A Modular Adaptive Control System

Copyright © IFAC Low Cost Automation 1989 Milan. Italy. 1989

A MODULAR ADAPTIVE CONTROL SYSTEM J. Fessl INORGA, Institute for Industrial Management Automation, Letenska 17, CS 118 06 Prague I, Czechoslovakia

Abstract. The modular adaptive control eystem lMACS) ccntaining a PID controller, predictive PI controller and LQ self-tuning controllers using single-step and multistep control criterion was designed. The MACS can be used for both microproceesor based controllere and a microcomputer to control eeveral control loops with single input and single output (and a feedforward, too), which can be interconnected. The MACS, control algorithms, and the application of the MACS to control a steam boiler are described. Keywords. Controllers; microprocessor control; adaptive control; predictive control; self-tuning controllers; power station control.

INTRODUCTICN

- in the microprocessor based controller (DIAMO-S) ; - in the microcomputer, - in the microcomputer using the DIAVO-S as an intelligent I/O device. The structure of the MACS, control algorithms and an application of the MACS to drum boiler control are described below.

The prssentsd modular adaptive control system (MACS) was designed for a microprocessor based controller applicable to control of several control loops. MOet control loops are satisfactorily controlled via PID controllers. But 5 to 10 per cent of control loops of various plants caueed troubles due to the varying dynamics which are changing with changes in load or production and the wear of equipment. Cne way to improve control performance is to apply adaptive controllers using on-line identification, which are often called a~ self-tuning controllers (STC). Other reason why to uee adaptive controllers is to avoid the often troublesome tuning of the controller parameters. Therefore, the following controllers to control any loop with single input and output and several measured disturbances form the MACS: a) standard rID contrcller in ssveral variations; b) PI controller with a predictor (PIR); c) LQ STC with a single-step quadratic control criterion (LQ STCl); d) LQ STC with a multistep quadratic control criterion (LQ STCW).

CONTROL ALGORITHMS P ID Controll ers The PID controllers are prepared in several usual versions. The basic form is: uk+l%uk+rC(xk-xk_l)+r_lBk+rl (zk-2zk_l+zk_2)

(1)

',here k denotes a sampling time, e is control error, x is control error or controlled variable, z is filtered control error or controlled variable and TO' r_l' r 1 are PID parameters. Anti wind-up algor1thms suitable not only for a single loop but also for cascade control loops are included. The basic module described by (1) is extended by connecting with other modules of the MACS. The limitation of control signal u andVor its changes can be added. The non1inear gain depending on the control error etc. can be applied. And similarly, the integrating and derivative terms can be served. Feedforward, as well as the limitations of control signal, depending on eome variable may be considered.

The LQ STC were chosen with respect to the good practical experiencee with them (Feesl, 1986, 1990a). One-step-ahead or multistep predictors based on positional or incremental regression models can be used for the controllers sub b), c), d), which allows effective control of systems having longer transport delays. The controllers can work a~ independent, or they may be coupled into cascade control loops, etc.

PI Controller With the Predictor (PIR) The PIR was described by Neuman (1988). The single step (or multistep) predictor, based on a discrete regression model, is used to predict the controlled variable Yk d ' du iJ 1. This predicted value is applied alterria¥ively for I, P or I+P terms of the PI controller instead of the actual measured controlled variable Yk. In such a way the robustness of PI controller according to system parameter variations is preeerved and advantages of using the predictor are taken.

The MACS extends the existing block-oriented system for sequential control which was developed earlier for the microprocessor based DIAVO-S controller, a Czechoslovak make. The usual configuration of the DIAVO-S is as follows: a Z80 microprocessor, 16 KB EPROV, 4 KB RAM (the both memcries can be extended), 4x8 AI, 3x16 DI, 2x4 AO, lx16 DO. A display and a keyboard can be added for communication purposes. The MACS can be applied:

77

78

1. Fessl

Multistep Predictor The controlled process can be described by the regression model. For the single input (u), single output (y) and one measured disturbance (v) this one is in the form: N N NC + Yk: ,. \ A.v k . d + ~ S.u . ~ l' -1- V ~ 1 k-1-du 1 1 k-1-dv

LC,v .

input) or its changes are weighted by the weight Q , and M is the control horizon. Minimization of (~) can be solved as a minimization of a quadratic form via square-root algorithms. Details on this LQ STC are found in (Peterka, 1986; KArny et al., 1985; Fessl, 1990a). The control law is in the form: T

