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Switching sequences for non-predictive

declutching control of wave energy

converters

Paula B. Garcia-Rosa ∗,∗∗ Olav B. Fosso ∗∗ Marta Molinas ∗∗∗

∗SINTEF Energy Research, 7465 Trondheim, Norway

(e-mail: paula.garcia-rosa@sintef.no).

∗∗ Department of Electric Power Engineering, Norwegian University of

Science and Technology, NO-7491 Trondheim, Norway

(e-mail: olav.fosso@ntnu.no).

∗∗∗ Department of Engineering Cybernetics, Norwegian University of

Science and Technology, NO-7491 Trondheim, Norway

(e-mail: marta.molinas@ntnu.no)

Abstract: Aiming at improving the energy absorption from waves, a number of studies

have considered declutching control – a phase-control method that consists of disengaging

the power take-oﬀ (PTO) system from the oscillating body at speciﬁc intervals of time. The

on/oﬀ sequences with the instants to engage/disengage the PTO are usually determined by

optimization procedures that require the knowledge of future excitation force, which remains

an open challenge for practical implementation. This paper presents a comprehensive numerical

study with diﬀerent PTO damping coeﬃcients for declutching control. It is shown that the

value of the damping plays an important role on the eﬃcacy of the control method and on

the optimal time to engage (or disengage) the PTO. Then, two switching sequences that

use current information of the body motion are proposed, and compared with the threshold

unlatching strategy. When the body velocity vanishes, the PTO is clutched (declutched) if

the current estimation of the mean excitation force frequency is lower (higher) than the body

resonant frequency. The instant to declutch (clutch) again depends on the damping coeﬃcient.

The resultant PTO force proﬁles are not optimal, but act in an eﬀective way to improve the

energy absorption, while not requiring wave short-term predictions and numerical optimization

solutions that can be time-consuming depending on the ﬁdelity of numerical models and the

prediction horizon. Numerical simulations consider real ocean waves and synthetic waves.

Keywords: Renewable energy systems, wave energy, declutching control, on-oﬀ actions,

numerical simulation.

1. INTRODUCTION

In order to absorb maximum power from waves, con-

trol systems require wave forecasting and bi-directional

power take-oﬀ (PTO) systems. In this framework, con-

trol schemes based on model-predictive control are widely

studied in the literature, see, e.g., Faedo et al. (2017)

for a review. Alternatively, passive control methods are

sub-optimal solutions that avoid the need for the PTO to

supply power (and hence are named passive) while still in-

creasing the absorption when compared to passive loading

(PL). In contrast to PL, where the PTO damping is con-

stant, passive control methods can modify the damping on

a timely basis, either by tuning it to the frequency of waves

(Garcia-Rosa et al., 2019) or by solving an optimization

problem to determine the optimal damping proﬁle, which

results in on/oﬀ sequences (Tom and Yeung, 2013) – a

characteristic of the declutching control (DLC) method.

Declutching is a phase-control method that consists of

disengaging the PTO system from the oscillating body

during some parts of the body motion cycle. The principle

is to engage and disengage the PTO in order to allow

the oscillating body to “catch up” to the excitation force,

and then, bring the body velocity into phase with the

excitation force.

The switching sequences for DLC are usually determined

by optimization procedures that require the knowledge

of future excitation force (Babarit et al., 2009; Teillant

et al., 2010; Cl´ement and Babarit, 2012), which remains

an open challenge for practical implementation. Babarit

et al. (2009) have used an optimization procedure based

on Pontryagin principle to determine the instants the PTO

system is either on or oﬀ. It is shown that changes in

the controller state, from oﬀ to on, are followed by zero-

crossings of the velocity, but a heuristic criterion regarding

the instants to switch back the controller state to oﬀ has

not been identiﬁed.

Furthermore, aiming at determining the best damping

proﬁle in terms of energy absorption for regular waves,

Teillant et al. (2010) have used a general parametrization

of the damping force that allowed for two phase-control

methods: latching and declutching. While latching locks

the body motion for speciﬁc intervals of time, declucthing

control modiﬁes the body dynamics without locking it.

