Elsevier

Information Sciences

Volume 526, July 2020, Pages 119-132
Information Sciences

Fuzzy robust fault-tolerant control for offshore ship-mounted crane system

https://doi.org/10.1016/j.ins.2020.03.068Get rights and content

Abstract

In this paper, a novel event-triggered fuzzy robust fault-tolerant control approach is designed to handle the offshore ship crane nonlinear system with actuator fault and external disturbance. The main objective of this study is to realize the tracking control ability of the outputs while saving the transmission resources, which is achieved by constructing the integrated adaptive sliding mode controller and event trigger mechanism. The fuzzy logic theory is used both in the observer and controller design processes to approximate the nonlinear unknown functions. First, the information of the crane system state, actuator fault, and lumped disturbance are acquired by designing a fuzzy composite observer. Then, a novel adaptive sliding mode controller is presented by using the estimated values. In the proposed control scheme, two adaptive parameters are contained to consider the disturbance elimination and to enhance the tracking performance. An adaptive law is also included to compensate for the fuzzy approximation error. Furthermore, a novel event-triggered controller is proposed to reduce the transmission load of the crane system while also maintaining the tracking ability of the crane system. The no Zeno phenomenon performance is analyzed and, finally, the application to the crane system is given to show the fault tolerance ability of the proposed method.

Introduction

Offshore ship crane system, which is mounted in a vessel, is critical in the rapidly developed oceanic industry to transfer the cargos between two ships. Generally, the crane system is a typical underactuated system, which consists of three parts, i.e., a trolley, a wire, and a payload [1]. In the control scheme of the ship crane system, on the one hand, to realize the precise position of the payload, the system should track a desired trajectory [2]; on the other hand, as the existence of sea waves and winds, the motion of the ship will intensively affect the payload trajectory, i.e., the payload may be forced to swing back and forth in the presence of the disturbance, which means the uncertainties and external disturbances should be taken into account when considering the tracking control performance of the crane system [3], [4]. Additionally, the unexpected actuator fault may occur because of the harsh sea conditions. When a component or actuator fault occurs, the system performance will certainly degrade and, even result in destructive events, which in return affect the tracking performance of the crane system. Therefore, it is paramount to guarantee or recover an acceptable performance of the crane system in the presence of actuator fault and external disturbance [5], [6].

For the ocean waves and gusty winds in the ship crane system, some methods have been investigated and the corresponding results have been achieved [7], [8], [9], [10]. For example, in [7], the offshore ship-mounted crane system with wave disturbance was considered, in order to realize the tracking control, an adaptive controller was designed to ensure the payload swing suppression and disturbance attenuation. In [8], the disturbance influences for a class of shipboard crane system was addressed; by designing a feedback control method, the swing elimination was achieved. In [9], the ship crane system with the challenges of sea waves and ocean currents was studied, to stabilize the system, a transformation was introduced and a nonlinear control strategy was presented to regulate the payload to the desired position. In [10], a class of double-pendulum crane system was addressed; a feedback controller was presented to suppress the swing and to stabilize the system even in the presence of sea waves. Other methods such as predictive control approach, sliding mode control (SMC) and output-based approach can be found in [11], [12], [13] and [14]. These achievements have tackled the system stabilization problems or trajectory tracking issues. However, in [8], the disturbance was assumed to be measurable; in [9] and [10], the disturbance was integrated in the ship states; in [14], the disturbance information was not used when designing the controller. For the ship crane system, the external disturbance may unknown in some cases, which means disturbance observer can be designed to help the controller design, unfortunately, only few results have investigated on this topic. For instance, in [15], the disturbance observer was designed for the ship crane system; however, the observer was constructed based on the assumption of the known system state. The assumption may be limited in some situations and this also motivates the high order disturbance observer design of this study.

On the other hand, as the severe working condition of the ship crane system, the actuator fault may occur, which will directly reduce the tracking performance. However, there are few studies consider the actuator fault condition of the ship crane system. It is worth to point that fault tolerant control (FTC) is an extremely effective performance recovery method in the nonlinear systems [16], [17], [18]. The most prominent feature of FTC is to compensate for the influences of the fault on the system and then maintain acceptable system performance. From the tolerance point of view, the disturbance attenuation mechanism is also integrated in the FTC scheme, i.e., both the fault compensator and disturbance rejection mechanism are designed in the FTC framework. For the ship crane system, as in the above literature [7] mentioned, the disturbances belong to the unmatched ones, which increase the complexity of the controller design compared with the traditional land fixed crane system. Fortunately, the unmatched disturbance and actuator fault are within the framework of FTC, which means that the FTC concept can be adapted to design the controller for the ship crane system, and this also motivates the FTC controller design of this study.

Note that the fuzzy logic system (FLS) theory is commonly applied to model or identify the unknown part or nonlinear function in the controller design procedure. Moreover, the integrated fuzzy FTC algorithms have been addressed for uncertain nonlinear systems recently [19], [20]. For instance, in [19], the FLS theory was used to model the nonlinear term, with which the fuzzy observer was designed, in the light of back-stepping control technique, a robust controller was presented to keep the desired tracking performance. In the ship crane system, the uncertainties which come from the harsh ocean currents are unknown and nonlinear. These uncertainties will certainly exacerbate the hanging oscillations of the payloads, which in return increase the challenges for the control strategy design. In other words, suitable accommodations should be made to deal with sway suppression. This also motivates the fuzzy composite observer design and the adaptive fuzzy controller design of this work.

