NL2010258C2

NL2010258C2 - Method of controlling a process with a control signal, computer program, computer program product and control system for controlling a process with a control signal.

Info

Publication number: NL2010258C2
Application number: NL2010258A
Authority: NL
Inventors: Jan Schuurmans
Original assignee: Dotx Control Solutions B V
Priority date: 2012-12-12
Filing date: 2013-02-06
Publication date: 2014-06-02

Description

Method of controlling a process with a control signal, computer program, computer program product and control system for controlling a process with a control signal

The invention relates to a method of controlling a process with a control signal, a 5 computer program, a computer program product and a control system for controlling a process with a control signal.

In a known application, a plant process is controlled using a modified control signal. The process does not react instantaneously to the modified control signal but reacts with a time 10 delay. The modified control signal is also used as an input for a first model part of the process, which models the process without the time delay. The output of the first model part is fed to a second model part of the process, which models the time delay. The output of this second model part is a prediction of the reaction of the process to the modified control signal. The prediction is subtracted from measurement results to obtain a prediction error. The measurement results are 15 obtained by measuring a parameter of the process. During measurement, measurement errors are made so that erroneous measurement results y(t) are available.

The prediction error is fed into a filter F(s) with unitary static gain (F(0)=1). A feedback signal is determined by adding the output of the filter F(s) to the output of the first model part. The feedback signal is subtracted from a set point with desired values for a control signal. The 20 result is fed into a PI controller. The feedback signal is also fed to a proportional gain operator K. The output of the proportional gain operator is subtracted from the output of the PI controller to obtain a modified control signal.

This method of controlling a process which reacts with a time delay, requires that the influence of the time delay can be modelled using a separate part of the model of the process. As 25 indicated above, the process is modelled using the first model part which does not model the time delay, and the second model part which models the time delay. However, it is not always possible to separate the part with and without time delay and the optimal controller for a process is often not PI.

30 For a given model, say Pm, of the process to be controlled and given a well-defined control objective, there are well known model based optimal control solutions. Such solutions, which may be based on LQR/LQG are described in by Kwakernaak, Huibert and Sivan, Raphael (1972) in “Linear Optimal Control Systems. First Edition.” (Wiley-Interscience. ISBN 0-471-51110-2.).

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Another example using Model Predictive Control is reviewed by Michael Nikolaou in “Model predictive controllers: A critical synthesis of theory and industrial needs, Advances in Chemical Engineering” (Academic Press, 2001, Volume 26, Pages 131-204).

An example using Nonlinear Model Predictive Control is reviewed by Findeisen et al, 5 “An Introduction to Nonlinear Model Predictive Control” (21st Benelux Meeting on Systems and Control, Veldhoven, p 1-23, 2002).

Model based control algorithms, such as LQR, LQG, pole placement, MPC, NMPC and feedback linearization are often not robust stable due to model mismatch. There is a model mismatch when the process model on which they were based, differs from the process they 10 actually control.

Another problem with model based control algorithms, such as LQR, LQG, pole placement, MPC, NMPC and feedback linearization, is that filtering the feedback signals before they enter the controller, can lead to reduced stability margins of the closed loop or even instability.

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It is an object of the invention to solve or reduce these problems or to provide a method of controlling which can be implemented with relatively low complexion.

The object is reached by a method of controlling a process with a control signal 20 according to the invention, comprising • controlling the process with the control signal; • measuring the value of at least one process output; • predicting the value of the at least one process output using a model modelling the reaction of the at least one process output to the control signal; 25 · determining a prediction error in the predicted value of the at least one process output by subtracting the predicted value from the measured value; • filtering the prediction error to obtain a filtered prediction error; • adding the predicted value and the filtered prediction error to obtain a feedback signal; 30 · determining a new value for the control signal based on the feedback signal; and • repeating the previous steps.

In this method, the feedback signal is obtained by adding the predicted value of the at least one process output and the filtered prediction error of the at least one process output themselves. Because the prediction error relates to the predicted values (and not to values which 3 are further processed in a second model part) and by filtering the prediction error, it is possible to increase the robust stability of the closed-loop with respect to model mismatch and to reduce the influence of noise on the control signal. The noise on the control signal is reduced by filtering the prediction error. Apart from the stability in case the model accurately describes the 5 process, robust stability in case of model mismatch is obtained because the value of the prediction error signal depends on this mismatch. The higher the mismatch, the larger the prediction error signal and hence the filtered prediction error signal and hence the larger the influence on the feedback signal compensating for the mismatch.

In the prior art method of controlling a process using a first model part and a second 10 model part, the prediction error signal is also larger for higher mismatches. However, in that prior art, the prediction error signal is not used to influence the predicted value as predicted by the second model part on which the prediction error is based, but on the prediction of the first part of the model, i.e. on another prediction. Hence, the larger prediction error signal does not compensate for the mismatch of that first part of the model accurately and depending on the 15 mismatch, the method of control of the prior art can be unsuccessful.

