Process and apparatus for determining optimum values for manipulated ...

United States Patent

Ttesp et al.

US005751571A [ii] Patent Number: [45] Date of Patent:

5,751,571 May 12, 1998

[54] PROCESS AND APPARATUS FOR

DETERMINING OPTIMUM VALUES FOR
MANIPULATED VARIABLES OF A
TECHNICAL SYSTEM

[75] Inventors: Volker Tresp, Miinchen; Bernd

Schurmann. Haimhausen; Martin
Schlang. Mtinchen, all of Germany

[73] Assignee: Siemens Aktiengesellschaft, Munich.
Germany

FOREIGN PATENT DOCUMENTS

[21] Appl. No.: [22] PCT Filed: [86] PCT No.: §371 Date:

[87]

[30]

[51] [52]

578,600
Jul. 1, 1994
PCT/DE94/00762
Jan. 4,1996

§ 102(e) Date: Jan. 4,1996
PCT Pub. No.: WO95/02213
PCT Pub. Date: Jan. 19,1995

Foreign Application Priority Data
Jul. 5, 1993 PE] Germany 43 22 365.6

Int Cl.6 G05B 13/04; G06F 15/18

U.S. Cl 364/148; 364/149; 364/157;

395/21; 395/906

[58] Field of Search 364/148. 149-151.

364/152-159. 164. 165. 176. 178. 179; 395/21-23. 904. 905. 912. 913. 919. 906

[56] References Cited

U.S. PATENT DOCUMENTS

5,016,188 5/1991 Lan 364/172 X

5,159,660 10/1992 Lu et al 364/148 X

5,353,207 10/1994 Keeleretal 364/164

5,414,619 5/1995 Katayama et al 364/151

5,428,559 6/1995 Kano 364/151 X

5,513,098 4/1996 Spall et al 364/157 X

OTHER PUBLICATIONS

Advances in Instrumentation, vol. 41. No. 2. (1986). "A
Modular Self-Tuning Control System", J.D. Lane, pp.
639-651.

Proceedings of the 1992 IEEE International Symposium on
Intelligent Control. Aug. 1992. "Least Mean Square Learn-
ing in Associative Memory Networks", M. Brown and C.J.
Harris, pp. 531-536.

Automatisierungstechnik at 37 (1989) 2. Modellgestuetzte
Regelungskonzepte: Ein Vergleich, (Model-based control
schemes: a comparison) P. Ronge, pp. 74-84.

Primary Examiner—Joseph Ruggiero

Attorney, Agent, or Firm—Hill, Steadman & Simpson

[57] ABSTRACT

Optimum values for manipulated variables sI ss of a

technical system (()>) are determined for prescribed operational variables bj(... ,bfl in order to optimize a prescribed

target function z=g(y2. .. .yN) of system properties y2

yN where y,=<t>,(Si.. • • -Sj-b, bB). Here, a set of functions

f^Wj.... ... . . . Jls=b) is used whose parameters wt, ... .w,,, are set in such a way that the functions f, model the system in such a way that the functions f, approximate the system functions <(>i as functions of their variables Xj.

xs+fl in terms of an interval of prescribed magnitude; the

manipulated variables s1( . . . .ss are determined by optimizing the function g(f1(w1,.. . .w,^ Sj.bj bB),

.... f/vCWj,. . . ,wh,,si ss,bL, . . . ,bB)) at fixed values

of wt. . . . ,wh, and bj bB.

9 Claims, 1 Drawing Sheet

5.751,571

1 2

PROCESS AND APPARATUS FOR functions f; model the system in such a way that the

DETERMINING OPTIMUM VALUES FOR functions f, approximate the system functions <|>i as functions

MANIPULATED VARIABLES OF A of their variables ^ \S+B in terms of an interval of

TECHNICAL SYSTEM prescribed magnitude and the manipulated variables s,,

5 . .. ,bs are determined by optimizing the function gCf/w,,

BACKGROUND OF THE INVENTION ww-si ss-br b«) f;v(wi- • • • -ww- si- • •

„. . . ,s,.b, b»)) at fixed values of w, w^ and b,, . .

The invention relates to a process for determining opti- b The technical system is therefore represented, for the

mum values for manipulated variables of a technical system purpOses of optimization, by a parametric function model

(<(»). In mis context, such a technical system can be of any whose parameters have been adapted in such a way that the

desired, for example electrical, mechanical or chemical function modei approximates the technical system with

nature and many others. An example of such a system (0) is adequate precision. As a result, the measurements of the

an internal combustion engine for motor vehicles, for system properties which are necessary for the adaptation of

example a gasoline engine which is to be optimized with me parameters are separated from the actual optimization

respect to some of its system properties yi y» such as process y^ measurements can therefore be carried out

for example the emission of NOX (nitrogen oxides), the under particularly favOrable conditions which—in contrast

emission of CO (carbon monoxide), the consumption of fuel to measurements for experimental optimizations—are no

or the engine power etc. Here, these variables y,.... ^ are longer influenced by the requirements of the optimization

weighted to different degrees in a global, possibly nonlinear process

target function z=g(Vl y*) which is to be optimized in Furthermore, this process has the advantage that

its entirety

J' the target function can be varied without the parameters

The system properties Yl yN usually depend on the f the set of functions f (w w ^ .