In the practical control system, the control laws are updated at every period time, which may cause communication resources waste when the control signal vibrates not so frequently. To reduce the transmission loads and save the communication resources, the event-trigger based control method is developed for nonlinear trajectory tracking control [21], [22], [23]. For instance, in [21], the fuzzy hyperbolic model was used to model the nonlinear function for a class of faulty nonlinear systems; an event-triggered FTC approach was designed to maintain the system performance and to save the communication resources. For the ship crane system, the control may not be updated at every period when the control signal is smooth. Thus, the transmission burdens are reduced if the event-based control is applied to the system.

The major interest of this study is to design a reconfigurable FTC method while reducing the transmission loads for the ship crane system. The main highlights are listed as follows. (1) A fuzzy composite observer which contains a state observer and a high order disturbance observer for the ship crane system is designed. Compared the results in [7], [9] and [15], in this study, the actuator fault is considered. In addition, the disturbance can be n times differentiable and the disturbance upper bound is not needed, which means that the disturbance can represent more complex cases, and this is reasonable for the ship cane system. (2) A novel observer-based adaptive fuzzy SMC approach is designed to suppress the sway and to maintain the precise trolley position; additionally, a novel event trigger mechanism is also established to save the computation resources. Different from the results in [1], in the proposed method, the estimated fault and disturbance values are utilized to design the compensator, which contributes to attenuating the disturbance and to compensating for the actuator fault.

The remainder of this paper contains four sections. In Section 2, the problem formulation of the crane system and FLS are given. In Section 3, the construction of the proposed method is presented. In Section 4, the simulation results are listed and, we conclude the study in Section 5.

Section snippets

System statement

The schematic of the ship crane system is shown in Fig. 1, where φ, l and θ represent the trolley position, the length of wire and the payload swing angle respectively. α(t) denotes the rolling angle of the ship, m and ml are the payload mass and the trolley mass.

The dynamics of the ship crane system can be developed in the following manner [7],M(q)q¨+C(q,q˙)q˙=Fτ+Fξ+Fg+Δ(t)where q=[φlθ]T is the generalized position, M(q) and C(q,q˙) denote the inertial and Coriolis-centripetal matrix,

The proposed method design

In this part, an adaptive event-triggered SMC approach is designed. Concretely, a novel fuzzy observer is proposed first to acquire the lumped disturbance and states information; with the estimated information, an adaptive SMC integrated with the event trigger mechanism is designed to maintain the trajectory tracking ability.

The proposed control scheme can be described in Fig. 2.

Result analysis

In this section, the proposed method is verified through the application to the ship crane system [7]. The actuator fault, disturbance, and fault efficiency factor are assumed as

Fτ1s(t)={0(0t10)1.2+0.1sin(2t3)(10<t20), Fτ2s(t)={0.4(0t6)0.4(6<t12)0.4(12<t20), Fτ3s(t)={0.5sin(0.3t)(0t9)0.3+0.5sin(0.3t)(9<t15)0.5(15<t20), Δ1(t)={0.1sin(2t3)(0t<10)0.2sin(0.5t)(10t20), Δ2(t)={0(0t8)0.5sin(0.3t)(8<t15)1(15<t20), Δ3(t)=0.2sin(0.5t)(0t20), hi=1(0t<6)+0.8(6t<20).

From [7], the

Conclusion

This study attempts to solve the tracking problem of the nonlinear ship crane system while handling the lumped disturbance and actuator fault. A novel fuzzy event-based adaptive SMC method is presented. First, to acquire the states and lumped disturbance, a composite fuzzy observer is established, in which the knowledge of disturbance bound is not needed. Based on the estimated disturbance and actuator fault information, a novel adaptive fuzzy SMC with the performance of fast convergence is

Author Contributions Section

  • 1.

    The ship crane system with actuator fault and disturbance is considered.

  • 2.

    A fuzzy composite observer is proposed for the ship crane system to estimate the state, actuator fault and lumped disturbance.

  • 3.

    A novel adaptive fuzzy sliding mode control integrated with the event-triggered control scheme is proposed for the ship crane system to guarantee the trajectory tracking control while reducing the communication loads.

CRediT authorship contribution statement

Bin Guo: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing. Yong Chen: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing.

Declaration of Competing Interest

All authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowlgedgments

This work is supported by the National Natural Science Foundation of China (grant no. 61973331, 61903064), and the National Key Research and Development Plan Programs of China (no. 2018YFB0106101)

References (24)

  • N. Sun et al.

    Dynamic feedback antiswing control of shipboard cranes without velocity measurement: theory and hardware experiments

    IEEE Trans. Ind. Inf.

    (2018)
  • N. Sun et al.

    Nonlinear stabilizing control for ship-mounted cranes with ship roll and heave movements: design, analysis, and experiments

    IEEE Trans.Sys. Man Cybern.

    (2017)
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