Extended Prediction Self-Adaptive Control

V [ u(t) J = I Lw(t +k) _P(z-1)y* ( t+k/t)]2 1 k=d or i V [ u(t) J= I Iw(t+k )-P (z-1 )y*(t+k/t) 1 2 k=d -n where P ( z -1) = Po + P1 z - 1 + ... + Pn z P

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[ 11] [12]

p

is a design polynomial with P(1) = 1 and w( . ) is the control set~a,int . It is interesting to notice the effect of p(z ) by writi ng w(t+k)-P(z-1 ) y*(t+k / t) as p [r(t+k) - y*(t+k/t)] with o por(t+k) = w(t+k)-P1 y*(t+k-1/t)- •.. Pn y*(t+k-n/t). k=d .. . i p

The controller will force the predicted process output to follow a reference trajectory r(.). If it would succeed. then y* (t+k-1/t)=r(t+k- 1) ••.•• y* (t+k-n It) = r(t+k - n ) and from [ 13] it follows p

p

that r(t+k) = w(t+k)/P(z- 1) [14] indicating that the reference traje c tory is nothing else but the (low- pass) filtered setpoint and initialized at y * (t+d -1 /t) • . .. y*(t+d-n It) . This technique has also been used elsewhere (eP. g . Richalet et al •• 1978) . However if there is no perfect tracking of the reference trajectory. there is a s ubtle difference with the well-known setpoint filtering technique. Indeed the relationship l 13] indicates that along the whole prediction horizon the reference trajectory r(.) is continuously reinitialized on the latest predicted output trajectory rather than on the reference trajectory itself as in 114] . Generalty p(z ) is chosen as a first - order filter p(z - ) = 0 . 0 1 a + (1-0.01a)z[15] where a is the only tuning parameter in EPSAC which is left for the user . It has a strong intuitive in terpretation as the controller's speed parameter (0% to 100%) . The prediction horizon i is normally fixed a priori at i = d+4. The minimization of V 1 can be solved analytically resulting in a simple closed form for Ilu( t) . PRACTICAL I SSUES IB EPSAC IXPLEMElTATIO.

Unaodelled dynaaics The models used in practical implementations of adaptive control are always crude simplifications of low order . Robustness to underspecified order is thus an important characteristic of a realistic candidate for adaptive control . Moreover the effi ciency of the parameter estimation depends on the properties of the input signal. The conditions on persistent excitation are related to the complexity of the estimated model. This implies that the requirements on the input signal become more severe if the model order is increased. Persistent excita tion is a great uncertainty when applying adaptive control to process industry. It is thus sound engi neering judgement to keep the models as simple as possible and to estimate only those parameters to which the control performance is sensitive. This is again in favour of an (adaptive) control algorithm that is robust w. r.t. order underspecification and that is preferably also insensitive to certai n pro cess parameters . These may then be fixed a priori. perhaps even at the cost of ultimate performance . Example 1. The continuous-time process 1/(1+s)3 was simulated by means of Runge - Kutta integration methods. A controller sampling period of 0 . 5s was

Extended Predict ion Sell-.\da pt i\l' ( :on t 1"01 chosen . The e~uivalent discrete - time system has the structure [1J with na=3, nb=2 and d=1. Noise was added to the process input and the output had to follow a square wave setpoint. The speed parameter Q was tuned so as to realize 90% of a setpoint change within 3s and was fixed for all experiments. In Figs 2 ~ and 2b the result of the EPSAC method is shown for the specified model structures (n =3 , a nb=2, d=1) and (n a =1, n =1, d=2 ) . Although the control performance degra8es (which is not surprising as neither of the poles is negligible) the closedloop remains stable and the set point is tracke d. Also notice that in (Astrom,et al ., 1984 ) it was shown that the system 1/(1+s) 3 sampled at 0 . 5s has a nonminimum-phase discrete -time equivalent . Example 2 . The continuous-time system - T S

