Stochastic control of wave energy converters with constrained displacements for optimal power absorption

An semi-analytical solution is derived for the optimal control of the power take-off of a single-degree of freedom heave point absorber with constraints on the displacement. At first the control force is derived during states, where the displacement constraint is active. This results in an open-loop control law dependent on the external wave load on the absorber. Next, the analytical solution for the optimal control in the unconstrained state is indicated, which turns out to be of the closed loop type with feedback from the present displacement and acceleration and from future velocities. The derived control law contains an undetermined constant, which is calibrated at the interface to the previous constrained state. The approach requires the estimation of the wave load during the constrained states, and the prediction of the future velocity response during unconstrained states. An algorithm has been devised in the paper for handling these problems. The theory has been validated against numerical solutions obtained by nonlinear programming.     

Optimal causal control of a wave energy converter in a random sea

This paper concerns the design of feedback control systems to maximize power generation of a wave energy converter (WEC) in a random sea. In the literature on WEC control, most of the proposed feedback controllers fall into three categories. Many are static; i.e., they extract power by imposing an equivalent damping or resistive load on the power take-off (PTO) devices. Others are dynamic and are designed to maximize power generation at all frequencies, which results in an anticausal feedback law. Other dynamic control design methods are causal, and are tuned to achieve the anticausal performance at only a single frequency. By contrast, this paper illustrates that the determination of the true optimal causal dynamic controller for a WEC can be found as the solution to a nonstandard linear quadratic Gaussian (LQG) optimal control problem. The theory assumes that the control system must make power generation decisions based only on present and past measurements of the generator voltages and/or velocities. It is shown that unlike optimal anticausal control, optimal causal control requires knowledge of the stationary spectral characteristics of the random sea state. Additionally, it is shown that the efficiency of the generator factors into the feedback synthesis. The theory is illustrated on a linear dynamical model for a buoy-type WEC with significant resonant modes in surge and pitch, and equipped with three spatially-distributed generators.     

On the design of a longitudinal motion control system of a fully-submerged hydrofoil craft based on the optimal preview servo system

The current control system of a fully-submerged hydrofoil craft based on optimal feedback control has several problems: it has no good performance of contouring waves and it cannot reduce the effect of wave disturbance. In this paper, we apply the optimal preview servo system to the longitudinal control system of a fully-submerged hydrofoil craft in order to settle the problems of current control system. The control system based on optimal preview servo system is composed of feedback controller and feedforward controller. Also in order to design the control system, the necessary prediction range of future information, the weight function in performance index, the future reference input and wave disturbance are determined. Finally, the validity of the proposed control system in this paper is confirmed by simulation. The simulation results show that the control system has good performance of contouring waves in following seas and is effective to settle the problems of current control system of a fully-submerged hydrofoil craft.     

Phase control through load control of oscillating-body wave energy converters with hydraulic PTO system

Oscillating bodies constitute an important class of wave energy converters, especially for offshore deployment. Phase control by latching has been proposed in the 1970s to enhance the wave energy absorption by oscillating bodies (especially the so-called point absorbers). Although this has been shown to be potentially capable of substantially increasing the amount of absorbed energy, the practical implementation in real irregular waves of optimum phase control has met with theoretical and practical difficulties that have not been satisfactorily overcome. The present paper addresses the case of oscillating-body converters equipped with a high-pressure hydraulic power take-off mechanism (PTO) that provides a natural way of achieving latching: the body remains stationary for as long as the hydrodynamic forces on its wetted surface are unable to overcome the resisting force (gas pressure difference times cross-sectional area of the ram) introduced by the hydraulic PTO system. A method of achieving sub-optimal phase-control is developed, based on the theoretical time-domain modelling of a single-degree of freedom oscillating body in regular and irregular waves, by adequately delaying the release of the body in order to approximately bring into phase the body velocity and the diffraction (or excitation) force on the body, and in this way get closer to the well-known optimal condition derived from frequency-domain analysis for an oscillating body in regular waves.     

