A high performance control system for spreading of liquid manure

A HIGH PERFORMANCE CONTROL SYSTEM FOR SPREADING OF...

14th World Congress ofIFAC

K-4a-Ol-2

Copyright © 1999 IFAC 14th Triennial World Congress, Beijing, P.R. China

A HIGH PERFORMANCE CONTROL SYSTEM FOR SPREADING OF LIQUID MANURE

Axel Munack, Eckhard Buning and HermanD Speckmann

Institute ofBiosystems Engineering, Federal Agricultural Research Centre (FAL), Bundesallee 50} 38116 Braunschweig, Germany, Phone: +49-531-596-309, Fax: +49-531-596-369} E-mail: [email protected]

Abstract: During spreading of liquid manure, the manure flow must be controlled according to the - position-dependent - reference input and the tractor speed. The speed is varying by wheelslip, particularly in hilly regions, and during driving up or stopping. Magnetic inductive tlowmeters proved to be most precise and robust for measuring the manure flow rate; however, due to built.. in measurement preprocessing, their signals suffer from lags and delays. This means that feedback control of the Hquid flow rate is either very slow or must be driven with small stability margin or even cannot be realized at all with conventional equipment. Two new control systems are presented which incorporate model-based adaptive control. One is equipped with a supervisory adaption loop, the other is based on extended Kalman filtering with a Smith predictor. Copyright 91999 IFAC Keywords: Precision fanning, Liquid manure, Adaptive control, Extended Kalman filter, Smith predictor

Therefore, the flow controller of the tank trailer must react to setpoint changes quite rapidly. This also holds - particularly in hilly regions - for varying tractor speed caused by wheelslip. A further situation, in which a high-speed action of the flow controller is required, is during start-up and stopping

1. INTRODUCTION During spreading of liquid manure, several influences may cause an application which is not in agreement with the needs of the plants. Taking the actual demand as being determined by soil analysis, there are some aspects which must be observed during the application. At first~ the manure may not be homogeneous, if it was stored in a manure tank for some time. This effect can be eliminated by intensive mixing of the manure within the stationary tank before filling the tank trailer. The actual N-content of the manure must then be determined in order to calculate how much of it (e.g. which volume) should be applied per hectare. According to the principles of precision fanning, the amount should be calculated for small portions of the field, since the demand may vary within small distances.

of the tractor when reaching the boundaries of the field. Different principles are known for operation of slurry tank spreaders. Here, flow control by branching is used~ The .. more or less constant - flow of the pump is split into one stream which is redirected into the tank and another stream \vhich is fed into the spreading device (Fig. 1). Other types of tank trailers use a volumetricaHy operating pump, where the pump speed is varied in order to influence the manure flow. A further principle of operation consists in the control of the tractor's speed such that the desired amount of manure per hectare is applied.

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Copyright 1999 IFAC

ISBN: 0 08 043248 4

A HIGH PERFORMANCE CONTROL SYSTEM FOR SPREADING OF...

14th World Congress of IFAC

1.0

0.8 -·~MfD1

slurry

I

slurry vo'ume per hectare (reference) - - - j

1

~

flow rate measuring device

....... MID2

0.6

appljcation width

0,4

(parameler) 0,2

Fig. 1. Slurry flow rate control by flow branching 4

Since the tractor management system may be not that advanced that it alJows a speed controJ under all circumstances, the last mentioned principle was not considered. The first mentioned principle has the advantages that it doesntt require a vDlumetrically operating pump and that the manure is continuously mixed in the tank trailer, since a certain part of the pump flo\v is re-fed into the tank again.

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10

time[s)

Fig. 2. Step responses of two different MIDfg

3. CONTROL

3.1 Commercial solutions 2. SENSORS AND ACTUATORS

Flow controllers installed on commercially available slurry tank trailers are usually equipped with threepoint switches as output device. This is reasonable since it reduces the cost of equipment substantially, compared with a fully analog power output. At the same time~ the probability of the valve to be stuck is considerably reduced by this, since the full hydraulic power can be imposed for every change in the valve's angular position. This is even more important for the electric motor, since its force is much ,veaker anyhow, and the valve s position will most probably not change, if there isn't applied the fu)] power of the motor.

According to Fig. 1~ a sensor for the true speed of the tractor must be available. This could consist of a Doppler radar device (D/J, 1993) or .. in the near future - of a DGPS Doppler device (Han, 1994). In this way, the DOPS system may serve for exact determination of the position and the speed vector. Thus, there exist two devices which provjde sufficiently precise and reliable measurement data for the actuaJ speed; therefore, the problem of speed measurement is considered as solved and will not be treated here further.