Teillant et al. (2010) have shown that declutching (latch-

ing) control is optimal when the wave frequency is higher

(lower) than the body resonant frequency. For declutching,

the damping changes from upper to lower boundary values

when the body velocity vanishes. The duration of time for

lower damping, as well as the upper and lower values, were

determined through an optimization process with a genetic

algorithm and the Nelder-Mead algorithm.

In (Feng and Kerrigan, 2013), the PTO is clutched when

the body velocity is zero, and a derivative-free optimiza-

tion algorithm that reduces the number of function eval-

uations is proposed to determine for how long the PTO

should be active. A comparison of the wave energy con-

verter (WEC) performance for optimization formulations

based on past and future wave data is also presented.

To avoid the prediction of future waves, a few studies on

declutching have used the threshold unlatching strategy

(Hals et al., 2011; Garcia-Rosa and Ringwood, 2016). As

suggested by the name, the strategy was initially proposed

for latching control. It consists of unlatching the body at

the instant when the excitation force (or other reference

variable) passes a chosen threshold (Lopes et al., 2009).

The aim of this paper is twofold. Firstly, to investigate

how the PTO damping coeﬃcient aﬀects the optimal de-

clutching/clutching duration and the eﬃcacy of the control

strategy in terms of improving the power absorption in

regular wave regimes. Rather than optimizing the PTO

damping, the purpose is to identify for which values of

damping, declutching control will not represent an eﬃcient

solution to improve the energy absorption, when compared

to a simpler strategy as passive loading. Then, the goal

is to propose switching sequences that do not require

estimation of future incident waves. Two strategies that

use current information of the body motion are proposed,

and compared with the threshold unlatching strategy. Fur-

thermore, in all switching sequences, the decision about

clutching (declutching), i.e. engaging (disengaging) the

PTO, depends on the current estimation of the dominant

frequency of the wave excitation force and on the body

resonant frequency. The sequences diﬀer on deﬁning the

instants to declutch (clutch) again the PTO.

2. DYNAMIC MODELING OF THE WEC

2.1 Equation of Motion

This study considers a single oscillating body represented

as a truncated vertical cylinder constrained to move in

heave. With the assumption of linear hydrodynamic the-

ory, and neglecting friction and viscous forces, the body

motion is described by the superposition of the wave

excitation force (fe), radiation and restoring forces, and

the force produced by the PTO mechanism (fp):

M¨x(t)+

t

Z

0

hr(t−τ) ˙x(τ)dτ +Sx(t) = fe(t)+fp(t),(1)

where x∈Ris the vertical position of the body, M=

[m+mr(∞)], m∈R+is the body mass, mr(∞)∈R+

is the inﬁnite-frequency added mass coeﬃcient, deﬁned

with the asymptotic values of the added masses at inﬁnite

frequency, S∈R+is the buoyancy stiﬀness, and the kernel

of the convolution term hr(t−τ) is known as ﬂuid memory

term (Cummins, 1962),

hr(t) = 2

π

∞

Z

0

Br(ω) cos(ωt −τ)dω , (2)

where Br(ω)∈R+is the radiation damping coeﬃcient, and

ω∈R+is the wave frequency.

The excitation force, i.e., the force due to the incident

waves is given by

fe(t) =

∞

Z

−∞

he(t−τ)ζ(τ)dτ , (3)

where heis the inverse Fourier transform of the excitation

force transfer function He(ω), which has low-pass ﬁlter

characteristics for ﬂoating WECs, and ζis the wave

elevation. Notice that (3) is non-causal, since in fact, the

pressure distribution is the cause of the force and not the

incident waves (Falnes, 2002).

The mean absorbed power over a time range Tis

Pa=−1

T

T

Z

0

fp(t) ˙x(t)dt , (4)

where ˙x(t) is the velocity of the body. By considering a

generic PTO system and PL, the PTO force is deﬁned as

fp(t) = −Bc˙x(t),(5)

where Bc∈R+is the PTO damping.

2.2 Steady-state Sinusoidal Motion

Under passive loading (5), the steady-state response of

the body velocity to fe(t) = Fe(ω) cos ωt is given by

˙xss (t) = |H(jω)|Fe(ω) cos(ωt +φ(ω)), where

H(jω) = 1

(Bc+Br(ω)) + j(ω(m+mr(ω)) −S/ω),(6)

φ(ω) = −arctan ω(m+mr(ω)) −S/ω

Bc+Br(ω),(7)

and Fe(ω)∈R+is the excitation force coeﬃcient.