+ D+ e

n,k

• pTd

k

+ e

uk:+l=-L .x k+du ' n,k

X~+dU = [Yk+dU' u k '··· , vk+du-dv"'" 1 1

where k denotes discrete time, e is stochastic term (noise) and d is data vectoP. The process model output (i.e. controlled variable) as well as the variables u, v are related to Bome referencevalues considered as constBnts or as the preceding measured values. In such a way the positional or incremental form of the pr~dictor may be chosen. The time delays dy, du, dv are considered in (2). Several dist.urbances may be used; their evolutions are described by the autonomOUB autoregressive model (with constant parameters). The recursivs least-square method numerically solved via square-root al~orithm (Karny et al., 1985; Peterka, 1986) is applied for on-line identific~tion (estimation) of unknown parameters, pT = LBo,Al,Sl, ... ,BN,Cl,,,,,CNC,D] and noise covariance P. Directional forgetting (Kulhavy, 1987) of the data vector components not bringing new information is applied to avoid the identification buret (i.e. covariance wind-up) appearing if an insufficiently exciting control signal (i.e. process input) is generated. The parameter estimates Pk are used to obtain the predicted values Yk+du' uk+du which are applied in the control law of the LQ STCM, LQ STCl and PIR. Two versions of predictor (2) are considered which differ by the delay dy: a) for dy=O .du ~O the predicted output values Yk+j = P:dk+j, j=l, • • • ,du (together with values Vk+j) are recursively calculated (with the simultaneous filling of dk+j); b) for dy ~ du and dv ~ du the values .Ylc+du, vk+du are obtained via a simple shifting of iteme in the data vector. Notice that the output Yk: in ths model (2) ie now independent of the pa~t values Y1c-l'''' but depend s on "artificially" dslayed values Yk-i-dy' Ths special case dy=dv=0 and du=0 (or du=l for PIR) leads to the single-step ahead predictor, computationally much simpler. Another version ef the single-step ahead predictor uses the regression model with different memory for u and y. ~: Time dAlay du can also be considered in the model (2) by the increasing cf the model order N. In such a case the first parameters Bi, i=C ••• du are estimated (near) zero. This is not a defect' for the PIR and LQ STCM but t ~ is results in the instability for LQ STC1. Multistep Self-Tuning Controller

HQ STeM

The LQ STCM ~se$ the model (2) with dy=O, du~C, d" ~ 0, and the multi step quadratic criterion: k+M (w . _ )2 Q 1 J"E { l+du Yi+du + uU i k) i=k+l

L

Id

( 5)

whers ths control signal (i.e. the process model

(6)

where L denotes the controller parameter obtained from parameter estimates P and the minimization of (4). If du=O in (2), th~ simple single-step prediction is applied; etherwise the multistep ~redictor calculating the values Yk+" v +., 1=1, ••• , du hae to be applied. J k J To automate the choice of the weight Qu, the varying weight Qu,k is calculated to fullfil the remands on the input increments variance (and the output variance too) -(Toivonen, 1983; Fessl, 1990b). The usually used algorithmic constraining of input values (often caused bv improper values of Q ) may result in the input s tuc king or oscilati8ns which l eads to troubles in pa rameter estimation and the following controller synthesis (Fessl, 1990b). Therefore the additional weight QU~k is calculated, if the input changes have to b~ constrainsd (according to Bohm (1985)). This Qu,k is added to Qu,k. The LQ STCM, as well a8 the LQ STC1, are protected against the controller wind-up caused by the limitation of the actuator or the valve. A solution suitable als o for cascade control is used (Fessl and JarkovsKY, 1987). Single-Step Self-Tuning Controller LQ STCl The LQ STCl uses the model (2), and the singlestep quadratic control criterion in the form: J = E[{w k+C Yk+i)2 +

Quii~+lldk

1, i=du+l

j=O

(7) (8)

j=l

where [Yk-dy+dU' u k '··· , Vk-dv+du' ••• ,1 ] and j is defined in (8) according to the type of input weighting, Px and x - see (2), and w denotes the se~ po~nt. The unknown future values of y, v occurrlng 1n the data vector x have to be uredicted via multistep predictor if dy
Q~k