operating conditions of the system. The latter are character- x -. having to be reset

ized by operational variables b,. . . . ,bfl (for example ^ ' £* cafl ^ ^^ at'vark)US worki ints b

rotational speed, torque, etc. in me case of a gasoline engine) ^ varfous Ferational variables without additional

and by manipulated variables s, s5 (for example ignition .,

angle, injection time etc. in the case of a gasoline engine). °U. y.' . , ., . , ,

The operational variables are prescribed here by wishes of a m e3UStlng **.*"* modf* f"^tion set) can be used as a

user orother circumstances. In me case of a gasoline engine «"*** Pou" ^ modeUing further systems and thus

the driver prescribes a rotational speed using the gas pedal. T for accelerating the modelling of further systems,

for example, in order to travel at a specific speed with a 3° to 8eneral terms the fes(f Ulventlo1n l* a Pr<*fss *or

selected transmission ratio. The manipulated variables s, . determining optmuun values for manipulated variables of a

. . ,ss must be set (that is to say in this example the engme tfdu^"1 ^tef for Prescribed operational variables with

must be controlled) in such a way that the desired or ** obJectlve of "I*TM* a prescribed target function of

prescribed operational variables are also actually set. ^^ Pr°Pf^es «at are a function of the manipulated _ . „ , , . .. , .35 vanables and the operational variables. A set of functions is

There is generally no clear solution to this problem. As is used whose ^ ^ set such mat &e 6uuiaom modei

generallyknown there are sporty and economical motor me m such ^ ^ ... a^Md]nate me system

vehicle drivers. Therefore, depending on the setting of the ^J^ as ^^ of ^ ^^ in tenns 'rf an

manipulated vanables st, . ,ss, different values for the intervaiofprescribedmagnitude. The manipulated variables

system properties yt,... ^for example fuel consumption. ^ are determined b op^^g ^ set of functions at fixed

emission of pollutants etc.) and thus different values for the yalues rf (he ^^ ^ me operational variables,

target function z=g(y,.. . . .y,,) are obtained widi the same Advantageous developments of the present invention are

operational vanables bL,... ,bfl. Therefore, it is desirable to as follows

set the manipulated variables in such a way that the pre- The s£t of 6uteaom is represented by an artificial neural

scribed target function is optimized. 45 ne(work of by a taWe of nu^ericaj va[ues which is stored

In the least commercially interesting technical systems, in a storage unit of a data processing system, or by an

the relationships y,=<|>,<Si Sj.bi bg) between the electronic drcuit arrangement which is a component of an

manipulated variables and operational variables on the one electronic data processing system that carries out the

hand and the system properties on the other are known process, or which interacts with such an electronic data

quantitatively in closed form. For this reason, for optimiza- 50 processing system.

tion one is generally obliged to have recourse to experiments Tbe process is used in one embodiment for controlling a

with the technical system itself. Such experiments are fre- technical system. The target function is the control error of

quently too expensive or are impossible for reasons of a controller and the manipulated variables of the controller

safety. being identified using this process.

SUMMARY OF THE INVENTION 55 The P16561* invention is also a control system for controlling a technical system using a controller with the

The invention is based on the object of disclosing a following features. The controller identifies manipulated

process for determining optimum values for manipulated variables for the system to be controlled (by means of

variables of a technical system in the aforesaid context, prescribed values for operational variables of the system to

which process can be carried out without experimenting so be controlled) by minimizing a control error. The system to

with the technical system and without a system model in be controlled supplies measured values for system properties

closed form having to be available. that are a function of the manipulated variables and the

According to the invention, this object is achieved by operation variables. The system properties are themselves

means of a process for determining optimum values for used to determine the control error. The control error is

manipulated variables of a technical system. In this process, 65 minimized by means of the following measures. A set of

a set of functions fXw,... . .w^jCj,... Jls+b) is used whose functions is used whose parameters are set such that the

parameters Wj ww are set in such a way that the functions model the system such that the functions approxi

5,751.571

3 4

mate the system functions as functions of their variables in arrangements. Such specific circuit arrangements can interterms of an interval of prescribed magnitude. The manipu- act with a data processing system in order to implement the lated variables are determined by optimizing the set of invention. The aforesaid properties of neural networks are functions at fixed values of the parameters and the opera- known to the person skilled in the art from the extensive tional variables. 5 literature on artificial neural networks.