By assuming the body resonant frequency is ωr≈

pS/(m+mr(ω)), the phase (7) between the velocity and

the excitation force can be rewritten as

φ(ω) = −arctan (m+mr(ω))(ω2−ω2

r)

ω(Bc+Br(ω)) .(8)

From (8), it can be noted that when

•ω < ωr, then φ(ω)>0, and the velocity leads the

excitation force;

•ω > ωr, then φ(ω)<0, and the velocity lags the

excitation force;

•ω=ωr, then φ(ω) = 0, and the velocity is in phase

with the excitation force.

Furthermore, for regular wave regime and PL, the optimal

constant damping and the average power absorbed by the

WEC are, respectively, calculated as (Falnes, 2002):

Bc,opt(ω) = p(Br(ω))2+ (ω(m+mr(ω)) −S/ω)2,(9)

Pc,opt =Bc,opt(ω)Fe(ω)2

2(Bc,opt(ω) + Br(ω))2.(10)

3. SWITCHING SEQUENCES FOR DECLUTCHING

CONTROL

Here we assume a generic PTO system, where the PTO

force is expressed as

fp(t) = −Bp˙x(t)u(t),(11)

Bp∈R+is the PTO damping, and the control signal u(t)

has two states: on (u=1) or oﬀ (u= 0).

As discussed in Section 2.2, when the incident wave

frequency is lower than the body resonant frequency, the

velocity is leading the excitation force by a certain phase

shift. Then, the phase-control method should act to slow

down the natural response of the body in order to force

the velocity to be in phase with the excitation force.

Conversely, the controller should act to speed up the

natural response of the body when the wave frequency

is higher than the WEC resonant frequency.

Following previous studies (Teillant et al., 2010), the

PTO force proﬁle is determined according to the inci-

dent wave frequency and the resonant frequency of the

oscillating body. However, only the clutching concept, i.e.

engage/disengage the PTO, is applied here. Thus, for

•ω < ωr: To slow down the device motion, the PTO

is connected, i.e. clutched (u= 1), when the body

velocity vanishes, and disconnected, i.e. declutched

(u=0), in a certain instant of time to be determined.

•ω > ωr: To allow the device to move “faster”, the

PTO is disconnected (u= 0) when the body velocity

vanishes, and connected (u= 1) in a certain instant

of time to be determined.

The objective is to propose causal control laws for DLC by

performing a comprehensive numerical study using regular

waves at ﬁrst. Using diﬀerent values of damping, optimal

clutching durations are determined for the cases when

ω < ωr, and optimal declutching durations, for the cases

when ω > ωr. In such a way, the eﬀect of the PTO damping

on the control strategy is also investigated. In what follows,

numerical simulations are performed considering the same

heaving cylinder adopted in (Garcia-Rosa et al., 2017).

The cylinder has a radius of 5 m, draught of 4 m, mass

m=3 ×105kg and resonant frequency ωr=1.2 rad/s.

3.1 Optimal clutching/declutching duration

The optimal clutching/declutching duration in seconds

(∆th,opt) that optimizes the power absorbed by the WEC

with decltuching control is determined via simulations

with a complete set of possible values for the time interval.

Figure 1 (right) illustrates the optimal intervals of time

obtained for diﬀerent PTO coeﬃcients and regular waves

with amplitude of 1 m and some speciﬁc frequencies. The

PTO damping coeﬃcients are deﬁned as

Bp=¯

BpBc,opt(ω),(12)

for each wave frequency ω, where ¯

Bpis a dimensionless

constant, 0.5≤¯

Bp≤20, and Bc,opt(ω) is the optimal

-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2

0

1

2

3

4

5

6

-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2

0

1

2

3

4

5

6

-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Fig. 1. Evolution of optimal time (right) and ratio of

power (left) versus PTO damping in regular waves. (a)

Optimal clutching duration, ω < ωr; (b) Optimal de-

clutching duration, ω > ωr. The lines in (a) represent

the latching duration for each one of the frequencies.

constant damping (9). It can be noted that, for ω < ωr, as

the value of the damping increases, the optimal clutching

duration reduces and tends to the latching duration. The

latching duration, denoted as ∆tLin Fig. 1.a (right), is

calculated as half the diﬀerence between the wave period

and the body resonant period (Babarit and Cl´ement,

2006). When the damping is too high (20Bc,opt(ω)) and

u=1, the PTO force (11) restricts the motion of the body,

and consequently, declutching control acts in a similar way

as latching control for the cases when ω < ωr. Conversely,

when ω > ωrthe optimal declutching duration increases

with the damping.