According to an embodiment of the invention, the control signal is determined by a controller arranged to stabilise the model.

By using this criterion for the controller, the so-called nominal closed loop is stable. The advantage of a stable so-called nominal closed loop is that it is relatively easy to select a filter 20 that gives a robust, stable closed loop. Here robust stable means that the closed loop remains stable even if there are mismatches between the process and the model.

According to an embodiment of the invention, the filtering of the prediction error comprises using a filter arranged such that the product of - the induced norm of the filter; and 25 - the induced norm of the system representation of the control method according to the small gain theorem; and - the induced norm of the model mismatch according to the small gain theorem is equal to or less than one.

By applying the small gain theorem, it can be seen that the filter can be chosen such that 30 robust stability is achieved, on the conditions that: - the controller stabilises the model of the reaction of the process on the control signal, and - the model is stable, and - the model mismatch is stable.

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This robust stability is achieved when the filter is conditioned such that the product of - the induced norm of the filter; and - the induced norm of the system representation of the control method according to the small gain theorem; and 5 - the induced norm of the model mismatch according to the small gain theorem is equal to or less than one.

When the model is perfect, the model mismatch can be seen to be zero, and robust stability is also obtained because the product then also is zero.

According to an embodiment of the invention, the filtering of the prediction error 10 comprises reducing a selection of frequency components.

By filtering the prediction error with a filter that reduces a selection of frequency components, the influence of variations in the prediction error can be suppressed so that the control method is less sensitive to the selected frequencies in the prediction error.

According to an embodiment of the invention whereby the measured value of the at 15 least one process output corresponds to a first value of the control signal, the method comprises determining a value for a disturbance of a process variable, the value corresponding to the first value of the control signal; and predicting the value of the at least one process output using the model based on the first value of the control signal and the determined value for the disturbance.

20 By predicting the process output based on the determined value of the disturbance in addition to the corresponding value of the control signal, the quality of the prediction improves. Because the quality of the prediction improves, the error signal decreases in value and the influence of the filter on the feedback signal decreases. Therefore the performance of the closed loop can improve.

25 It will be clear to the person skilled in the art, that the value for the disturbance of the process variable corresponds to the first value of the control signal, in that the disturbance takes place while the process output is under control of the control signal. In a process without time delay, this occurs when the process is under control of the control signal.

According to a further embodiment of the invention, the value for the disturbance of the 30 process variable is determined based on a measured value of the process output.

Values for the disturbance cannot always be measured directly. The advantage of this embodiment is that in such a case the disturbance can still be accounted for, based on a measured value of a process output.

It will be clear to the skilled person, that the measured process output can comprise 5 values of a process output which is not controlled, such as a process variable, or a process output which is controlled.

According to a further embodiment of the invention, the value for the disturbance of the process variable is determined by estimating the value of the disturbance of the process variable 5 based on the feedback signal and the first value of the control signal.

Because the prediction error is obtained by subtracting the predicted value from the measured value, the prediction error is influenced by the disturbance. As the feedback signal is obtained using the prediction error (after filtering), it is also influenced by the disturbance. Because the feedback signal is obtained by adding the filtered prediction error and the predicted 10 value, it feeds back to the controller what the process output will be with application of the first value of the control signal under influence of the disturbance. This can for instance be useful in case it is difficult or impossible to measure disturbance directly in the process.

According to a further embodiment of the invention, the determined value of the disturbance is filtered before being used for predicting the value of the at least one process 15 output.

By filtering the determined value before using that determined value for predicting the value of the at least one process output, it is possible to enhance the control over the process. For instance, the influence of steps in the determined value can be decreased or the influence of undesired frequencies present in the determined value on the predicted value can be decreased.

20 According to an embodiment of the invention, the model accounts for a response time between controlling the process with the control signal and the reaction of the process on the control signal.

When the model accounts for the time delay of the process, the model can be more accurate and the quality of the method is improved.

25 According to an embodiment of the invention, there is provided a control system for controlling a process with a control signal, the control system comprising: - a controller for controlling the process with the control signal; - means for receiving the measured value of at least one process output corresponding to the control signal; 30 - predictor means for predicting the value of the at least one process output using a model of the reaction of the at least one process output on the control signal; - calculation means for determining a prediction error by subtracting the predicted value from the measured value; - a filter arranged to filter the prediction error to obtain a filtered prediction error; and 6 - feedback means for adding the predicted value to the filtered prediction error to obtain a feedback signal; whereby the controller is arranged to determine a new values for the control signal based on the feedback signal.

5 In the device according to the invention, the feedback signal is obtained by adding the predicted values and the filtered prediction error. By filtering the prediction error, it is possible to increase the robust stability of the control system with respect to model mismatch and it is possible to remove signal content from control signal u, without loss of stability.

