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The purpose of this paper is to show a novel fault-tolerant tracking control (FTC) strategy with robust fault estimation and compensating for simultaneous actuator sensor faults. Based on the framework of fault-tolerant control, developing an FTC design method for wind turbines is a challenge and, thus, they can tolerate simultaneous pitch actuator and pitch sensor faults having bounded first time derivatives. The paper’s key contribution is proposing a descriptor sliding mode method, in which for establishing a novel augmented descriptor system, with which we can estimate the state of system and reconstruct fault by designing descriptor sliding mode observer, the paper introduces an auxiliary descriptor state vector composed by a system state vector, actuator fault vector, and sensor fault vector. By the optimized method of LMI, the conditions for stability that estimated error dynamics are set up to promote the determination of the parameters designed. With this estimation, and designing a fault-tolerant controller, the system’s stability can be maintained. The effectiveness of the design strategy is verified by implementing the controller in the National Renewable Energy Laboratory’s 5-MW nonlinear, high-fidelity wind turbine model (FAST) and simulating it in MATLAB/Simulink.

With the increasing demand for energy, the importance of new energy development increases with each passing day. Wind energy is an important part of new energy, and actively developing wind energy to improve the energy system structure, ease the energy crisis, and protect the environment is of great significance [

In recent years, the application of model-based fault-tolerant control in wind turbines has gradually expanded. Sloth et al. designed an active and passive fault-tolerant controller based on the linear variable parameter (LPV) for the pitch fault. The optimization method for the linear matrix inequality was applied to active fault-tolerant control, and the bilinear matrix inequality method was applied to passive fault-tolerant control [

However, the current fault-tolerant control strategies generally aim at only a single fault. Thus when faults appear in both wind turbine actuator and the sensor at the same time, guaranteeing the stable operation of the system in the specified performance index becomes challenging.

To solve the above problems, this paper proposes a fault-tolerant control strategy for the pitch system for a wind turbine based on multiple fault reconstruction. The proposed fault-tolerant control strategy consists of two parts. The first part adopts the active disturbance rejection control technology to ensure the stable output of the wind turbine power in the case of no fault. In the second part, a descriptor sliding mode observer is designed to realize the continuous estimation of the original system state, pitch actuator failure, and pitch sensor fault, and a fault-tolerant controller is designed based on the state estimation and fault estimation information to maintain the stable operation of the system under simultaneous pitch actuator and pitch sensor faults.

The remainder of this paper is organized as follows. Wind turbine modeling is presented in Section

A wind turbine system is characterized by nonlinear aerodynamic behavior and the dependence on a stochastic uncontrollable wind force as a driving signal. To conceptualize the system from the analytical and control design requirement standing points, an overall model of the turbines is required. In this section, a generalized nonlinear wind turbine model, its pitch system, and its faults model are presented.

The model is shown in the form as follows [

The state vector

The mechanical power captured by the wind turbine is described as

The system of hydraulic pitch is modeled as a closed-loop transfer function. Essentially, these position servo systems can be modeled quite well via describing a second-order transfer function as follows [

To facilitate the subsequent controller design, the state space model of the pitch system is as follows:

The fault considered for the pitch actuator is hydraulic leakage. The dynamics of the pitch systems will be changed by a drop of oil pressure. The pressure level is modeled as a convex combination of the vertices of the parameters

The corresponding state space model is as follows:

Equation (

There are three common faults for the pitch sensor: biased output, fixed output, and no output. The only difference between the front two faults original from the pitch sensor is that detecting a fixed output is necessary [

The closed-loop pitch system and the pitch angle measurement are affected by a biased pitch sensor measurement. While the bias occurs, the pitch sensor fault model is as follows:

A fixed output on a pitch sensor is an abrupt fault and can occur at any time leading to the following measurement equation:

No output on a pitch sensor causes the same changes in the measurement equation as a fixed output. Contrary to a fixed output, the control system is informed when there is no output from the pitch sensor. The fault model is as follows:

Considering the following wind turbine pitch system with four conditions, pitch actuator fault, pitch sensor fault, system uncertainty, and external disturbance [

Some assumptions are made in this paper for subsequent theoretical analyses and controller design.