e d K/(1+TS).(1+s) with K=1, T= 5s , Td= 5s simulates a heating process with transport lag . It was controlled by a PI-regulator and the EPSAC strategy both with sampling period T =1s. The PI-controller was tuned at gain K =1 and i~tegration time T.=1 0s, the EPSAC speed pJ'rameter was a= 100% . In Ffgs 3a and 3b , the results can be compared. The model order for EP SAC was underspecified (n =1, nb=1, d=6). Moreover only the b and b1-parame~ers were estimated,
Example 4. The nonminimum-fhase system (1-0.7z- )y(t) = (1+2z- )u(t -1 ) was controlled by the EPSAC method. During the first few samples the system was run in open-loop in order for the estimator to settle. After closing the loop at time 25, a square-wave setpoint signal had to be tracked. At each downwards step the speed parameter was changed . The results 1n Fig. 5 have to be compared to those given for several other methods in (Clarke, 1984). Unknown or varying dead-time The dead-time index seems to be the most critical design parameter. Robustness w.r.t. unknown dead time can be_ argely improved by extending the order of the B( z ) -r.0lynOmial with (d max -d. ml.n ) parameters s~rh that 1,] c~? be replaced oy A(z )y(t) = B (z )u(t-dmin)+v(t) with -n B'(z-1) = b'+b'z-1+ .•• +b , z b + o 1 nb

1

+b'

z

- (nb +dmax -dmin )

nb+dmax-dmin (Wellstead & Zanker, 1982). A simple method whi ch avoids the increase of the parameter vector is d:fcribed in (De Keyser, 1985). The original B(z ) polynomial is estimated but the dead-time index d is adap ted in real-time according to the criterion :

decrease dead - time index increase dead-time index. An example illustrat es the pow e r of the method. Example 5 . Th e heating process of example 2 was controlled in an expe r i ment lasting 500 s during which the gain K, the time constant T and the dead time Td all varied linearly in the range : K : from 1. 0 to 0.5 from 5. 0s to 10. 0s T . from 5.0s to 7 . 5s Thes
Cutter Suction Dredging Ship One of the most frequently used types of large dredgers is the cutter suction dredger, particularly because it can cope with hard materials combined with the advantage of hydraulic transport. Today 41 % of the world dredging fleet are cutter suction dredgers with on-board installed power of 15000 h.p. and more. Newly built cutter suction dredgers are becoming more and more powerful and complex in order to increase their efficiency. One of the latest developments is the automatic dredger controller. The main features of a cutter suction dredger are illustrated in Fig. 7 (Claeys, 1978) : - the cutter (1) to dislodge the soil; - the ladder (2) to fix the dredging depth. It holds the shaft for the cutter and also the suction pipe (and pump); - the spud (3) to fix the length of the cut or step. A cutter suction dredger is a stationary vessel : the dredger swings around the spud and steps forward relatively to the spud at the end of each swing; - the swing-winches (4), wires (5) and anchors (6) which, by moving the dredger, determine together with spud and ladder position the quantity of soil to be cut per unit of time; - the pipeline (7) and the sand pumps (8) to transport the dislodged soil over the required distance and height. Several process variables have to be controlled continuously by the dredgemaster or by an automatic control system : - the load of the cutter motor - the concentration of the soil / water mixture in the pipeline - the load of the swing-winch motors - the velocity of the mixture in the pipeline - the load of the pumps and driving diesel engines - the vacuum before the suction pump - the tension in the side wires - the total pressure after the pumps, etc. The process outputs are mainly affected by the swing velocity of th& dred 5 er aro un d the spud be-

K. \1. C. De Kc\scr and :\. K. \·an Call\\"<:nbl'q~hl'

cause, as explained earlier, it determines the quantity of soil to be c ut and transported per unit of time. Of course this statement is only valid if the soil characteristics remain constant along the swing. I n pra c tice they a re not, and drastical variations in & stochasti c sense are quite normal .