The ratio of power, calculated as r=Pa/Pc,opt, is also

shown in Figure 1 (left). For ω < ωrand Bp<2Bc,opt(ω),

DLC will result in less power absorption than the optimal

PL power, Pc,opt (10), or about the same value. Thus,

the value of damping is also important for the eﬃcacy of

the strategy. This is further evidenced by Figure 2, which

shows the evolution of the ratio of power for diﬀerent wave

frequencies, PTO damping coeﬃcients, optimal clutch-

ing duration (Fig. 2.a) and optimal declutching duration

(Fig. 2.b). For ω > ωrand the WEC considered in this

study, the damping for the declutching strategy should

be higher than 2Bc,opt(ω) to allow an energy absorption

greater than optimal passive loading.

Fig. 2. Ratio of power as a function of PTO damping and

wave frequencies in regular waves with (a) optimal

clutching duration (b) optimal declutching duration.

To illustrate how the behaviour of system variables

changes according to PTO damping for ω < ωr, Figure 3

shows the time-series of normalized variables ( ¯

fe,¯x, ¯

˙x, x ˙x)

and the control signal (u). Constants ¯

Bp= 1.5 (Fig 3.a),

and ¯

Bp= 5 (Fig. 3.b), are used with their corresponding

optimal clutching duration. The instants uchange from

on to oﬀ occur very close to the instants the position is

zero, or equivalently, when the signal x˙xhas a positive

zero crossing. Nonetheless, the same conclusion cannot be

drawn when ¯

Bp= 5 (Fig. 3.b). In such a case, the high

damping force employed after the velocity zero crossing

causes the velocity to remain around zero, almost stopping

the body motion, and thus, neither xnor x˙xprovide a good

indication for disengaging the PTO.

For ω > ωr, the instants when ˙x= 0 deﬁne the instants to

disengage the PTO. Figure 4 illustrates the time-series of

normalized variables and the control signal when ¯

Bp=2.5

(Fig 4.a), and ¯

Bp= 5 (Fig. 4.b), with their corresponding

optimal declutching duration. It is noted that the intervals

while u=1 coincide with intervals the body is speeding up,

i.e. acceleration and velocity are in the same direction, and

the optimal instant the PTO is switched on occurs when

the device starts to slow down (Fig.4.a), i.e. ˙x¨x < 0, or a

few seconds after it (Fig. 4.b) depending on the damping.

3.2 Switching sequences without prediction of future waves

This section proposes two strategies to determine the in-

stants the control signal uis either on or oﬀ, based on the

100 105 110 115

-1

0

1

100 105 110 115

-1

0

1

100 105 110 115

-1

0

1

100 105 110 115

-1

0

1

Fig. 3. Time-series of normalized variables and control

signal for (a) Bp= 1.5Bc,opt, and (b) Bp= 5Bc,opt .

(ω=0.75 rad/s, optimal clutching duration).

100 105 110 115

-1

0

1

100 105 110 115

-1

0

1

100 105 110 115

-1

0

1

100 105 110 115

-1

0

1

Fig. 4. Time-series of normalized variables and control

signal for (a) Bp= 2.5Bc,opt, and (b) Bp= 5Bc,opt .

(ω=1.65 rad/s, optimal declutching duration).

observations from Section 3.1. The strategies are evaluated

through a comparison with the unlatching threshold strat-

egy, when the WEC is submitted to synthetic irregular

waves and real ocean waves. Since such waves are not

deﬁned by a single frequency, and the oscillating body has

low-pass ﬁlter characteristics, the mean centroid frequency

of the excitation force (ω1,fe) is adopted in replacement to

the wave frequency ωof regular wave cases.