Embodiments of the invention will now be described, by way of example only, with 10 reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which: - Fig 1 depicts a schematic overview of a method of controlling a process without applying the invention - Fig 2 depicts a schematic overview of a method of controlling a process using the invention 15 - Fig 3 depicts a simplified schematic overview of a method of controlling a process using the invention - Fig 3a depicts a generic simplified schematic overview of a method of controlling a process using the invention - Fig 4 depicts the gain of the transfer function of the control system for different filter settings 20 - Fig 5 depicts a simulation of an application of a control system controlling a model, a process and a control system according to the invention controlling a process - Fig 6 depicts simulation results of two different filters - Fig 7 depicts simulation results - Fig 8 depicts a schematic overview of a control system or control method according to the 25 invention - Fig 9 depicts simulation results of an application of a control system controlling a model, a process and a control system according to the invention controlling a process - Fig 10 depicts a schematic overview of a control system controlling a model 30

Embodiments

Embodiments of the invention are now described using examples wherein a process is controlled in different ways, without and with using the invention, for the purpose of explaining the invention.

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Example 1

In an example there is a process (P) that needs to be controlled by a device arranged to apply a control method (fig 1). A nominal output (yp(s)) of the nominal process (P) can be represented 5 in the Laplace domain by + CFi.2)

Here s represents the Laplace variable and T a delay time between 0 and 0.25 seconds. The delay time represents the time before the nominal output reacts on the control signal. The process (P) is disturbed by a disturbance (d). The disturbance (d) is not under control, i.e. it is 10 not controlled.

In the example, the output of the process (P) as measured is represented as yO)=yP(s) + v (FI.3)

This is further also referred to as the output (y) of the real process.

For the purpose of explaining the invention, an output variation (v) in the measured output of the 15 process is present, wherein v = sin (37rt) (FI. 1)

In this example, the variation (v), or noise signal, is not a stochastic noise signal, but a simple sinusoid, to allow easy verification. In a real implementation the variation can be caused by variations such as turbulence and stochastic processes.

20 The device uses a nominal process model (Pm), which can be represented in the Laplace domain as P,«: (El.2) 5 + 1

The nominal process model (Pm) receives input, but the output of the nominal process model (Pm) is not used in the control method. The device comprises a PI controller (C). The PI 25 controller (C) is fed with setpoint information (r) and is used to determine a control signal (u). The control signal (it) is used to control the nominal process (P) and thereby the output of the process as measured. Hence, the nominal process model (Pm) is a model of the reaction of the process output (y) to the control signal (it). A control challenge is to minimise deviations of the output (y) of the process from the setpoint information (r). A further control challenge is to have 30 a minimal response of the control signal to the noise signal (v). The controller (C) can be represented as C: M = + (E13) 5 8

In this example, the measured output (y) of the real process (P) is used to determine a feedback signal (yc) to be used by controller (C) without any further changes.

With this controller, it is easy to verify that the nominal closed loop is stable, i.e. the PI controller (C) stabilises the nominal process model (Pm).

5 It is to be noted that when the PI controller (C) is used to control the process (P), the closed loop is unstable when the delay time T=0.25 s.

The example is now modified (fig 2) in that the nominal process model (Pm) is used to determine a prediction (ym) of the reaction of the output (y) (or of the process (P)) on the control signal 10 (it). The prediction (ym) is subtracted from the output (y) of the real process to obtain an error signal (z). The error signal (z) is filtered using a filter (F). The filtered error signal is added to the prediction to obtain a feedback signal (yc), which is fed to the PI controller (C). The control signal (it), the nominal process model output (ym) and the feedback signal (yc) are now represented by 8(5 + 1). .

u=-(r-yc) s 15 ym =J-U (El 4) 5 + 1 yc =ym +F(s)(y~ym)

The filter (F) is selected in the following way, such that the closed loop is robust stable. The filter (F) is selected using the small gain theorem (fig 3). According to this theorem the closed loop is stable if 20 ΙΜ-<1 (El.5.0) with the transferr function (Tc) given by ( CP λ T = fa -2— V1_aW (El.5.1) whereby Δ represents the mismatch between the nominal process model (Pm) and the real process (P), given by 25 Δ = —— 1 -e~Ts -1 (El.5.2)

Pm

The filter F is now chosen in such a way that the gain of the frequency response of the transfer function (Tc) is less than 1 for any delay time T between 0 and 0.25 seconds.

Figure 4 shows such a plot for two different settings of the filter (F) when the delay time T = 9 0.25 seconds, because this delay appears to lead to the highest gain of the transfer function (Tc).

Figure 5 shows three simulations results to confirm these results. In each simulation, the disturbance (d) changes stepwise from 0 to 2 at t=5 s.

5 In the first simulation, the controller (C) controls the nominal process model (Pm) and the controller is according to equation El.3. As the nominal process model (Pm) is not disturbed by disturbance (d) and as the nominal process model (Pm) does not incorporate the output variation, the process output (y) is equal to the nominal process model output (ym). In this simulation, the controlled output (ym) remains close to the 10 setpoint (r) in a stable manner.

