CACSD-Frame for Robust Low-Complexity Control Law Design

Copyright © IFAC Computer Aided Control Systems Design. Gent. Belgium. 1997

CACSD-FRAME FOR ROBUST LOW-COMPLEXITY CONTROL LAW DESIGN Georg Griibel DLR Institute of Robotics and System Dynamics, Control Design Engineering Group Obe rpfafJenhofen, D-8223.j WessIing, Germany

Contents. Robust low-complexity control laws design is the ultimate goal which Computer-Aided Control System Design (CACSD) aims for. We recognize seven classes of services CACSD tools and environments have to support w.r.t. this view: physical system modelling with modelling uncertainty descriptions; mathematical system modelling with suited uncertainty models; system model analysis in state space, time- and frequency domain; control law synthesis; multiobjective (multicriteria and multimodel) synthesis-parameter tuning; nonlinear assessment via simulation; control code generation. We deal with state of the art aspects of such services and their integration within an interactively controlled automatic design feedback loop. This is illustrated by experience gained during the two-years GARTEURa design challenge project on Robust Aircraft Flight Control, where 12 teams from 6 European countries demonstrated 11 different CACSD synthesis methods to design a landing-approach autopilot controller based on a Beluga-type aircraft model from Airbus Industries . 4Group for Aeronautics Research and Technology in Europe

DESIGN GOALS

PHYSICAL PLANT

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At the 1994 IEEE/IFAC Joint Symposium on Computer-Aided Control System Design, Prof. H. A. Barker proposed a reference model for a CACSD-software framework.

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In such a software framework, you may distinguish 7 classes of services to be supported within an open envlronme t: • • • • • •

process communication user Interaction application task control function tool control numerical algorithms model definition engineering data repository

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Here, I propose a reference model for DESIGN GOALS

a CACSD-task frame with 7 classes of services to be supported by tools:

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simulation experimenting [~.r ~~~.~ !y~~~ _~ii! HIW·tn·u,. loop

ALGOR . CONTROLLER

PHYSICAL PLANT

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CACSD services in the narrow sense (2) mathematical system modelling (3) linear system analysis (4) linear system synthesis

CACSD control (4 synthesis )

(2) plant analysis

[~near syntheSis . model I

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CACSD services in the narrow sense Remember: very first CACSD package ASP by Kalman & Englar, 1996; first software-engineered CACSD package VASP by White & Lee (NASA), 1971 direct VASP derivative: RASP (RUB, DLR), 1972 - now

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CACSD services in the wide sense = CACSD with links to real world

DESIGN GOALS

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CACSD

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synthesis ~

simulation experimenting nonlinear dosed-loo rapid pro to typing

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physical system- & uncert~i~ty. !110d~~_g

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ALGOR. CONTROLLER

PHYSICAL PLANT

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DESIGN GOALS

H/W-In-Ihe loop

rapid prololyplng

PHYSICAL PLANT

ALGOR. CONTROLLER

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7 CACSD services for supporting: (1) physical system modelling with uncertainty descriptions (2) mathematical system modelling with uncertainty models (3) linear system analysis in state-, time- & frequency domain (4) control law synthesis (5) multiobjective synthesis parameter tuning (6) nonlinear assessment via simulation ~

(7) automatic control code generation

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Lecture Notes i n Contro l and Informatio n Sc i ences 224 Spr i nger 1997

Aircraft (real world) example GARTEUR Design Challenge on Robust Flight Control

• robust, low-complexity • autopilot for landing approach scenario: ~

mass c.o.g. (x) ~ c.o.g. (z) ~ 'r (EFCS) ~ air speed enqine failure (1) L\

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(1) Physical system modelling Need for a unified representation of hybrid systems: causal as well as acausal models

• causal models: ~

signal flow e.g. control block diagrams

• acausal models: energy flow ~ interconnected physical objects

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System modelling: aircraft example (1) Controlled aircraft

plant sensor

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(1) Physical system modelling Object-oriented system modelling is part of the solution. Engineering systems can be modelled • graphically ('pick & drag') by • domain-specific icons & • component object diagrams.