Maximizing the Absorbed Power of A Point Absorber Using An FA-Based Optimized Model Predictive Control

This paper presents an extended model predictive controller for maximizing the absorbed power of a point absorber wave energy converter. Owing to the great influence of controller parameters upon the absorbed power, the optimization of these parameters is carried out for the first time by a firefly algorithm (FA). Error, the difference between output velocity of buoy and input wave speed which leads to power maximization in the optimized MPC is compared with the classical MPC. Simulation results indicate that given the high accuracy and acceptable speed of the algorithm, it can adjust the parameters of the controller to the point where system error decreased effectively and the absorbed energy increased about 4 MW.     

Research on Pitch Control Strategies of Horizontal Axis Tidal Current Turbine

Based on blade element momentum theory and generator characteristic test, a dynamic simulation model of 150 kW horizontal-axis tidal current turbine was established. The matching of the dynamic characteristics between the turbine and generator under various current velocities is studied, and the influence of the pitch angle on the matching is analyzed. For the problem of maximum power output in case of low current speed and limiting power in high current speed, the relation between optimal pitch angle and output power is analyzed. On the basis of dynamic characteristic analysis, the variable pitch control strategy is developed. The performance of the turbine under various tidal conditions is simulated. The research results show that the designed controller enables the turbine to operate efficiently under the condition of low current speed, and achieve the goal of limited power at high current speed.     

An assessment of fuzzy logic vessel path control

A fuzzy logic controller for ship path control in restricted waters is developed and evaluated. The controller uses inputs of heading, yaw rate, and lateral offset from the nominal track to produce a commanded rudder angle. Input variable fuzzification, fuzzy associative memory rules, and output set defuzzification are described. Two maneuvering situations are evaluated: track keeping along a specified path where linearized regulator control is valid; and larger maneuvers onto a specified path where nonlinear modeling and control are required. For the track keeping assessment, the controller is benchmarked against a conventional linear quadratic Gaussian (LQG) optimal controller and Kalman filter control system. The Kalman filter is used to produce the input state variable estimates for the fuzzy controller as well. An initial startup transient and regulator control performance with an external hydrodynamic disturbance are evaluated using linear model simulations of a crude oil tanker. A fully nonlinear maneuvering model for a smaller product tanker is used to assess the larger maneuvers     

海底管线检修潜水器垂直面控制及自航模试验

论述了纵倾控制律设计及自航模试验。首先选择一系列深度,对同一深度采用频域校正法单独设计控制律,使之对不同的速度和漂角具有足够的稳态精度和抗干扰性,这些控制律被集成统一为纵倾控制器,并根据潜深变化进行切换,对于其它深度采用同样的方法设计。控制器首先通过计算机仿真,然后进行自航模试验验证。设计的纵倾控制系统同时在其他试验项目中(水下管线跟踪和动力定位)发挥了重要的作用。     

Nonlinear adaptive control of an underwater towed vehicle

This paper addresses the problem of simultaneous depth tracking and attitude control of an underwater towed vehicle. The system proposed uses a two-stage towing arrangement that includes a long primary cable, a gravitic depressor, and a secondary cable. The towfish motion induced by wave driven disturbances in both the vertical and horizontal planes is described using an empirical model of the depressor motion and a spring-damper model of the secondary cable. A nonlinear, Lyapunov-based, adaptive output feedback control law is designed and shown to regulate pitch, yaw, and depth tracking errors to zero. The controller is designed to operate in the presence of plant parameter uncertainty. When subjected to bounded external disturbances, the tracking errors converge to a neighbourhood of the origin that can be made arbitrarily small. In the implementation proposed, a nonlinear observer is used to estimate the linear velocities used by the controller thus dispensing with the need for costly sensor suites. The results obtained with computer simulations show that the controlled system exhibits good performance about different operating conditions when subjected to sea-wave driven disturbances and in the presence of sensor noise. The system holds promise for application in oceanographic missions that require depth tracking or bottom-following combined with precise vehicle attitude control.     