In the second simulation, the same controller (C) is connected to the process (P) with the delay time (T) having a value of 0.25 s. In this simulation, the closed loop is unstable, since the controller (C) is not robust against this model mismatch between the process (P) and the nominal process model (Pm).

15 In the third simulation, the control system according to the invention and as depicted in Figure 2 is applied in accordance with equation El.4, with the filter (F) according to: F= 1/(0.4 s+1) (El.6)

As can be seen from the simulation results in Figure 5, the controller (C) as implemented 20 in a control system according to invention, is robust stable and the feedback loop is well damped. However, the control signal (u) still responds to the noise (v). It is a control challenge to have a minimal response of the control signal to the noise (v). To avoid this, the filter (F) is extended (placed in series) with a notch filter (Fn) according to s2+0)2 F =- η o _ 2 s + Iqcos + ω 25 wherein ς represents damping, ω represents a notch frequency, i.e. frequency that needs to be blocked.

The effect of extending the filter (F) with a notch filter will be explained using two simulations of which the results are depicted in Figure 6. In each simulation, 30 the disturbance (d) changes stepwise from 0 to 2 at t=5 s.

In the first simulation, the control system according to the invention comprises a filter (F) according to: F= 1/(0.4 s+1) 10 and in the second simulation, the filter (F) is chosen as 1 f s2 + ω2 ' 0.45 + 11^52 + 1.2as + ω2, with ® = 0.3;rrad/s

Clearly, the control signal (u) has a low response to the noise ripple, and still, 5 the closed-loop damping is good which shows as a well damped process output (y) in figure 5.

Example 2 Control of a nonlinear wind turbine system by a nonlinear controller A challenge in the control of a multi-megawatt wind turbine is to maximise 10 power output, while minimising fatigue and ultimate loads. A control system plays an important role in achieving this objective. In this example, it is shown how the invention can be used to allow advanced nonlinear controllers to be applied in practice, and therefore opens the possibility to achieve performance improvements of multi-megawatt wind turbines. For the sake of simplicity and reproducibility, in this example only 15 generator speed control is considered. The model has been chosen in such a way that the invention can easily be verified.

Description of the process (P)

In the example, the process (P) to be controlled relates to the operation of a wind turbine 20 with a drive train between rotor shaft and generator. The process (P) is defined by the following set (E2.1) of equations dü,r

Jr = Τα(θ, ΩΓ, d) — Tsh dQ.a 1

Jg = — (Tsh ~ Tloss) — Tgen άγ 1 — = Ω--Ω dt r itr 3 άξ1 -^ = -60fc-900fc+μ άξ2_, dt θ = 900ξ2 dv 11

Tsh ~ &dtY Y &dt Ta = R3^pnV2Cq(0,A)

Cq(e,X) = —0.0005(0 + 0.6)2(U - 6)2 + 0.01) + 0.02

nrR

λ = ΊΓ

The elements (variables, parameters and outputs) of the model of the process (P), their meanings and their values are shown in Table 1. The variables in have the 5 following meaning: t = time (s)

Qg = generator speed (rad/s)

Qr = rotor speed (rad/s)

Ta = aerodynamic torque exerted by the blades (Nm) 10 Θ = collective pitch angle (rad) μ = collective pitch angle demand (rad) V = rotor effective wind speed, perpendicular to rotor plane (m/s)

Tg = generator torque demand (Nm) γ= torsion angle between rotor and generator (rad) 15 Cq(6,X) = torque coefficient (-) λ = tip speed ratio (-) ξχ, ξ'2= pitch states 20 Table 1 Process parameters

Parameter Meaning Value R rotor radius 70 m

P density of air 1.25 kg/mJ

Jr inertia of rotor 5 x 106 kg m2

Jg inertia of generator 8 x 102 kg m2 itr gearbox ratio 60 I)oss conversion losses 2000 Nm 12 <7dt stiffness of drive train 89543000 Nm/rad 5dt drive train damping 639590 Nm s/rad

Prated rated generator power 2 MW

ilral rated generator speed 114rad/s

Tg generator torque demand 17544 Nm

The process contains nonlinear aerodynamics, a dynamic drive train model, and dynamics of a pitch actuator.

To demonstrate the invention and, in particular, to demonstrate its ability to 5 preserve robust stability in case of model mismatch, the nominal process model (Pm) is a simplified version of the process (P) according to Equation 2.1. In the simplification, the conversion losses are ignored, as well as the drive train dynamics and pitch actuator dynamics. The nominal process model (Pm) is a model of the reaction of the process output to the control signal.

10 The nominal process model (Pm), to be used in control, is given by: dt Je{ am tr 9)

Pm: Tm = Ft±Kp\£Cq(nXm) (E2.2) λ -y">R 7ΤΓ with Je = 7.88 x 106 kg m2 (effective inertia), ym = generator speed (rad/s) and Vm the wind speed (m/s). Vm represents a determined value for the rotor effective wind speed (V). In the example there are disturbances acting on the rotor effective wind speed (V).