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System modelling: aircraft example (2) Flight dynamics

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Object-oriented modelling: Component class libraries for e.g. block diagrams, basic electrical components, drive train components, multi body mechanical systems, aircraft flight dynamics, finite state machines & petri nets, etc. (hltp:llwww.op .dlr.de/FF-DR-ERI)

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Object-oriented modelling: Local object encapsulation of data & equations makes generic know how easily reusable in application-specific system aggregations of different kind. multi-disciplinary computer-processable model documentation

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Modelica

Object-oriented symbolic modelling language a European initiative supported as EUROSIM Techn. Committee, combines & extends the goodies of Oymola, Omola, NMF/IOA, gPROMS, SlOOPS, 20SIM, ALLAN, Smile release with compilers in September 1997 http://www.dynasim.se/Modelica/

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(1) Physical system modelling ~ (2) Mathematical system modelling Object-oriented symbolic modelling is the solution: + Symbolic models can be parameterized w.r.t. parameter-uncertainty bounds. + Symbolic processing concurrently of differential, algebraic & boolean equations. + Symbolic reduction of big, sparse DAE systems to state equations or index-l DAEs, ~

which can be efficiently simulated, linearized, standardized (e.g. lFT)

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System modelling: aircraft example (4)

LFT model for 11 analysis perturbations

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plant

parameter bounds: /1 mass /1 c.o.g. (x) t,. c.o.g. (z) t,. delay t,. complex perturbation

controller

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Computer-aided LFT generation from parameterized symbolic model

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Physical/mathematical system modelling & code generation

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neulral OSbtock Simulation

model

Fortran, C Code

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automatIcally generated

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(3) Linear system analysis in state-, time- & frequency domain Needs for: • well conditioned methods • stable & efficient numerical algorithms • robust, portable software implementation This requires a coordinated effort (WGS) ---7 NICONET

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NICONET (WGS) Network for performant numerical software development in Control Engineering (OLR) based on RASP Library SLlCOT Library (NAG) et a!.

see paper by S. van Huflel and A: van den Boom this conference

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Linear system analysis: aircraft example (1)

e.g. 11 stability-robustness analysis

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(4) Control law synthesis 3 different ways of control law synthesis: • develop a domain-specific control structure with controller tuning parameters T • choose an analytic synthesis method with' method tuning parameters T • specify control by linguistic rules (fuzzy-logic) with method tuning parameters T.

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Control law synthesis: aircraft example

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(5) Synthesis-parameter tuning

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structural synthesis P T analytical synthesis P = I (T, synthesis model) -t problem 01 "nominal" synthesis model

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(5) Multiobjective synthesis-parameter tuning

multiobjective:

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multi criteria multi models

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Interactive multicriteria compromising evaluation criteria c, > 0 ideal point: c, = 0 pareto-optimal solution set

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multicriteria: aircraft example

Specifications

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Multi-Criteria

step: zero steady state error settling time< 45 5

min

Handling qualities: 0.28 < CAP < 3.6

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Control rate: <25

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Interactive search in criteria space

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Multicriteria visualization

Parallel Coordinates make high dimensional criteria vectors visible

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best compromise solution

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concurrency

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Multimodel robust design: 1) discretize system dynamics continuum due to parameter uncertainties by 'worst-case' design models 2) find a common controller simultaneously for all 'worst-case' design models ~

model-concatenated multicriteria problem

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Synthesis-parameter tuning: aircraft example

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Synthesis I Design Methods GARTEUR Design Challenge on Robust Flight Control

Industrial Evaluation ENo,1

R.....'ks

2 .6

3.4

2.8

high-order controller,

FuzzV Logic Conlrol

3.0 2.9 3.9 3.7

3:3 3.5

inle,.sling paI.nlial nonline., feedback dillicull design erile,l. lormulallon

Classical Conlrol Model Following

3 .3 3 .1 3.0 3.4

3.9

'rel.rence' design clear cut conlrofter structure;

MOPS

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4.3

easy formulation

Modal Conlrol

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at desjgn criteria

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2 unsatisfactory. 3 acceptabfe. 4 favourabfe. 5 highfy favourabfe

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(6) Nonlinear assessment via simulation

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(7) Automatic control code generation

(6) Nonlinear assessment via simulation

lateral controller

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(7) Automatic control code generation

-- Pr~d~~t-6bj~~tiv~~ - -I 1 & Design Variables ----J fSpecilicalion ~~ 1_

Multidisciplinary Control/Dynamics Engineering & Simulation

~S.Control-Unit Engineering~r-

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& Development --- ----------

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hardware-software co-design with certification

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Concluding Remarks Cost-efficient engineering solutions aim at performant, robust, low-complexity controllers. This requires CA-support of complex control engineering design processes by CACSD services in the 'wide sense', i.e .... & • physical/mathematical modelling with uncertainty engineering • multiobjective goal attainment with requirements engineering • nonlinear, mission oriented evaluation with ass9ssment engineering • certified control code generation with H/W-S/W Co-design

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