) case 2: Pcf > Psf – Pef comprised between the priorities of (Psf,Pcf) Two cases too: Psf >Pef >Pcf ; Pcf >Pef >Psf

• τd = τs (delay of the sensor frame) + τc (delay of the

controller frame) + Te/2 (delay of the ZOH module)  . Phase margin decrease : ω0 τd 180/π

• Families of transfer functions which can be

implemented on the network if the applications tolerate some “ damage “ in the performances  utiliser les relations: ω0 τ = 0.47 , K τ = 0.51 Study 2-1-1 : Dedicated CAN network Influence of the intrinsic delay τd in the loop  Families of admitted transfer functions

Upper bound of the phase margin decrease … 1O 5O 10O … ω0max(rd/s) 79 398 797 τmin (ms) 6 1.2 0.59 Kmax (rd/s) 87 429 874

Study 2-1-2 : Dedicated CAN network One regulation application ( tr # 1.8/ ωn) .Relation for tr : 4<( tr / Te)<10, Astrom relation

 tr = 4Te= 4 x150μs = 600μs

ωn= 3 103 rd/s => K= 2024 rd/s

• τ = 0.252 ms

Reference

Study 2-2-1 : Shared CAN network Previous regulation application and one external flow

(Psf, Pcf) > Pef

• case 1 Psf > Pcf
• case 2 Pcf > Psf

Period of the external flow (128µs) UR rate = 1

Study 2-2-2: Shared CAN network Previous regulation application and one external flow Explanation of the difference between the two cases case 1: Psf > Pcf case 2: Pcf > Psf

Study 2-2-3: Shared CAN network Previous regulation application and one external flow

Pef > (Psf, Pcf) Period of the external flow must be > 128µs  200µs

• Case 1 (Psf>Pcf)  cannot be implemented

Study 2-2-4 : Shared CAN network Previous regulation application and one external flow

Pef > (Psf, Pcf) Period of the external flow : 200µs

• Case 2 (Pcf > Psf)  can be

implemented

Study 2-2-5 : Shared CAN network Previous regulation application and one external flow

Pef > (Psf, Pcf) Period of the external flow : 500µs

Case 1 (Psf>Pcf) Case 2: Pcf > Psf

Conclusion of the study 2

• 1- Process control application with two flows

(sensor flow (sf) and controller flow (cf)): Result  Priority of cf > Priority of sf

• 2- In the case of high network load and , if the flows
• f a process control application have not the highest

priority, this application cannot get sufficient control performances and then cannot be implemented.

•  Necessity of a new priority scheme which

will allow to always implement such applications

Idea of a new priority scheme

• Static priority: « a priori » specification which does not

consider transient behavioural aspects (very important in a context of process control)

• Concept of « Needs » of a flow in terms of

transmission urgency  Constant, Variable (weak, strong)

• New priority scheme based on a pair : ( Flows, Needs)
• Concept of Priority threshold for the Constant Needs

( In order to not prevent very strong «variable needs» to be considered)

Hierarchical and Hybrid Priority Scheme: Data structure with two fields (levels)

T T

. First level  Flow priority (static) . Second level  Need priority (static if a constant need; dynamic if variable need). .A static priority is represented by one bit combination. .A dynamic priority can take several bit combinations. .Second level is examined at first. .Less scheduling power than with a flat data structure

Hierarchical and Hybrid Priority Scheme: Data structure with two fields (levels)

T T

. First level  Flow priority (static) . Second level  Need priority (static if a constant need; dynamic if variable need). .A static priority is represented by one bit combination. .A dynamic priority can take several bit combinations. .Second level is examined at first. .Less scheduling power than with a flat data structure

Example of Implementation in CAN

• m=7 (128 priorities for needs), n=4 (16 flows)

0000  Flow ef; 0001 Flow cf; 0010 Flow sf . Flow cf and Flow sf : Needs with dynamic priority They can take all the bit combinations ( 128 values) . Flow ef: Needs with static priority

• Priority threshold for the flow ef ( Pef )
• value 13: 90% of the maximum priority
• value 32: 75% of the maximum priority
• value 64: 50% of the maximum priority

How to express the dynamic priority ? Proposal

• Use of the Control Signal u of the process

control application

• Translation into a Priority by considering

an increasing function of the signal u characterized by a saturation for a value of u = 2/3 umax .

