System GAMMA features - System gamma: the directives of finite-frequency identification Ljubov Mikhailova, Elektrostal...

System GAMMA features
Family of systems GAMMA was developed since 1970 (Alexandrov, Nebaluev and etc.,1975; Alexandrov and Panin, 1997). To describe the features of GAMMA architecture let us introduce the notion of group of the user of CAD tools:
The first group is the engineers-developers of control system. Such specialist uses the CAD tools for solution of different problems of control system design in concrete domain (aircraft, power engineering and etc). He has the deep knowledge of concrete plants and principles of control system design. But it is possible he has not deep knowledge of mathematical methods of his problems solution. Besides the program implementation of these methods is not his employment duty. It is clear that the matrix systems like MATLAB in some cases are not convenient for such users because the users of these system should write the programs using the set of elementary m-functions.
The second group is the scientists who use the CAD tools for exploring and program implementation of different methods of control system design (further such specialists are referred as the researchers). The researchers are the experts in the control theory besides they have some skills of programming.
The GAMMA system has been created as the CAD tool for engineers-developers of control system primarily. So it is based on the following principals:
The engineer need not develop the program for solution of its problem.
The system must support the problem description in the “natural” language. For the control engineer it means that the interface of system provides the input of initial data in the form of matrixes, vectors, differential equations and etc. On the other hand it means that the system allows to solve the design problems when the design purpose is described by the technical indices (steady-state errors, the bounds of input and output of the plant, the settling time and etc).
The problem must be solved automatically without user participation.
The system must have the tools for its modernization by a researcher.
Some of these principals were discussed in (Alexandrov, Isakov etc, 2005; Shumann, R., S. Kornera and etc, 1996; Syska, 2002).
The main features of GAMMA is the sharing the functions of different user-groups on the level of the system interface. GAMMA is the two-level system: the first level (the engineers environment) is the set of design procedures (we refer them as the directives) that provide the automatic solution of design problems by an engineer-developers of control system. The second level (the researchers environment) intends for development and modernization the software of first level by a researcher. The principal scheme of GAMMA architecture is shown in Figure 1.
3.1 The engineers environment
The Engineers environment’s basis is a directive. The directive is the special program that has the following features:
The directive solves the definite class of problems of a design of control algorithm.
The directive is complete self-documenting program such that the non-expert user can use it for solution of rather complicated design problem.
The interfaces of all directives are unified.
The directive consists of three parts: the interface part , the calculation part, the operations of input and output.
The directive is the program written in language INSTRUMENT (it is described in next subsection). The calculation part consists in calling of calculation modules written in C and functions written in INSTRUMENT.
All directives are subdivided into three classes:
Synthesis (LQ-optimization, - suboptimal control, controller synthesis under the given tolerance on steady-state errors and etc);
Identification (finite-frequency identification, identification with selftuning of test signal, identification with selftuning of identification time and etc);
Adaptive control.
In Engineers environment a user chooses the directive from the directives list; after a request of computer, he enters in natural form the initial data: the differential equations of plant, disturbance boundaries, technical indices tolerances, etc in dependence on class of problem. The dialog form for initial data input is shown in Figure 2. Then a directive is performed automatically (without user participation). Analyzing the results he makes a decision on an acceptability of outcome. The example of the report of directive executing is shown in Figure 3.
3.2 The researchers environment
The researchers environment intends for directives development. The main components of researchers environment are the modules library and interpreter of language INSTRUMENT.
The directives of GAMMA are developed with use of program modules. Each module solves the elementary problem of control theory (for example, controlability analysis, Fourier filter and etc.). The researcher may use any high-level programming language for modules writing, but there are the some rules that he must observe.
The modules library stores the detailed description of the modules. It includes the modules ID, modules name, inputs and outputs description and so on. This information is used by interpreter during directive executing. The modules library contains about two hundred modules. It is divided into some groups in according to the modules intends: transformation, analysis, synthesis, identification, adaptive control, simulation and etc. The window of the modules library with description of the module is shown in Figure 4.
The problem-oriented language INSTRUMENT is used for directives implementation in the GAMMA system. The interpreter of this languages is the part of GAMMA. Before INSTUMENT-1 had the limited set of operators: operators for input and output of data, operator for running of calculation modules, conditional and unconditionally control transfer. So the calculation modules were writing in C and PASCAL.
Now the possibilities of INSTUMENT are substantially increased. All standard operation were added into the INSTRUMENT: loops, conditional, subroutines, operations with arrays and etc. As the result the most of calculation modules are wrote in the INSTRUMENT now. Besides the possibility for using modules written in the another languages (C or PASCAL or the other) is maintained as in the previous version of INSTRUMENT.
4. GAMMA software for finite-frequency identification
The software for finite-frequency identification is implemented as the number of directives:
D123su -- the finite-frequency identification where the amplitudes and the frequencies of the test signal and the identification time are given numbers;
D123sdsu -- the finite-frequency identification with self-tuning of identification time;
D123sursad -- the finite-frequency identification with self-tuning of amplitudes of test signal.
Let us describe the directive D123su.
4.1 The structure of the directive D123su
The directive has the following structure:
>=
=<PMV1> .
The initial data of the directive:
d,k,m – polynomials of the plant;
np – plant order;
par – external disturbance parameters;
h – sampling time,
om – test frequencies;
rho – amplitudes of the test frequencies;
Ptau – identification time (number of periods of the minimal test frequency);
Tfi – start time of filtration (number of periods of the minimal test frequency);
х - initial conditions;
Tbegin – start time of simulation.
The results:
vdd – estimates of the denominator coefficients of the plant transfer function;
vkd - estimates of the numerator coefficients of the plant transfer function;
4.2 The modules of the directive D123su
The following modules were used in the directive:
Cauchy1 – conversion of the plant model to the state space form.
Syntax: Cauchy1[d,k,m][A,B,C,D],
where A,B,C,D – the matrixes of the state space form;
PMV1 – computation of plant inputs and recalculation of test frequencies
Syntax: PMV1[om,rho,par,h,Ptau,np,TBegin][t,u1,u,om1],
where t – time vector, u,u1 – plant inputs, om – new test frequencies.
ABtoFR – computation of matrix of discrete-time model.
Syntax: ABtoFR[A, B, h][F, R],
where F,R are the matrix of discrete-time model.
Analysis – plant simulation.
Syntax: Analysis[F,R,C,D,u1,t,x0][x,y],
where y is the plant output.
FourSu – computation of the FDP estimates.
Syntax:
FourSu[y,u,om1,rho,np,h,Ptau,Tfi][valf,vbet],
where valf,vbet – the estimates of the plant FDP.
Freqd – solution of the frequency equations of identification
Syntax:
Freqd[om,h,valf,vbet][vkd,vdd],
where vdd and vkd are the estimates of coefficients of discrete-time model of the plant.
Example
The following plant has been used to test the directive D123su:
Discrete-time transfer function of this plant under sampling time h=0.2 is
(11)
The initial data of the directive:
Polynomials of the plant .
Plant order np=3;
External disturbance ;
Sampling time h=0.2;
Test signal ;
Identification time Ptau=3;
Start time of filtration Tfi=1.
The following results were obtained:
; .
Identified discrete-time model of the plant:
(12)
The coefficients of model (11) and (12) are sufficiently closed.
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