=

[Bo{wk+dU+I-Px,k·xk+dU)-B~uk+1J/Uk+l (10)

else Q *,,- = u '"

a.Q* , u,u-l

C
is dewhere the uk+l is limited value, and fined by (8). u k+l

MODULAR ADAPTIVE CONlROL SYSTEM STRUCTURE OF THE WACS The WACS upgrad~s the capabilities of the earlier block-oriented system prepared especially for ~e­ quential control. This one contains the usual lo ~i c al and combinational blocks, blocks for input/ output operations, measured data filtration, calibration, etc. These blocks were programmed for in assembly language. The modules of the WACS (designed as subroutines) were programmed in standard FORTRAN IV (now they are being reprorrammed in assembly lanEnlage t oo). The WACS is formed from basic and fi nal modules and comprises the modules usually used in control, i.e. the modules of static nonlinearities, algebraic modules, dynamic elements (first order lag, lead-lag, time delay, etc.), functions generator, and the mentioned predictors and controllers. The modules for data shifting in vectors etc., used in predictors, are considered t oo. (All matrices in al ~o rithms are transformed to vectors.) To save memory, the basic modules describe usually only partial functions, which are being used several times, for instance the various static nonlineari t ies, varying weight calculation for the LQ STC, th e i nitialization parts of contr ollers and predictor s , data shifting in vectors, etc. The f i nal controller modules including the predictors are created f r om these basic modules. The predictors, for instance, are composed of two initialization modules, two or three modules for the calculation and moving of items in the data vectors, and one module (REOICF) for the calculation proper of parameter estimates via the square-root version of recursive least-square method. This REOICF is standard used in all prsdictors. The LQ STCW is f ormed from the predictor modules, the controller itself, the varying wei ght module, limiter modules, etc. The basic modules (about 40) as well as the prepared final modules are saved in a special memory. The special logical variables are included into th ~ parameters of most modules. The using of these logical variables enables to change not onl y the module functions but also allows the on/off switching of the modules resulting in partial changes to the controller function and structure in real time without a reprogramming of user programs. In such a way a certain trade- off between fixed and programmable controller capability is done. The internal program bus can be formed containing the measured and calculated variables (i.e. controller outputs) which are loaded into and again chosen by various modules. This creates a pos s ibility to change variables ap plied in the contr ollers ( for instance, f or feedforward), and i n thi~ way to modify t he struct ure of contr ol l oops and their i nterconnection without any change in electri cal co nnection of the I / O board. ~ he user program is generated from the WACS basic and final modules combined with the above mentioned bl ocks designed earlier. The sampling period depends on the chosen controllers and their number, the minimum value T=C.2 50s can be used f or PlO con t r ollers. The moat complicate d LQ STCW may use th e eampling period about 3s or more; this is influenced bv the complexity of predictor t oo . Ther e f ore t he WACS can be used for usual processes but no t f or tho s e very fast. The typical field f or t he WACS is steam boiler contr ol, heat furnace control, etc.

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Czechoslovak make, configured as follows : 64 KB, 8 AI, 8 AO, 32 OI, 32 00, two floppy disks, keyboard, display, line printer. Such configuration enabled not only control but also other funct i ons not ensured by ths WACS - communication, data displaying and storing, etc. which helped to improve the WACS modules. The loops of steam pressure, combustion air and underpreesure in the combustion chamber were controlled using the WACS. A simplified control loops with WACS modules are s~own in Fig. The mentioned loops influence one another; therefore, in extraordinary conditions the control signals are interrelated, they li.it one another. If the flue gas fan is on the high limit and ths deviation of underpressure in the combustion chamber is above the high l i mit the contrcl sirnal of combustion air and steam pressurs loops, i .e. the positions of air fan and coal feeders (tr~nsporting coal into the mill) cannot be increased: Similarly, the reaching of the air supply hi gh limi t influences coal supply. These requirements were full filled in the following way. The memory modules YEW were used in the combustion air and s'team pressure lo ops having control signals UA and UC. The moduls output depends on the value of the lo gical signal (LPF ) i ndicating the reaching o f the both underpressure l oop limits. If these limits are reached (LPF=l), the last values of control signals UA and UC are saved. The module NLIVD is controlled b y the logical signal LPF; if LPF=l, t he signal (UA, UC) is limited according to the other one (the value of MEW output). In such a way the ab ove mentioned demands are ensured. The modules NLIW make simple limitation of signal on the low and high limits. The PI and P controllers were used in combustion air and underpressure loops. Steam pre s sure was alternatively controlled via PlO, PIR, LQ STCl or LQ STCM to verify their modular desi~n. Because of t he steam boiler had the direct blowin~ system (without coal bunkers ) and a larger combustion ch~mber, the steam pressure dynamics are ver y slow wi th a si gnificant t ime dela y . Therefore the single-step predictor with t he increased m0del order or the mul t iatep predictor were used. The best control results were obtained with the LQ STCW using the multistep predictor. Applying the wei ght Qu,k in the LQ STeW made the setting of co ntroller parameters eas y , removed t he problem ad j usting this parameter, and improved control performance. The chosen concept of the MACS with l ogical parameters involving the (c onditional) on/ off switching o ~ t he modules proved and en abled to modify the control loops according to the new requirements.

