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 Controller Process to control Output Input + Control _ signal  Implementation through a distributed system Process to Output Input + Controller control _ Local Area Network (LAN) Output Samples Samples Received (Period T) (period T 0 , Shannon Th.) Delay Consumer task Producer task Losses

Distributed System and Process Control Architecture

Tranfer Function considering the Implementation Output + Input _ Sampler (T 0 ) Zero order hold Delay τ D 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 Controller Process to control 1 input+ output K s(1+ τ s) - - Open loop transfer function G(s) = K/s(1+ τ s) - Closed loop transfer function - Stability Criteria (Phase margin Ф m) Ф m = π + arg{G(j ω )} = π - π /2 – arctan ( ωτ ) for ω 0 such that | G(j ω )| = 1 Ф m defines Damping ξ and Overshoot D% - Sub class of this type which is considered Ф m = 65°  ω 0 τ = 0.47 , K τ = 0.51 , ξ = 0.7 , D% = 5%

� Implementation on a Network Sensor task (T-T) ; Controller task ( E-T) (3) (3) Process C2 Z D (2) + to O Controlle A _ r Control H C3 Network T C1 A D (1) Sampling (3) (3) • 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

Considering the Network CAN (1Mbit/s)* • Internal flows (periodic) of the regulation application – Sensor flow frame : 72 µ s – Controller flow frame : 72 µ s – Sampling period Te : > (72 µ s + 72 µ s)  150 µ s => Use Request ( UR) rate: (144/150 <1) • One external flow (ef) : periodic – One frame : 128 µ s – 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

Study 2-1-1 : Dedicated CAN network Influence of the intrinsic delay τ d in the loop  Families of admitted transfer functions • τ d = τ s (delay of the sensor frame) + τ c (delay of the controller frame) + Te/2 (delay of the ZOH module)  . Phase margin decrease : ω 0 τ d 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: ω 0 τ = 0.47 , K τ = 0.51 Upper bound of the phase … 1 O 5 O 10 O … margin decrease ω 0 max(rd/s) 79 398 797 τ min (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/ ω n ) .Relation for tr : 4<( tr / Te)<10, Astrom relation  tr = 4Te= 4 x150 μ s = 600 μ s  ω n = 3 10 3 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 Period of the external flow (128µs)  UR rate = 1 (Psf, Pcf) > Pef - case 1 Psf > Pcf - case 2 Pcf > Psf

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

� 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  200 µ s 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 : 200 µ s 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 : 500 µ s 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 of 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) . First level  Flow priority (static) . Second level  Need priority (static if a constant need; dynamic if variable need). T T .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) . First level  Flow priority (static) . Second level  Need priority (static if a constant need; dynamic if variable need). T T .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 ( P ef ) - 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 u max . • 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 r(t) y(t) • Open Loop Transfer Function →

The Reference System r(t) y(t) • Open Loop Transfer Function → • Expected performances t resp = 100 ms, damping ζ = 0.7 � and � � ( tr~ 40 ms ) ( overshoot = 5%) → K = 1.8 rd/s and T d = 0.032 s • Control performance evaluation → using a cost function

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

Static priorities on CAN (Pef> Pcf >Psf) Results: J and Δ J/J0 Δ J/J0 UR(%) J 8.11% 30 2.773x10 -4 27.9% 80 3.281x10 -4 52.6% 90 5.331x10 -4 108% 99 3.915x10 -4 463% 100 1.445x10- 3

RESPONSE TIME with CAN

RESPONSE TIME with CAN Conditions : UR = 100% Pef > Pcf > Psf