15 The determined value for the disturbance is an element of the disturbance vector (dc).

In this example, only above rated wind speed conditions are considered. One control strategy is then to maintain the generator torque (Tg) fixed, and to control the generator speed at rated speed (see Table 1) by pitching (i.e. by adjusting the collective 20 pitch angle demand (μ)) which forms the control signal (u). In the example the pitch angle demand and the control signal are used interchangeably. If the generator speed (Ω5) is controlled at target (rated speed), the power output is at target as well (i.e. 2MW).

Nonlinear controller (Cl (full information case) 25 For this example 2, the invention will first be explained with a controller (C) that is 13 assumed to have access to all information required (including generator speed (Ω^) and wind speed (F)). This case is denoted as the full information case. Hence, in this case, the measured process output (y) is a vector comprising a first component (yx) and a second component (y2). The first component comprises a value for the generator speed (i.e.

5 yx = üg) and the second component comprises a value for the rotor effective wind speed (i.e. y2 = V). The control signal (u) is formed by the pitch demand and the disturbance (d) is the wind speed (V) which obviously is not controlled. For the purpose of explaining the invention, in this example, there is no noise (which can be thought of as v = 0).

The controller (C) is given by the set equations E2.3: du ^{-^^(Tac-itrW-Kciüg-O.aS) dt

Kc = 20

Tac = R3^pnV2Cq(u, Xc) ilaR

Ac=fv ltrv 10

The controller (C), given by Equation E2.3, was designed using feedback linearization (applied to the nominal process model (Pm)). The controller (C) was designed in such a way that any initial control error (üg — ürat), i.e. a deviation between the nominal output of the generator and the rated generator speed (which also forms the 15 set point for the generator speed), converges to 0 exponentially in the absence of changes in the disturbance (i.e. in absence of changes in the rotor effective wind speed (V)). As there is no noise, the initial control error is equal to the deviations of the output y of the process from the setpoint (r), which therefore also converges to 0 thereby achieving a control challenge.

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Figure 7 shows three simulations results. In each simulation, the rotor effective wind speed (V) acts as a disturbance on the process (P) and changes from 11 m/s to 12 m/s at t= 10 s, i.e. it changes stepwise.

In the first simulation, the controller (C) according to equation E2.3 controls 25 the nominal process model (Pm)· In this first simulation, the generator speed (Ωβ) indeed converges to the rated generator speed (ürat) at a value of 114 m/s, i.e. the set point, 14 exponentially after the stepwise change in the rotor effective wind speed (V).

In the second simulation, the same controller (C) is also connected to the process (P), given by equation E2.1. In this simulation, the closed loop is unstable, since the controller (C) is not robust against the model mismatch between the process (P) and 5 the nominal process model (Pm).

In the third simulation, the controller (C) is applied in a method for controlling the process (P) according to an embodiment of the invention. A schematic overview of this control system is shown in Figure 8. In this embodiment, the controller (C) estimates the disturbance in the rotor effective wind speed (V)) based on the feedback 10 signal (y) and the set point values (r). A disturbance filter (Fd) filters the estimated Λ t disturbance (dc) before it is fed to the nominal process model (Pm). The disturbance filter output is the filtered estimated disturbance (dFd)

In this embodiment the first component of the error signal vector (z) is the measured generator speed minus the generator speed as predicted by the nominal process 15 model (Pm). This first component ztoithe error signal vector (z) is filtered by a filter (F) according to FW = —!— (E2.4) 0.5s +1

The second element z2of the error signal vector (z) is the measured rotor effective wind speed minus the rotor effective wind speed that was fed to the nominal process model 20 (Pm). This second element is not filtered (both F=1 and Fd =1). Therefore, the filtered estimated disturbance (dFd) is equal to the estimated disturbance (dc), which in turn is equal to second element of the error signal vector (z). Hence, in this case, the input Vm, for the nominal process model (Pm), given by Equation (2.2), is set to Vm=V = V which is measured directly (by assumption). Since the rotor effective wind speed (V) is a 25 disturbance with external cause, it cannot affect robust stability. Through application of the filter (F) the closed-loop is stable.

Nonlinear controller C (reduced information case)

In practice, the wind speed sensor of a wind turbine usually is not a suitable 30 measurement of the rotor effective wind speed (V), due to the fact that it measures the wind speed at one point in space only. In this example, the controller (C) given by Equation (2.3) is extended with an estimator (0) for the wind speed. In total, the controller (C) now becomes: 15

dt 4 Je SQ V s g’ Je dV

\ e g J \ e J

d^=if{fa-ijgyKo{^g-cig) O: fa=R^pnV2Cq{u,X) (E2.5)

xM

KV K„ =40

Herein estimated variables are indicated by a Λ sign, so that the estimated wind speed is represented by V.