CONCL USIONS Th e modular adaptive control s ystem (MACS) was desi ~n~d f or bot h micropr ocessor based controllers and microcomputers. The modular solution enables to compose the cont rollers in various complexity accord ing t o t he dif f erent re qui rements. Th e using e f co nt r ollers with th e pr~dictors, i .e. t he predictive P I c ontroller or the LQ STCl and LQ STCW, thou gh they are rather complicated, makes improving the control performance possible. Using those contr ollers to~et h ~r with the PlO controllers enables t o control s everal loops with one devi ce and this results in lower coets of automation compared with the hardware which would be otherwise needed to obtain t he same performance.

THE APPLICAT IO N OF THE WACS The WAC~ and the designed controllers were verified on a coal fired steam boiler. This drum boiler (75tph, 6 .1VPa) delivers steam into a common collector ( together with three other boilers). The WACS was implemented on a TN5-TC 8-bit microcomputer of

The results of the application re s earch concerned especially with the anti wind-up algorithms (for bc th PlO and LQ src) and the varying weight calcul a tion fo r the LQ STC increased the vapability c f controllers with eaeing their putting into practi ce.

80

J,

Fessl Fessl, J., and J. Jarkovskj (1987). Cascade control using adaptive controllers with on-line identification. 10th IFAC World Congress, Munich. K!rny, W., A. Halouekovn, J. BOhm, R. Kulhavy, and P. Nedoma (1985). Design of linear quadratic adaptive control: Theory and algorithms for practice. Kybernetika, 21, Nos. 3-6 (A Supplement). Kulhavy, R. (1987). Restricted exponential forgetting in real time identification. Automatica, n, 589-603. Neuman, P. (1988). Self-tuning predictive regulator. 8th !FAC Symp. Id.At. Syst. Param. EsHII., Beijing. Peterka, V. (1986). Control of uncertain processes: Applied theory and algorithms. Kyber~, 22, Nos. 1-6 (A Supplement). Toivonen, H.T. (1983). Variance constrained selftuning control. Automatica, 12, 415-418.

Two application of the MACS are prepared now fcr steam boiler control. ( ne for adaptive control of steam pressure and combustion on a 220 tph drum boiler (toFether with other loops using PID controllers), the other for control of several loops on a fluid steam boiler. The first application is preparsd for the microcomputer, the other with the microprocessor based controller. REFERENCES Bohm, J. (1985). LQ self tuners with signal level constraints. 7th IFAC/ lFORS Symp. Ident. Svst. Param. Estim., York. FeBsl, J. (1 986). An application of multivariable self-tuning reFUlators to drum boiler control. Automatica, ~, 581-585. Fessl, J. (1990a). Applications of multistep LQ self-tuning c ontroller to Bteam boiler control. Submitted to 11th IFAC Congress, Tallinn. Fessl, J. (1990b). LQ self-tuning controllers with varying cost function weight. Submitted to 11th IFAC Congre8B. Tallinn.

UFW :

P

~-U-F-----oj I

P

,

'- - - - - - - - - - - - - - - - - - fC- - - - - - - - - -

'LA J

-- -- ------ ----,1

LP

~ND : LPF

02W

,-------

-------------,------------~

NINS

steam pressure

,LQ STC1

ILQSrcM

L _________ _

, 1

L _

Figure.

LPF -I. __ :

Simplified Control Scheme of Control Loops: Steam Pressure, Combustion Air, Underpressure in the COllbustion Chamber.

MEM

log i cal s i gnal SS ' " t he ac t uato r syst em SM' " the main sys t em