Nonlinear output feedback control of underwater vehicle propellersusing feedback form estimated axial flow velocity

Accurate propeller shaft speed controllers can be designed by using nonlinear control theory and feedback from the axial water velocity in the propeller disc. In this paper, an output feedback controller is derived, reconstructing the axial flow velocity from vehicle speed measurements, using a three-state model of propeller shaft speed, forward (surge) speed of the vehicle, and the axial flow velocity. Lyapunov stability theory is used to prove that a nonlinear observer combined with an output feedback integral controller provide exponential stability. The output feedback controller compensates for variations in thrust due to time variations in advance speed. This is a major problem when applying conventional vehicle-propeller control systems. The proposed controller is simulated for an underwater vehicle equipped with a single propeller. The simulations demonstrate that the axial water velocity can be estimated with good accuracy. In addition, the output feedback integral controller shows superior performance and robustness compared to a conventional shaft speed controller     

Adaptive output feedback control based on DRFNN for AUV

The tracking control problem of AUV in six degrees-of-freedom (DOF) is addressed in this paper. In general, the velocities of the vehicles are very difficult to be accurately measured, which causes full state feedback scheme to be not feasible. Hence, an adaptive output feedback controller based on dynamic recurrent fuzzy neural network (DRFNN) is proposed, in which the location information is only needed for controller design. The DRFNN is used to online estimate the dynamic uncertain nonlinear mapping. Compared to the conventional neural network, DRFNN can clearly improve the tracking performance of AUV due to its less inputs and stronger memory features. The restricting condition for the estimation of the external disturbances and network's approximation errors, which is often given in the existing literatures, is broken in this paper. The stability analysis is given by Lyapunov theorem. Simulations illustrate the effectiveness of the proposed control scheme.     

Laboratory experiment on heaving body with hydraulic power take-off and latching control

A heaving axisymmetric floating body is tested with sinusoidal incident waves in a wave channel. It is connected to the piston of a pump, and it may be latched by an electromagnetic mechanism. Experimental results are compared with a linear mathematical model, for heave response, hydrodynamic parameters, absorbed wave power and converted hydraulic power. Heave resonance occurs at 1.1 Hz. For sub-resonant frequencies, latching control results in a significant increase in heave response and in absorbed, as well as converted, power. Hydraulic energy capture increases by a factor of 2.8 or 4.3 for frequency 0.75 or 0.5 Hz, respectively.     

On a near-optimal control approach for a wave energy converter in irregular waves

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers–Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal (one being odd and other even), full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this difficulty and the non-causality of the exciting force impulse response function, this paper investigates the use of propagating-wave surface elevation up-wave of the device to synthesize the necessary forces. Long-crested waves are assumed, and the approach is based on the formulations of Naito and Nakamura [2] and Falnes [22]. A predominantly heaving submerged device comprised of three vertically stacked discs driving a linear power take-off is studied. The overall formulation leads to smooth control that is near-optimal, given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. Absorbed power performance with the near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results for wave spectra over a range of energy periods and significant wave heights are compared for the three situations studied. While practical implementation presents engineering challenges, in terms of time-averaged absorbed power, unconstrained near-optimal control is found to perform significantly better than single-frequency tuning in the spectra with longer energy periods (>10 s for the present device), and somewhat better in the spectra with shorter energy periods (here ≤10 s).     

Near-optimal control of a wave energy device in irregular waves with deterministic-model driven incident wave prediction

This paper investigates wave-by-wave control of a wave energy converter using incident wave prediction based on up-wave surface elevation measurement. The goal of control is to approach the hydrodynamically optimum velocity leading to optimum power absorption. This work aims to study the gains in energy conversion from a deterministic wave propagation model that accounts for a range of group velocities in deriving the prediction. The up-wave measurement distance is assumed to be small enough to allow a deterministic propagation model, and further, both wave propagation and device response are assumed to be linear. For deep water conditions and long-crested waves, the propagation process is also described using an impulse response function (e.g. [1]). Approximate low and high frequency limits for realistic band-limited spectra are used to compute the corresponding group velocity limits. The prediction time into the future is based on the device impulse response function needed for the evaluation of the control force. The up-wave distance and the duration of measurement are then determined using the group velocity limits above.A 2-body axisymmetric heaving device is considered, for which power capture is through the relative heave oscillation between the two co-axial bodies. The power take-off is assumed to be linear and ideal as well as capable of applying the necessary resistive and reactive load components on the relative heave oscillation. The predicted wave profile is used along with device impulse response functions to compute the actuator force components at each instant. Calculations are carried out in irregular waves generated using a number of uni-modal wave spectra over a range of energy periods and significant wave heights. Results are compared with previous studies based on the use of instantaneous up-wave wave-profile measurements, both without and with oscillation constraints imposed. Considerable improvements in power capture are observed with the present approach over the range of wave conditions studied.     