1

For sensing the manure flow rate, different devices are available. Details on comparative tests were reported by Buning (1997) and Buning et al. (1998). Precision and dynamic responses of magnetic inductive devices (MID) proved to be the best of all sensors tested. But even the dynamics of the MIDis turned out to be too slow for control purposes. A typical step response for tvvo different MIDis is shown in Fig~ 2. MIDi exhibits a time delay of 1.2 s, followed by a fast rise (lag time approx. O~25 s). MID2 shows a shorter time delay of 0.5 s which, however, is accompanied by a fIrst order lag with lag time of more than 1 s. The latter may be adjusted within narrow bounds.

The time needed for a full opening of the valve) starting from the comp)etely closed and ending at the completely opened position, whjch means a change in the angular position a valve from 0 0 to 50 0 ~ was measured as 0.3... 0.4 s for the hydraulic cylinder and 3.5 s for the electric motor. This means that closedloop control with the electric actuator is achievable while a stable operation of the control loop with th~ hydraulic actuator is not possible - the valve is compJetely opened/closed, before, due to the slow dynamics of the MID, the measurement value has reponed any change in the flow rate..

3.2 A model-based approach with supervisory loop

As for the actuators, the three way valve may be manipulated by hydraulic cylinders or an electric motor. Due to the power requirements for a fast motion of the three way valve and the fact that a usual tractor provides higher hydraulic than electrical power, the hydraulic motion is favourable~

In order to achieve a fast and stable operation of the control loop with hydraulic actuator, a model-based controller \vas designed and implemented; its schematic diagram is sho\vn in Fig. 3. The model which is applied consists of a dynamic-free

5553

Copyright 1999 IFAC

ISBN: 0 08 043248 4

A HIGH PERFORMANCE CONTROL SYSTEM FOR SPREADING OF...

14th World Congress ofIFAC

actuator

controller

valve slurry flow I----~.VS rate (controlled variable)

slurry volume per hectare (reference)

angular position

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MID

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actual speed (measurement)

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Kval ve

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Fig. 3. Schematic diagram of the model-based adaptive controHer i~eal

3~3

proportional system; the estimated flow rate

position

Ctvafve

by a gain factor Kval ve

Vest(t):::=: Kvalve - Ci valve Ct) .

Model-ba~edapproach by

This problem can be solved by a continuous estimation of the gain K valve by an extended Kalman Filter (EKF). The (delay-free) model equations used in this case are

(1)

The gain factor is adapted by a supervisory loop (Hang et al., 1993). This supervisory system is triggered in times when the valve's position remains unchange~ for a certain amount of time, such that the

TMlD

readout VM1D of the MID has settled to a constant value, enabling for computation of an actual value for the gain

d V*MID (t) + dt

Kvalve

=---.

V* MID (t)

:=:

(3)