The observer (0) is here a nonlinear Leuenberger observer which is integrated 5 in the controller (C). The observer (0) was designed so that the estimation error converges to 0 exponentially; the speed of this convergence is determined by the gain of the estimator (Ko). If the observer convergence speed is chosen sufficiently high, the overall control system (comprising the controller (C) and the observer (0)) has the same stability and performance properties as a feedback controller with full state information.

10 The controller (C), now using the estimated wind speed (V) from the observer O, is then given by M-2#7'flf.-irTt)-Kc(ps -njl du _ If? \_)_ 2 du V V ))

Kc - 20

dt [4 Je c£2g)y 8 8;{Je dV J

C ^ = -^) E2·6

Ta=R3^pnV2Cq(u,i)

xM

KV K0= 40 15 Figure 9 shows three simulations results. In each simulation, the wind speed 16 (V) changes stepwise from 11 m/s to 12 m/s at t= 10 s. All differential equations were solved using a backward Euler integration scheme with a time step of 0.01 seconds.

In the first simulation, the controller (C) (as defined by equations E2.6) controls the nominal process model (Pm), defined by Equation (2.2). The nominal process 5 model (Pm) receives the estimated wind speed V as input. In that case, the generator speed (Ω5) indeed converges to the rated generator speed (ΩΓαί;) at a value of 114 m/s, i.e. the set point, exponentially after the stepwise change in the rotor effective wind speed GO-

However, if the same controller (C) is connected to the process (P), as is done 10 in the second simulation, the closed loop is unstable.

In the third simulation, the controller (C) is used in a control system according to the invention as in Figure 8, with the process output (y) being formed by the measured generator speed (Ω^). Furthermore, in the third simulation, the nominal process model (Pm) receives the estimated value for the rotor wind speed after applying a filter Fd 15 (i.e. Vm = Vf). The filter (F) is according to: F{s) = —i— 0.55 + 1 and the filter (Fd) according to: FAs) = 7r^— 0.55 + 1 and 20 Vf=Fd(s)V Generic example

In a generic example of the invention (figure 8) the signals y, z, ym, u, r, yc, d, d and v represent multiple variables. The signals are indicated by lower case letter. The process output signal (y) is 25 a vector of N measured signals representing measurements of variables of a process (P). The signal u is a vector of control signals, which form input signals for the process (P). The disturbance (d) represents a vector of disturbances acting on the process (P). The signal d represents a determined value of the disturbance (d) of the process (P). The determination of the values is conducted by estimation or by measurement.

30 The process output signal (y) of measurement values of the variables in the process (P) is subject to noise of a noise signal (v). The noise may in practise be introduced by measurement noise or 17 otherwise such as by turbulence. It is desired that the control method is insensitive to the noise, possibly only at certain frequencies, such as high frequencies. The signal ym represents the outcome of a nominal process model (Pm), i.e. the prediction by the nominal process model (Pm). The nominal process model (Pm) is a model of the reaction of the process output (y) to the 5 control signal (u). The difference between the process output signal (y) and the model outcome signal (ym) is indicated by an error signal (z).

Apart from the nominal process model (Pm), the control system (or control method) comprises a controller (C) and a filter (F) and optionally a further filter (Fd). The controller uses setpoint information (r) and a feedback signal (yc) to determine a control signal (u) for controlling the 10 process (P).

The filter (F) comprises stable subfilters (Fi) for each error signal zi (i=l,2, ..., N) according = (1) whereby s represents the Laplace variable, aik(k = 1,..., na) and bik(k = 1,..., nb) are 15 coefficients and na and nb are natural numbers (with na>nb> 0). Each subfilter Fi has it’s own set of coefficients. The coefficients ai k and bi k do not have to have fixed values. They may vary as function of a signal (for instance a measured signal) or a calculation or estimation.

The determined value (d) of the disturbance is optionally filtered by a further filter (Fd), 20 which also comprises filters according to equation (1) for each signal element dt.

The control system is put together by modelling the process (P) to obtain a nominal process model (Pm) to simulate the response of the process (P) on the control signal (u) and where present also on process variations which are not controlled, the so called disturbance (d) in not 25 controlled process variables. This nominal process model (Pm) can be obtained by a person with ordinary skill in the art skilled in several ways, among which physical modelling (in which case the equations are obtained by applying relevant physical laws such as Newton’s laws of mechanics) and black-box modelling (in which case the model is fit to measured values).

Then a controller (C) is designed presuming that there is no mismatch between the model (Pm) 30 and the process (P). For the design it is presumed that the controller (C) receives the setpoint information (r) and the process output (y) to determine a control signal (u) which is fed to the process (P). The process (P) can be subject to a disturbance (d) in one or more process variables that changes in time.

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The controller (C) may be optimized for a stable performance over a large working range or for a high performance in a smaller working range. Other choices may also be made.

This controller (C) is applied in the control scheme of figure 8.

