Fig。 6。 Identification process for unknown cable dynamics。

Fig。 8。 Frequency responses of the disturbance model (cable model)。

Fig。 9。 Feedback system representation。

Fig。 10。 Feedback system representation based on robust control ap- proach。

Fig。 7。 Responses of disturbance model (cable model)。

as the following transfer function:

any loss of generality, and a generalized plant with controller based on the Hmethod is illustrated in Fig。 11。  Therefore, the control system design objective is equalized to obtain a

controller K (s) which satisfies the norm condition:

7。68 10s 3。79 103

Gd (s) 3 2 3 4 。

s  27。78s  1。64 10 s 1。43 10

4。 Controller design and experiment

is    the    transfer    function    from w   to

z zT zT , and  W (s) is a weighting function to shape the

Based  on the proposed  idea and  identification  results,  we

design a robust control system。

For example, if we introduce the Hcontrol theory [11, 12], a feedback system configuration is obtained as shown in Fig。 9 where  the  cable dynamics Gd (s) is considered  as disturbance

and uncertainty (s), because the cable motions produce force

output sensitivity function。

Let us describe the transfer functions and W (s) in Fig。 11 as  follows:论文网

variations for the winch  system  as described  in  the previous

section。  Then,  Fig。  9 is directly depicted  as Fig。  10 without

Then, the feedback system with the controller K (s) is stable if  and  only  if  there   exist   the   positive   definite   matri- ces X   and Y  which satisfy the following conditions [11, 12]:

and the elementary matrices in Eq。 (11) are defined as follows:Using MatLab Tool, the controller satisfying the given con-

Then,  a  controller  stabilizing  the  closed-loop  system and and the weighting function  W (s) is selected as follows:

satisfying the constraint

Based on these results, we present the simulation results。 First,  Fig。  13 shows  the disturbance  rejection performance

Fig。 12。 Step type disturbance input to the vessel : simulation。

Fig。 13。 Disturbance rejection performance with designed controller : simulation。

Fig。 14。 Control input made by controller : simulation。

Fig。 15。 Sinusoidal type disturbance (frequency range: 1 to 15 Hz, amplitude: 1 N) : simulation。

of the proposed control system where a step type disturbance shown in Fig。 12 exists and the distance target of the con- trolled vessel is 0。05 m。

Fig。 14 depicts the control signal produced from the control- ler to cope with the disturbance input。

Fig。 16 shows the control performance when the vessel is exposed to the sinusoidal disturbance input as shown in Fig。 15, and Fig。 17 is the control signal made by the controller。

As shown in the simulation results, it is clear that the de- signed control system with proposed control strategy works well。