Kvalve(t)· cx. valve (t) + Wl (t) dKvalve (t)

~~~-=

VMJD

extended Kabnan

filtering

Vest is computed by multiplication of the angular

dt

(2)

a valve

) O+W2 ( t,

(4)

VMID(t) = V*MIO (t)+v(t),

It can easily be concluded from the diagram that • with ~espect to the controlled variable "slurry flow

(5)

where wand v are zero-mean) Gaussian white noise comJ?onents; T MID =: 1 s~ Since 0 ~ o.valve ~ 50° and o ~ Vs$; 500 L/min, a reasonable first estimate· for the valve gain is K valve = 10 L/(min . deg).

rate't (Vs) - the control is almost always open-loop. Permanent closed-loop operation is only obtained for the variable Uangula: valve position However., also the control loop for V s is closed cyclically, namely at times when the automatic calibration procedure is active. t

••

The system is linearized, and the Kalman gain - after some suitable assumptions for the system and measurement noise components - results in

In practice, this system worked very well in cases where the supervisory loop was triggered often enough~ If, however, there are frequent changes in the reference variable of the control loop (e.g. by varying tractor speed or changes in the desired slurry volume per hectare), then the adaptation does not occur often enough to provide meaningful gain estimates.

L(a.) == (

0.042 . ex + 034) 0.1

(6)

Until now, the delay of the MID has not been considered yet (tMJD = 0.5 s). For the continuoustime filter this was included by a Smith predictor (SP), which is built around the Kalman gain. The Kalman feedback gain is considered as the regulator of the EKF model control loop. This means that

5554

Copyright 1999 IFAC

ISBN: 0 08 043248 4

A HIGH PERFORMANCE CONTROL SYSTEM FOR SPREADING OF...

14th World Congress ofIFAC

r:

slurry flow rate (controUed variable)

s

valve and pump; 500 Vm;n _Cl_(t)

~~

_--.L_--.

250. ( 1 + sin

angular position

(~- 0,5 ). 11:)

time Jag of MID

rl

I

tc=

delay of MID

j

modelforSP

sensor

de/ay for EKF

•

Fig. 4:

Schematic diagram of the silllulation models for the valve and the MID, as well as the implemented estimator

a delay-free design of the control loop is possible, as done above, and the delay is taken care of via the SP. The structure of the complete estimator is shown in Fig. 4, \vhere the upper loop is the Smith predictor loop, whereas the lower loop is the classical Kalman filter. The nonlinearity in the input represents eqn. (1), which remains unchanged. On top of the filter, a reasonable non-linear function for the valve characterjstics and the MID model are included in order 10 demonstrate the plant and the corresponding estimator in one figure.

nleasurement (to say nothing of the stability problems). Here the noise fi Itering feature of the Kalman filter is very profitable.

Fig. 6 shows a detail of Fig. 5, i.e. the tiII!e interval from 50 to 65 s. In Fig. 6b, the courses VMID and Vest are combined. This demonstrates that the prediction by the filter works very well; the delay of 0.5 s is nicely compensated.

4. CONCLUSIONS

This combination of EKF and SP perfonns very well, as can be seen in Figp 5 a-d) where the true course o.(t) is shown in Fig. 5a, the measurement signal from the MID is contained in Fig. 5b, the estimated signal is demonstrated in Fig. 5e, and the estimated gain is denoted in Fig. 5d.

A model-based adaptive control strategy is presented for a high-precision and fast operation of the flOVlrate control of a slurry tank trailer. In a fITst impJementatioD_, the model is adapted via a supervisory loop in times of stationary operation of the control loop only. The second implementation uses a dynamic filtering approach with extended Kalman filter and Smith predictor. The results of a practical test of the first implementation were reported in Buning et al. (1998); a practical test of

The nonlinearity of the valve characteristics is only treated as a gain factor. This means that the gain must be re-calculated again for every new set point. Fig. 5d demonstrates this feature clearly.

the second implementation is on its way.

~s

can be seen from Fig. 5b and Fig. Se, the estimate Yest is much smoother than the noisy measurement VMID. This means that the controller, based on the estimated signal, will exhibit much less switchings, compared with a control based an the actual

5555

Copyright 1999 IFAC

ISBN: 0 08 043248 4

A HIGH PERFORMANCE CONTROL SYSTEM FOR SPREADING OF...

5. ACKNOWLEDGEMENT The authors thank the German Ministry for Education, Science, Research and Technology (BMBF) for financial support of the project.

REFERENCES Buning, E. (1997). Ein Beitrag zur Optimierung der Langsvertei!ung van Flussigmist. Dr.-Ing. Dissertation" Technical University of Braunschweig, Gennany.

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Buning, E., A. Munack and H. Speckmann (1998). Components and control systems design for high performance spreading of liquid manure. Proc. of the} 3th 1nt. CIGR Congress on Ag. Eng., Rabat~ Val. 2, pp. 333 - 338_,. DJJ (1993). Technical Data of Dickey-John Corporation, Auburn, lll.~ USA,. Han~ Y. (1994). Personal Communication. AERODATA, Braunschweig,. Hang, C.C.~ T.H. Lee and W.K. Ho (1993). Adaptive ControL Instrument Society of America, Research Triangle Park, N.C., USA.

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14th World Congress ofIFAC

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a) 50

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c) 50

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d)

O~-_-...l.--------~-----'

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Fig. 5. Signals from the

e~tended Kalman

50

100

150

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time [s]

filter with Smith predictor

a): true flow rate Vs(t) according to u (t), b): measurement VMID , c): estimate Vest, d): estimate K

5556

Copyright 1999 IFAC

ISBN: 0 08 043248 4

A HIGH PERFORMANCE CONTROL SYSTEM FOR SPREADING OF...

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14th World Congress of IFAC

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Fig. 6. Details of the time. courses of Fig. 5 . a): true flow rate Vs(t) according to a. (t), b): comparison of measurement VMTD and estimate Vest

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Copyright 1999 IFAC

ISBN: 0 08 043248 4