海洋平台磁流变阻尼器控制技术研究

为了更有效地减小海洋平台动力响应,采用基于模糊控制算法的磁流变阻尼器对海洋平台的振动进行控制.以海洋平台位移响应误差和误差变化为输入变量,以最优控制力为输出变量,优化设计出模糊控制器.考虑实际磁流变阻尼器输出控制力上限存在限制,采用半主动控制算法计算接近于最优控制力的半主动控制力.以一固定式海洋平台为算例研究磁流变阻尼器的振动控制效果及其模糊性,仿真结果表明模糊磁流变控制器对于平台的振动可以实现非常有效的控制,且控制效果对结构阻尼和环境的不确定性具有较好的模糊性.     

含有控制时滞系统的输出反馈扰动抑制

研究在持续外界扰动作用下,具有控制时滞线性系统的动态输出反馈扰动抑制问题。首先利用模型转换将控制时滞系统转化为形式上无时滞的系统,通过求解Riccati方程和Sylvester方程,推导出前馈—反馈最优扰动抑制控制律。然后构造能同时预估状态和扰动的降维观测器,不仅解决前馈控制和状态反馈的物理不可实现问题,而且得到了近似于最优扰动抑制控制律的动态输出反馈扰动抑制控制器。仿真实例证明此控制律的有效性。     

光学浮标控制系统硬件设计

以光学浮标为控制对象, 以工作稳定、低功耗为目的, 设计海上工作控制硬件。采用嵌入式PC/104 CPU主板和以单片机为核心多功能板组合, 由PC/104 CPU主板完成采集数据、保存数据、通讯等工作, 多功能板实现计数、I/O控制、A/D转换、定时等功能。单片机结合日历时钟和电源总开关组成二级“看门狗”, 实现了海洋光学浮标控制系统无人值守、全天候、全过程独立工作。     

An internal model control approach to the design ofyaw-rate-control ship-steering autopilot

This technical communication is concerned with the design of inland ship-steering autopilots characterized by turning rate regulation rather than heading regulation found on most ocean-going vessel autopilots. The autopilot design is based on the internal model control approach which allows clear connections between the controller structure and that of the ship model to be established. To fully utilize the limited rudder power without introducing the controller wind-up, which may lead to undesirable long transients, an inverse of the rudder saturation (SAT) and slew rate limitation (SRL) is implemented in the controller. Specifically, an inversion by feedback technique is employed by implementing the noninverted dynamics in a local feedback loop. This resolves the difficulty associated with inversion of the SAT and SRL mathematically. Consequently, high turning rate maneuver can be achieved in case of emergency encounters without causing the controller wind-up. This feature is particularly important for inland ships, since unexpected encounters with other ships are quite common and the capability of quick response is vital to ensure safe maneuvers     

Constrained near-optimal control of a wave energy converter in three oscillation modes

This paper investigates the performance of a small axisymmetric buoy under wave-by-wave near optimal control in surge, heave, and pitch modes in long-crested irregular waves. Wave prediction is obtained using a deterministic propagation model. The paper describes the overall formulation leading up to the derivation of the feedforward control forces in surge and heave, and the control moment in pitch. The radiation coupling between surge and pitch modes is accounted for in the model. Actuation is relative to deeply submerged reaction masses. Heave oscillations are constrained by the swept-volume limit. Oscillation constraints are also applied on the surge and pitch oscillations. The paper discusses time-domain simulations for an irregular wave input with and without the present control. Also discussed are results obtained over a range of irregular wave conditions derived for energy periods from 7 s to 17 s, and a significant wave height of 1 m. It is found that, while the gains in power capture enabled by the present control are significant, the actuation forces are also very large, given the small size of the buoy. Further, due to the small size, heave is found to be the dominant contributor to power capture, with relatively modest contributions from surge and pitch.     

Latching control of deep water wave energy devices using an active reference

This paper investigates latching type control on a floating wave energy converter in deep water. An on-board, actively controlled motion-compensated platform is used as a reference (‘active reference’) for power absorption and latching. A variational formulation is used to evaluate an optimal control sequence in the time domain. Time domain simulation results are presented for a heaving buoy in small-amplitude waves. Results are compared with an equivalent system where latching and power absorption are from a sea-bottom-fixed reference.