The mean centroid frequency of the excitation force can

be estimated, e.g., by the extended Kalman ﬁlter (EKF)

as shown in (Garcia-Rosa et al., 2019). In such a case,

fe(t) has to be estimated as well. Note that the switching

sequences proposed here rely only on the estimation of the

frequency. Thus, an alternative scheme using real wave

measurements and He(ω) could be adopted to obtain an

estimation of the mean frequency of the excitation force.

The following switching sequences, denoted respectively as

D1 and ¬D2, are proposed for the cases when ω1,fe< ωr:

u(t) = 1, x ˙x(t)≤0,

0, x ˙x(t)>0,(13)

and for the cases when ω1,fe>ωr:

u(t) = 0,˙x¨x(t)≥0,

1,˙x¨x(t)<0.(14)

For threshold unlatching strategies, denoted here as D3

and D4, ˙x=0 triggers the control state until fe(t) passes a

chosen threshold (Lopes et al., 2009). Table 1 summarizes

the switching sequences, where D1–D4 are applied when

ω1,fe< ωr,¬D1–¬D4 are applied when ω1,fe> ωr. The

symbol ¬represents logical negation.

Three wave elevation records oﬀ the west coast of Ireland

(as in Garcia-Rosa et al. (2019)), referred as sea states

S1–S3, and six irregular waves (Ir1–Ir6) are adopted as

inputs to the WEC. For each real sea state, two irregular

waves are generated by modifying the parameters of Ochi

spectral distributions (Ochi, 1998). Figure 5 illustrates the

wave spectra of sea states and synthetic waves (top), and

the corresponding excitation force spectra (bottom). The

signiﬁcant wave height Hsof the wave spectra, and the

mean centroid frequency for both the wave (ω1) and the

excitation force spectra (ω1,fe) are shown in Table 2.

The simulation interval is about 30 min for each case. A

comparison in terms of power absorption for the switching

sequences (Table 1) with PL power is shown in Figure6.

The ratio rcis calculated as Pa/Pc, where Pais the power

absorbed by the WEC when DLC is applied, and Pcis

the PL power with damping tuned at frequency ω1,fe.

As suggested by the analysis of Fig. 3, D1 results in the

greatest energy absorption when the damping is around

1.5 to 2.5Bc(ω1,fe) for waves Ir1–Ir3 and Ir5. Such waves

have mean centroid frequencies much lower than the body

resonant frequency (1.2 rad/s). As the damping increases,

the best strategies become the threshold unlatching (D3,

D4). Such strategies do not rely on the dynamic motion of

the WEC to switch oﬀ the control signal. Furthermore, the

beneﬁt of applying DLC using D1–D4 in Ir4 is lower than

the other cases, since ω1,feis very close to ωr. Finally, when

ω1,fe>ωr(Ir6) and Bp<4Bc(ω1,fe), sequence ¬D2 is the

best choice. ¬D2 deﬁnes the time interval in which the

WEC is speeding up (slowing down) as the time interval

the control signal is oﬀ (on), and thus, it allows the body

to gain momentum.

In order to compare the strategies with best performances

in terms of power absorption for ω1,fe< ωr, Table 3

summarizes the obtained results for S1–S3 with D1 ( ¯

Bp=

2) and D4 ( ¯

Bp= 5). A comparison of the peak-to-average

power ratio (PTO rating), maximum PTO force, and

maximum displacement of the body are included with the

ratio rc. Although the strategy D4 with ¯

Bp= 5 results in

the greatest power in most of the cases, it requires higher

PTO forces and larger displacements of the body than D1.

It is important to note that constraints on the PTO force

and body motion are not considered here, but for practical

Table 1. Switching sequences

Condition u(t) Str. Condition u(t)

D1 x˙x≤0 1 ¬D1 x˙x≤0 0

x˙x > 0 0 x˙x > 0 1

D2 ˙x¨x≥0 1 ¬D2 ˙x¨x≥0 0

˙x¨x < 0 0 ˙x¨x < 0 1

D3 trigger: ˙x=0 1 ¬D3 trigger: ˙x=0 0

thres: ˙

fe=0 0 thres: ˙

fe=0 1

D4 trigger: ˙x=0 1 ¬D4 trigger: ˙x=0 0

thres: fe=0 0 thres: fe= 0 1

0 1 2 3

0

0.2

0.4

0.6

0.8

1

0 1 2 3

0

1

2

3

4

51011

0123

0

0.1

0.2

0.3

0.4

0123

0

5

10

15 1010

0123

0

0.2

0.4

0.6

0123

0

0.5

1

1.5

2

2.5 1011

Fig. 5. Wave spectra of real data and synthetic irregular

waves (top), and excitation force spectra (bottom).