This co nstitut es the whol e problem in controlling this kind of process . The main control obJective is to maximize the production, which is normally realized by manipulating the swing velocity continuously so as to keep at l east one of the process variables at its prescribed load limit. Commercially available cutter controllers (PID type) fail due to the extremely random and time - vary i ng nature of the process characteristics and loads . This type of vessel is used to dredge clay , sand as well as rock. The relationship between process input (swing velocity) and process outputs (cutter load, mixture concentration, ... ) is changing al most continuously. This gives an idea of why this type of process is a challenge for adaptive control to prove its superiority . To give an idea of the irregularity of the process we refer to Fig. 8. The load of the cutter motor and the mixture concentration at the measuring - spot in the pipe (near the sand pumps 8) is illustrated under manual control by the dredgemaster . A first step in the project was the modelling of the cutter suction dredger . The several submodels of the multi-input/multi-output process were identified based on a priori kno wl edge , physical (mechanical, electrical, hydraulic) laws and para meter estimation. Extensive use was made of time series obtained by active testing aboard of the real dredger . The result was the const ruction of a comprehensive real - time simulator of the dredging process. It is implemented by means of a multi-microcomputer system with 4 parallel- operating microprocessors (De Keyser et al., 1985 ) . The simulator is now extensively used for training, for the study of the dredging process and for testing new versions of the automatic cutter controller before they are installed on board of the ship. The next step was the successive design of the adaptive controllers for the different loops. The prototype versions are operational aboard of the real dredger since 1982 . They are implemented in the on - board minicomputer. The new large cutter suction dredgers of the fleet will now systematically be equipped with the adaptive cutter control ler but the new versions are now being impleme nted in multi-microcomputer systems . This new te chnology seems to be more reliable in the extreme circumstances the ships are frequently operating in (tropical regions with high temperatures and rela tive humidity, dust and vibrations). In Fig. 9 the control of the cutter load is illustrated, while in Fig. 10 the controlled mixture density is shown. Notice that the concentration (density) control is hindered by a seve re dead - time (transportation lag) because the measuring - instru ments are located near the pumps (8) which is about 50 meter away from the suction inlet (1). Moreover the dead-time changes due to the varying mixture velocity in the pipe (bet ween 4m/s and 9m/s). Because the mixture velocity is not measured, the controller has to be robust w.r.t. the unknown, varying dead - time . Residence Heating Energy conservation in building heating can be obtain by taking several well-known measures : better heat - insulation techniques , an appropriate heating plant and a performing control system . Each of these methods can also contribute to a more comfortable environment . It was the intention to develop more powerful control algorithms for house heating . The tests are executed in a family residence in which good atten tion has been paid to the two other energy saving measures: the house is well insulated and the

heating plant consists of an oil - fired low-tempera ture boil€r producing water at an average temperature of 35 °C . This tepid water circulates through heating pipes in synthetic material laid in the floor of the rooms. The he at is emitted mainly by radiation at low temperature at the surface of the floor. This leads to a very comfortable and economic heating system : an almost ideal temperature gradient between floor a nd ceiling of the rooms , lower room air temperatures lead ing to smaller heat losses and reduced transportation and standstill losses. Although the automatic control of any house - heating system in general can be much improved as far as optimization and e nergy conservation are concerned, particularly the control of floor-h ea ting systems is a hard task due to the large time-constants and dead - times . Conventional commercial controllers are not very well suited to be used on this type of heating system . That is probably the main reason why these systems are frequently used in a constant operating regime, avoiding possible uncomfortable situations during daily start/stop procedures. To keep the rooms nicely at a constant temperature might be most comfortable , but certainly it is not the most economic way of house heating! For that reason it was decided to investigate the potential possibilities of more advanced (adaptive) control strategies to the computer automation of heating systems in general and floor-heating systems specifi ca lly. The control algorithms have been implemented in a personal computer and have been used successfully in the first author's residence during the winter 84- 85 . The house is conceptually divided in heating zones (each consisting of one or more rooms) which are controlled independently. For each zone the user can specify an occupation schedule to the computer : the period of day during which the zone will be occupied and the required zone temperature. Based on the long-range prediction capabilities of the algorithms, the computer is able to decide itself on the start and stop times for the zone heating (optimal start / stop control of heati ng systems). The input of the "process" is the heat supply to the zone, the output is the room air temperature . In Fig. 11 some typical results for a specific zone are shown. The occupatlon schedule was 7 a . m. to 11 p.m . and the speclfled temperature was 19 °C. In Figs 1 la and 1 lb the room a ir temperature T is plotted against time ; also the external temperature T , whi ch varies rath~r drastically in Fig . llb, is illustrated . In Fig . l l c the supply water tempera ture T co rresponding to Fig . 11 b is shown. The maximuffi supply water temperature during start- up was 55 °C . Notice specifically in Fig . llc the very fast reaction of the controller around 5 p . m. (17 hr) . Thanks to the smart control the room air temperature stays far within the preliminarily speci fied band of +/- 0.5 °c around the setpoint . The control system can without difficulty also be applied to radiator heating systems , which are indeed much easier to control . Some results of a si mulation study are given in Fig. 12 . The performance of the EPSAC - based heating controller is compared to that of the typically used thermostatic control (on - off with +/- 0 . 5 °c hysteresis ) . Fig . 12a shows the results for a slow heating system (floor heating), Fig . 1 2 b those for a faster heating sys tem (radiator heating). The external temperature varies sinusodially with amplitude 5 °C . Notice that the EPSAC algorithms and all tuning parameters (e xcept for the sampling period) were identical in both applications.