• The computation of the dynamic priority is

done by the controller and transmitted to the sensor (following figure)*

Implementing the dynamic priority

(Re-estimation at each sampling period)

Non Linear Functions considered for the expression of the dynamic priority

Study 3

• The Reference System .
• Summarizing results when implementation

with the network CAN and using the Static Priority Scheme for the Scheduling. * Considering the new Scheduling scheme

The Reference System

r(t) y(t)

The Reference System

• Open Loop Transfer Function →

r(t) y(t)

The Reference System

• Open Loop Transfer Function →
• Expected performances

damping ζ = 0.7 and

tresp = 100 ms,

(overshoot = 5%) (tr~ 40 ms)

→ K = 1.8 rd/s and Td = 0.032 s

• Control performance evaluation → using a cost

function

r(t) y(t)

Response Time (Reference System) J= 2,56 x10- 4 =J 0

Static priorities on CAN (Pef> Pcf >Psf) Results: J and ΔJ/J0

UR(%) J ΔJ/J0 30 2.773x10-4

8.11%

80 3.281x10-4

27.9%

90 5.331x10-4

52.6%

99 3.915x10-4

108%

100 1.445x10-3

463%

RESPONSE TIME with CAN

RESPONSE TIME with CAN

Conditions : UR = 100% Pef > Pcf > Psf

ΔJ/J0 : function f1

9.67% 8.07% 8.07% 80 0.23% 0.23% 0.0% 30 15.3% 15.3% 13.6% 90 73.5% 55.7% 46% 99 115.4% 102.9% 85.3% 100

Pef level: 90% Pef level: 75% Pef level: 50% UR(%)

8.07% 8.07% 3.35% 80 0.23% 0.23% 0.0% 30 15.3% 13.6% 6.63% 90 55.7% 29% 19.7% 99 115% 96.8% 55.7% 100

Pef level: 90% Pef level: 75% Pef level: 50% UR(%)

ΔJ/J0 : function f3

27.9% 80 52.6% 90 8.11% 30 463% 100 108% 99

ΔJ/J0

UR(%)

Static priorities

function f1 function f3

Time response with UR= 100% and Priority Threshold = 50% Pmax

Control Signal Dynamic priorities

Critical analysis of the Hierarchical and Hybrid Priority Scheme

Consequence of the previous analysis

• The oscillatory behaviour of the dynamic priority

shows that the initial correction action (higher priority) is insufficient in terms of DURATION

• Then the idea of increasing this duration
• If then the dynamic priority has a value

between Pmax and a value Pmax/2 , we keep this value during 4 sampling instants (~tr)

• If then the dynamic priority is inferior to

Pmax/2, we re-estimate it after each sampling instant ( as previously)

Study 4: HHP scheme + Time Strategy

• If the dynamic priority has a value

between Pmax and a value Pmax/2 , we keep this value during 4 sampling instants (~tr)

• If then the dynamic priority is inferior to

Pmax/2, we re-estimate it after each sampling instant ( as previously)

Control signal (HHP + TS) Dynamic Priorities (HHP+ TS

Adding a Time Strategy to the previous scheduling scheme

Time response (hhp+ts)

Time response with UR = 100% , Function f3 and Priority Threshold = 50% Pmax

Conclusion

• Necessity to characterize separately the Flows

and the Needs of the flows

• NCS  Flows have variable needs
• Variable Needs  Dynamic Priority
• Dynamic priorities linked to the Performances of

the Process Control applications

• Multidisciplinarity activity (knowledges in

Networks, Scheduling , Automatic Control)