In a next step, the filter (F) is chosen as a low pass filter, i.e. a range of frequencies above an 5 upper frequency, the so called cut-off frequency, is selected to be reduced. In this step, any determined values (d) of the disturbance are blocked or only very low frequency components are passed on to the model (Pm), for instance by using temporary settings of the optional further filter (Fa) such that the further filter (Fd) acts as a low pass filter with a very low cut off frequency.

10 The filter (F) is chosen to obtain a stable and robust closed-loop by choosing it as a low pass filter.

A simple option is to choose the filter (F) (or the subfilters in the filter (F) as the case may be) as first order low pass, with a low cutoff frequency because if this cutoff frequency is low enough, the closed-loop will be robust stable from the onset. Then, subsequently, the cutoff frequency of 15 the filter (F) is increased to the highest value where robust stability of the closed-loop still holds. In case the filter (F) comprises subfilters, in this step their cutoff frequencies are increased to the highest values where robust stablility of the closed-loop still holds. The cutoff frequencies of the subfilters can be increased simultaneously or in an order of choice.

More advanced model based techniques for choosing the (sub-)filters (F), such as shown 20 in example 1 in relation to figure 3, are also possible. In a preferred embodiment the filter (F) is selected based on ΠΙΜΙΙφι ci with ||.|| denoting any induced norm.

In formula C.l M denotes the system, comprising the nominal model Pm and the 25 controller C in the configuration as shown in Fig 3a with input W2 and output wi, where the controller C is designed to stabilise Pm. In formula C.l the model mismatch is represented by Δ, chosen such that P = Pm + Δ.

Formula C. 1 means that the product of - the induced norm of the filter; and 30 - the induced norm of the system representation of the control method according to the small gain theorem; and - the induced norm of the model mismatch according to the small gain theorem is equal to or less than one. In simple cases (such as in example 1 in relation to figure 2) the selection formula (C.l) reduces to the conditions for a transfer function as expressed by formulas 19

El.5.0, El.5.1 and El.5.2.

Optionally, the filter (F) is extended with additional low pass or notch filters for removing undesired frequency contents from the control signal (u). Hence, additional frequencies are selected to be reduced. This option is available both in case the simple option is used to choose 5 the filter (F) and in case the advanced model based technique is used (both also in case subfilters are used).

For choosing the (sub-)filter(s) (F) to obtain a stable and robust closed-loop and best performance, the gain of the transfer function (or the product of the induced norm of the filter and the induced norm of the system representation of the control model according to the small 10 gain theorem and the induced norm of the model mismatch according to the small gain theorem is brought below 1 for as little frequencies as possible.

While specific embodiments of the invention have been described above, it will be appreciated by the person of ordinary skill in the art that the invention may be practiced otherwise than as 15 described, but still according to the teachings above. The description is intended to be illustrative, not limiting. For instance the invention may be used with discrete time samples, for instance by using the Tustin approximation.

Furthermore, the invention may be used on stable and unstable processes, but it is advised that the nominal process model Pm is stable. In case of an unstable process (P), pre-stabilisation (i.e. 20 first apply a controller that stabilises the process P) before applying the invention, will help obtaining a stable closed-loop.

Also, variants of the invention may include linear models incorporating time delay effects in the model or nonlinear models with or without time delay effects in the model. The filters may take the form of analogue filters or discrete filters. Also the controller (C), or the nominal process 25 model (Pm) may take the form of analogue circuit components. In case the controller (C), the model (Pm), the filter (F) or the further filter (Fd) works in the discrete time domain, they may be embodied in a computer running a computer software program stored on a storage medium, such as a SSD, a hard drive, an optical disk, a USB-stick or a memory card.

Also one or more of the signals y, z, ym, u, r, yc, d, d or v can relate to a single variable, but can 30 also relate to a plurality of variables. The filter (F) or further filter (Fd) can vary as function of one of the signals y, z, ym, u, r, yc, d, d or v or according to another calculation. The filter (F) may be applied to each variable in the error signal (z) or some of them. The further filter (Fd) can be applied to each variable in the observatory signal (d), some of them, or not at all.

The control system can be a computer running software for performing the control method. The 20 computer can receive the measured values of the process output via one or more I/O ports and send the control signal via one or more I/O ports. The computer can for instance receive the measured values and send the control signal via an USB-port, an Ethernet port, via WiFi or via RS-232C ports. Alternatively, the control system is an analogue system.

5 21

Clauses 1 Method of controlling a process (P) with a control signal (it)according to the invention, comprising 5 · controlling the process with the control signal; • measuring the value of at least one process output (y); • predicting the value of the at least one process output using a model (Pm) modelling the reaction of the at least one process output to the control signal; • determining a prediction error (z) in the predicted value of the at least one process 10 output by subtracting the predicted value from the measured value; • filtering the prediction error to obtain a filtered prediction error; • adding the predicted value and the filtered prediction error to obtain a feedback signal (yc); • determining a new value for the control signal (it) based on the feedback signal; 15 and • repeating the previous steps.

2 Method according to clause 1, wherein the control signal is determined by a controller (C) arranged to stabilise the model.