Table 2. Signiﬁcant wave height Hs(m),

wave mean centroid frequency ω1(rad/s),

and excitation force mean centroid frequency

ω1,fe(rad/s) for S1–S3 and Ir1–Ir6.

S1 Ir1 Ir2 S2 Ir3 Ir4 S3 Ir5 Ir6

Hs1.26 1.50 2.00 1.43 1.85 1.49 1.39 1.67 0.90

ω10.70 0.54 0.91 1.18 1.12 1.37 1.18 1.09 2.18

ω1,fe0.55 0.54 0.61 0.73 0.75 1.18 0.59 0.61 1.74

12345

0.5

1

1.5

2

2.5

12345

0.5

1

1.5

2

2.5

12345

0.5

1

1.5

2

12345

0.5

1

1.5

12345

0.5

1

1.5

2

2.5

12345

0.5

1

1.5

2

2.5

Fig. 6. Ratio rcfor irregular waves (Ir1-Ir6).

application studies, the physical limits of both the body

excursion and PTO have to be taken into account. Figure

7 shows a sample of time-series simulation for S1 with D1

(¯

Bp= 2) when the excitation force frequency is estimated

by the extended Kalman ﬁlter.

Table 3. Ratio rc, PTO rating, maximum PTO

force, and maximum body displacement for D1

and D4 in S1–S3.

Sea Strategy rcPmax /Pafp,max (kN) xmax (m)

S1 D1 ( ¯

Bp=2) 2.07 8.93 750.5 1.13

D4 ( ¯

Bp=5) 2.47 8.84 1.29×1032.27

S2 D1 ( ¯

Bp=2) 1.69 14.12 624.5 1.03

D4 ( ¯

Bp=5) 1.68 15.02 1.02×1031.64

S3 D1 ( ¯

Bp=2) 2.02 13.73 808.1 1.33

D4 ( ¯

Bp=5) 2.16 12.33 1.25×1032.16

900 905 910 915 920 925 930 935 940 945 950

0.55

0.552

0.554

900 905 910 915 920 925 930 935 940 945 950

-1

-0.5

0

0.5

1

Fig. 7. Time-series of EKF estimated frequency (top),

normalized excitation force, velocity, position, and

control signal for S1 with D1 and ¯

Bp=2 (bottom).

4. CONCLUSIONS

A comprehensive numerical study with diﬀerent PTO

damping coeﬃcients showed that the value of damping

plays an important role on the eﬃcacy of the declutching

control method and also on the optimal time to engage

(or disengage) the PTO. Thus, the switching sequences for

non-predictive control should take into account the value

of the damping, or the PTO force applied.

Furthermore, the switching sequences proposed here rely

on current estimations of the mean centroid frequency of

the excitation force and on the body resonant frequency.

The decision about clutching (declutching) the WEC, i.e.

engaging (disengaging) the PTO, is deﬁned according to

current estimations only. When the body velocity van-

ishes, the PTO is clutched (declutched) if the estimated

mean frequency is lower (higher) than the body resonant

frequency. The switching sequences diﬀer on deﬁning the

instants to declutch (clutch) the PTO again.

For a generic PTO system, the results showed that when

the declutching damping is twice PL damping as deﬁned

by (9), the variables of motion (position, velocity, acceler-

ation) can be used for deﬁning both the instants to clutch

and declutch. For instance, when the mean excitation force

frequency is higher than the body resonant frequency,

the PTO is disengaged while the body is speeding up

(i.e. velocity and acceleration are in the same direction

˙x¨x(t)≥0) to allow the body to gain momentum, and

engaged while the body is slowing down (i.e. ˙x¨x(t)<0).

However, the switching sequences relying on the motion

to deﬁne both instants to clutch and declutch are only

meaningful if the body motion is not excessively restricted

by high damping forces during clutching (e.g., when the

damping is ﬁve times the passive loading damping). In

such cases, the threshold unlatching strategy is the best

option for deﬁning the switching sequences if wave fore-

casting is to be avoided.

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