The control error is identified from the system properties Once the parameters of such a function system have been

and from desired values for these system properties. The set in such a way that this function system models, that is to

control error is identified from system properties and from say approximates with adequate precision, the technical

desired values for these system properties. system under consideration, the function system can be used

10 in a specific embodiment of the invention to generate a table

BRIEF DESCRIPTION OF THE DRAWING of niTmericai values which contains the values of ^ &<,

The features of the present invention which are believed functions of the system for a sufficiently large number of

to be novel, are set forth with particularity in the appended values of its variables K! xs+fl as entries. For the

claims. The invention, together with further objects and purposes of the invention, this table then represents the

advantages, may best be understood by reference to the 15 function system. It has the advantage that it can be stored for

following description taken in conjunction with the accom- example in a storage unit of a data processing system. As a

panying drawing, in which: result, there is no longer a need for processing power or

The single FIGURE shows a control system with a closed sPeciflc circuit technology for calculating function values,

control loop for controlling a technical system, the controller A function system of the type mentioned above can

identifying the manipulated variables using the process 20 however also be represented by specific software routines

according to the invention. which can be executed by a data processing system in order

to implement the invention.

DESCRIPTION OF THE PREFERRED Which function system the person skilled in the art will

EMBODIMENTS select in order to model a given technical system and how he

For tms purpose, a technical system (<j>) is considered, for 25 wil1 represent this function system for a specific

example a gasoline engine which is to be operated with application—as a table, as a specific circuit, as a software

prescribed operational variables b, bB. By suitably routine etc—depends on the specific conditions of the

selecting the values of a number of manipulated variables. application.

the system can be transferred to the operating state b1% Such a model of a technical system in the form of a

... .b^. In this operating state, the system has the properties parametric set of functions is used according to the invention

yi yN where yH>,<Si s^,. . . ,bB). In a given to replace this technical system for the optimization of the

operating state, the properties of me system are therefore ^S61 function Z=g(y,. . . . .y^) in such a way that the

still dependent on the values of the manipulated variables. manipulated variables sx ss are determined by opti

In most technical systems. Ihe selection of the manipu- 35 mizing the function gfffa, .. w^ s^. . ba).

lated variables is not unambiguous for prescribed opera- • ; • >f~<wi TM*-si t 1- •' ' ' ' fl)) *

tional variables; instead, the manipulated variables can be f wi-' • vww andbi V By «?u* of mjs replacement.

set in very different ways and the prescribed operating state ** *""*** ^^ ?"> of *c ""^own W***

is nevertheless obtained. Generally, one will therefore want Properties y» yw becomes a function of the known

to select the manipulated variables in such a way that the „, Parameters Wl ww and operational variables bx, ,bB

system properties are optimized in such a way that a to be fixed and of the mampulated variables^ ss which

prescribed target function z=g(yi Yjv) is optimized. are to be determined and varied.

The invention achieves this object using a suitable set of . .*»? sdtable optimization process can be used to optimize

functions f,.(Wl w^, xs+B) which approximates tlus fuactloa- *fge numbers of very different optimization

the system or the system function? yH^- . ,ss.bl. 45 Processes are taown to Ae person staUed in tiie art from the ... 4>*> in terms of an interval of prescribed magnitude. Such mathematical literature for engineers. Which of these profunction systems, which depend on parameters Wl.... .ww <jesse*ls Particularly suitable m a concrete appkcation and with which the behaviofof any technical system can be dePcnds on *e sPeclflc condltlons of this application, modelled within any prescribed range of precision, are One possible optimization process is the so-called process known in large numbers to the person skilled in (he art. 50 of steePest descent' This Process is appropriate if the Examples of these are orthogonal function systems, inter- searched for optimum of the target function to be optimized polation polynomials, spline functions etc. In the standard is a local optimum (local minimum or maximum), and if the works on numerical mathematics for engineers or those on tar8et ^^^ is adequately smooth. Here-starting from approximation theory, the person skilled in the art will find initial estimated values sO/i of the manipulated variables Sl, a large number of numerical techniques for determining the 55 ' ' ' -s* which must Ue " the domain of auction of the

parameters w, w^for which a selected function system searched for optimum—the manipulated variables are incre

approximates. that is to say models, a given technical system mentally changed according to the schema: with adequate precision.

Finally, so-called artificial neural networks are also para- £* = i,-* - n • ( -1s- ) = ».•* - n • I 9g ( y, ) metric function systems in which the parameters are fre- 60 ^ *' ' »* } 7a \ « / «•> quently referred to as (synapse) weights or weighting coefficients. Because of the nonlinearity of their dependence on Here. r\ is a preliminary factor whose values are to be

the weights (parameters Wj w«,) and the particularly selected as a function of the specific conditions of the

efficient learning methods with which these weights can be application. The mathematical literature for engineers gives

set. neural networks are particularly suitable for modelling 65 comprehensive indications to the person skilled in the art as

virtually any technical systems. In addition, they can be to how he has to select the values for T| for the optimization

represented in a simple way by means of specific circuit process to have a successful result. However, the invention