COJlCLUSIOJlS The principles of the Extended Prediction Se lfAdaptive Control strategy have been explained . Much attention has been paid to the implementation as

Extended Prediction Sclf-.\d;lptilc C"nt!,,1 De Keyser R. M.C . , A. R. Van Cauw enberghe ( 1979) . A se l f - tuning predictor as operat or guide . Ln : R. I sermann ( Ed. ) , I dentific at ion and System Parameter Estimation - 5 th I FAC Symposium, Oxford, Pergamon Press, 1249 -12 56. Al so in : A self- tuning multistep predictor applicatlons . Automatica, 17 (1), 167 - 17 4 . De Keyser R. M.C:-;- A.R. Van Cauwenberghe (1 982). Simple se l f-tuning multist e p predictors . I n : G.A . Bek e y, G. N. Saridis ( Eds.), Identifica tion and System Parameter Estimation - 6th I FAC Symposium, Oxford, Pergamon Press , 15581563. De Keyser R.M.C. (1985) . Adaptive Dead-Time Estima tion. I nternal Resear c h Report, Automatic Control Laboratory, University of Gent. De Keyser R&M.C., L. De Coen, P. Verdiere ( 1985). Multi-Microprocessor simulation of a Cutter Suction Dredging Ship. 7th IFAC Conference on Digital Computer Applications to Process Control, Vienna, Austria. Martin G.D. (1981). Long-range Predictive Control. Proc . AIChE, 27 (5), 748- 753 . Richalet J. , A.Rault, J.L. Testud, J. Papon (1978). Model Predictive Heuristic Control: Applications to Industrial Processes . Automatica, 14 (5) , 413-428. Rouhani R. ~ R.K. Mehra (1982) . Model algorithmic Control - Basic Properties. Automatica , 18 (4), 401-414. Van Cauwenberghe A. R., R. M.C. De Keyser (1985) . Self- Adaptive Long -Range Predictive Control . ACC Boston. Wellstead P.E., P. Zanker (1982). Techniques of Self- Tuning. Optimal Control Application & Methods, 3 (41, 305 - 322 . Wittenmark B.,-K.J. Astrom (1984). Practical Issues in the Implementation of Self- tuning Control. Automatica, 20 (5), 595 - 605.

pects , which are also typical for other adaptive techniqu e s . In f a c t in this method optimali ty and robustness in practical app l ications are weighed one aga~nst anoth e r. Several examples on computersimulated processes have been used to illustrate the concepts. Two important real-life applications have ~monstrated the practical applicability of the algori thms : the control of a cutter suction dredging ship and of a residence heating system. AKJiOWLKDGEIIEIi'l'

The work on the dredger automation is done as a collaborative project between Dredging International N. V. and the State University of Gent . Thanks are due to ir . C. Cl aeys, Director of the Engineering Department of D.I., and to many other people at D. I. for making this collaboration possible.

Astrom K.J., P. Hagander, J . Sternby (1984). Zeros of Sampled Systems. Automatica, 20 (1), 31-38. Brufjn P.M., H.B. Verburggen (1984). Model algorithmic Control using impulse response models. . . Journal A, 25 (2), 69- 74. Cla"eys C. ( 1 978T. Production limiting factors of cutter suction dredgers. 7th International Harbour Congress, Antwerp , Belgium . Clarke D.W., A.J . F. Hodgson, P.S. Tuffs (1983). The offset problem and k- incremental predictors in self- tuning control. Proc. lEE, 130, PtD (5), 217 - 225. Clarke D.W. (1984). Self- tuning Control of Nonminimum-phase Systems . Automatica, 20 (5), 501 517. Cutler C.R., B.L. Ramaker (1980) . Dynamic Matrix Control - A computer Cont ro l Algorithm. JACC, San Francisco, paper WP5-B.

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