The conditions for the uncertainty and external disturbance are bounded as the following norm, and pitch actuator fault and pitch sensor fault are held:

The pair

The matrices

The purpose of this paper is to get the estimates of pitch system state and fault simultaneously. For the objective, we can define the new augmented variables and matrices as follows:

By the above definitions, we can construct a new descriptor system equivalently as follows:

The descriptor observer can be designed by the lemma as the following shows, by the summaries from [

There always exists a matrix

On the basis of Lemma

We can define the design matrix

If Assumption

The final step is to form the input term

Then, we can define the surface of sliding mode with

Constraint (

It is presented that

First, we can rewrite the observer (

Using Lemma

Adding

Subtracting (

Then, we can derive the system equation of sliding mode estimation state. First, we can rewrite the observer state Eq. (

which is equivalent to

We can decompose the matrices

From

and from (

Subsequently, the state Eq. (

Second, an estimation state is constructed based on the integral sliding mode surface

Assuming that there exist matrices

Substituting (

Combine the sliding mode estimation state Eq. (

Based on the sliding mode input scheme as

The fault-tolerant control of a wind turbine in area 3 (above rated wind speed) is mainly studied in this paper. The output power of the generator must be adjusted to the rated power to ensure the output quality and wind turbine safety. There are two general methods for power regulation [

An active fault-tolerant control for the pitch system (

The active disturbance rejection control (ADRC) technique is used in wind turbine pitch control under the fault-free case in this paper due to its facilitation and robustness. The ADRC controller design procedures are summarized as the following three steps [

Firstly, to avoid a large overshoot of the system, the step input signal is transformed into a continuous and smooth signal by designing the tracking differentiator [

Second, an extended state and disturbance nonlinear observer is designed to estimate and compensate for the unknown time varying nonlinear disturbances in the system online.

Finally, the pitch control is realized by a conventional PD controller.

It is assumed that the output of the system is the speed of the low speed shaft and that the input is the pitch angle. From (

Its second-order derivative can be obtained as

Assuming that all nonlinearities of the system represented as

Then, system (

Defining

Defining

In this controller, the actual perturbation is compensated in real-time by estimating the unknown perturbation of the system with a nonlinear observer. The pitch controller can be expressed as

With the above-mentioned stability conditions, we can guarantee the reachability of the sliding surfaces

Because it is not as easy to obtain a solution under limit (

Therefore, we can transform the LMI conditions of (

With the descriptor sliding mode observer (

To prevent the signals

We can summarize the parameters of the descriptor sliding mode method and the fault-tolerant control design process into the following four steps:

Choose

Choose

Design the gain matrix

Design

In this paper, the faults considered for the pitch system are hydraulic leakage on pitch actuator and a biased output on pitch sensor. Hence, following the design procedures mentioned above, the effective design and verification for the proposed controller can be shown via pitch system (

The simulations are carried out within FAST-MATLAB/Simulink combined environment, and the detailed parameters of NREL’s 5-MW benchmark wind turbine model are described in Table

Parameters of NREL’s 5 MW wind turbine model.

Power rating | 5 MW |

Rotor orientation, structure | Upwind, three-bladed |

Control | Variable speed, variable pitch |

Rotor, hub diameter | 126 m, 3 m |

Hub height | 90 m |

Cut in, rated, cut out wind speed | 3 m/s, 11.4 m/s, 25 m/s |

Rated rotor, generator speed | 12.1 rpm, 1173.7 rpm |

Maximum blade pitch rate | 8 deg/s |

Rated generator torque | 43093 Nm |

Maximum generator torque | 47402 Nm |

Effective wind speed.

Let the parameter

We select

By selecting the scalar

We select the matrices

The norm controller (

The simulation results are shown in Figures

Estimate of newly defined pitch actuator fault

Pitch actuator original fault

Pitch sensor fault and its estimate with

Pitch angle and its estimate with

Generator power output with

Generator speed and its torque with

Generator power output with

Generator speed and its torque with

In this paper, a new architecture for active FTC controller is proposed for a wind turbine pitch system with simultaneous pitch actuator and sensor faults based on fault estimation and reconstruction to maintain nominal pitching performance. The FTC controller included both a normal controller, which was designed by using the active disturbance rejection control technique for estimating and compensating for the uncertainties, and a reconfigurable controller, which was designed by using the state and fault estimates obtained from an augmented descriptor sliding mode observer. The simulations performed in the FAST-MATLAB/Simulink demonstrate that the proposed FTC design can ensure the stability of the generator power output in the event of a fault or in cases without a fault.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The National Natural Science Foundation of China (no. 51205046), Frontier and Applied Basic Research Projects (no. cstc2014jcyjA90005) funded by Chongqing Science and Technology Commission, The 56th Postdoctoral Science Foundation of China (no. 2014M562283), and Special Financial Grant (2015T80956) from the China Postdoctoral Science Foundation and Postdoctoral Special Projects (no. Xm2014003) funded by Chongqing Government are gratefully acknowledged.