20 3 Method according to clause 2, wherein the filtering of the prediction error comprises using a filter (F) arranged such that the product of - the induced norm of the filter; and - the induced norm of the system representation of the control method according to the small 25 gain theorem; and - the induced norm of the model mismatch according to the small gain theorem is equal to or less than one.

4 Method according to clause 1, 2 or 3 wherein the filtering of the prediction error (z) 30 comprises reducing a selection of frequency components. 1

Method according to any of the clauses 1, 2, 3 or 4, wherein the measured value of the at least one process output corresponds to a first value of the control signal, the method comprises determining a value for a disturbance (d) of a process variable, the value 22 corresponding to the first value of the control signal; and predicting the value of the at least one process output using the model (Pm) based on the first value of the control signal and the determined value for the disturbance.

5 6 Method according to clause 5, wherein the value for the disturbance (d) of the process variable is determined based on a measured value of the process output.

7 Method according to clause 5, wherein the value for the disturbance (d) of the process variable is determined by estimating the value of the disturbance of the process variable based 10 on the feedback signal (yc) and the first value of the control signal (u).

8 Method according to clause 5, 6 or 7, wherein the determined value of the disturbance (cl) is filtered before being used for predicting the value of the at least one process output.

15 9 Method according to any of the preceding clauses, wherein the model (Pm) accounts for a response time between controlling the process (P) with the control signal (u) and the reaction of the process on the control signal.

10 Computer program comprising program code means for performing all the steps of 20 any of the clauses 1 to 9 when said program is run on a computer.

11 Computer program product comprising program code means stored on a computer readable medium for performing the method of any one of the clauses 1 to 9 when said program product is run on a computer.

25 12 Control system (C,Pm,F) for controlling a process with a control signal (it), the control system comprising: - a controller (C) for controlling the process with the control signal; - means for receiving the measured value of at least one process output corresponding to 30 the control signal; - predictor means for predicting the value of the at least one process output using a model (Pm) of the reaction of the at least one process output on the control signal; - calculation means for determining a prediction error by subtracting the predicted value from the measured value; 23 - a filter (F) arranged to filter the prediction error to obtain a filtered prediction error; and - feedback means for adding the predicted value to the filtered prediction error to obtain a feedback signal (yc); whereby the controller is arranged to determine a new values for the control signal based 5 on the feedback signal.

Claims

A method for controlling a process with a control signal, comprising - controlling the process with the control signal, 5. measuring the value of at least one process output; - predicting the value of the at least one process output with a model of the response of the at least one process output to the control signal; - determining an error in the prediction of the at least one process output by subtracting the predicted value from the measured value; 10. filtering the error in the forecast into a filtered error in the forecast; - determining a feedback signal by adding the predicted value and the filtered error in the prediction; - determining a new value of the control signal using the feedback signal; and 15. repeating the previous steps.

The method of claim 1, wherein the control signal is determined with a control device adapted to stabilize the model.

Method according to claim 2, wherein for filtering the error in the prediction a filter (F) is used arranged such that the product of the induced norm of the filter; and - the induced standard of the system representation of the method according to the small gain theory; and 25. the induced standard of the modeling error according to the small gain theory is less than or equal to one. Method according to claim 1, 2 or 3, wherein filtering the error in the prediction comprises damping a selection of frequency components. Method according to claim 1, 2, 3 or 4, wherein - the measured value of the at least one process output corresponds to a first value of the control signal; - a value corresponding to the first value of the control signal for the disturbance of a process variable is determined; and wherein predicting the value of the at least one process output is based on the first value of the control signal and the corresponding determined value for the disturbance of the process variable. 5

The method of claim 5, wherein the value of the disruption of the process variable is determined based on a measured value of the process output.

The method of claim 5, wherein the value of the disturbance of the process variable 10 is determined using an estimate based on the feedback signal and the first value of the control signal.

8. Method according to claim 5, 6 or 7, wherein the determined value of the disturbance is filtered before it is used for predicting the value of the at least one process output.

A method according to any one of the preceding claims, wherein the model is adapted to take into account a response time between controlling the process with the control signal and the reaction of the process to that control signal. 20

A computer program comprising program code for performing the steps of any of claims 1 to 9 when the program is running on a computer.

11. Product provided with program code for performing the method according to any of claims 1 to 9, wherein the program code is stored on a computer-readable medium.

A control device for controlling a process with a control signal, comprising: 30. control means for controlling the process with the control signal; receiving means for receiving the measured value of at least one process output corresponding to the control signal; - predicting means for predicting the value of the at least one process output with a model of the response of the at least one process output to the control signal; - calculating means for determining an error in the prediction by subtracting the predicted value from the measured value; - a filter to filter the error in the forecast to a filtered error in the forecast; 5. feedback means for determining a feedback signal by adding the predicted value and the filtered error in the prediction; - wherein the control means are adapted to determine new values of the control signal on the basis of the feedback signal.