Jan-Willem van Wingerden

Subspace identification of Bilinear and LPV systems for open- and closed-loop data

In this paper we present a novel algorithm to identify LPV systems with affine parameter dependence operating under open- and closed-loop conditions. A factorization is introduced which makes it possible to form a predictor that predicts the output, which is based on past inputs, outputs, and scheduling data. The predictor contains the LPV equivalent of the Markov parameters. Using this predictor, ideas from closed-loop LTI identification are developed to estimate the state sequence from which the LPV system matrices can be constructed. A numerically efficient implementation is presented using the kernel method. It turns out that if structure is present in the scheduling sequence the computational complexity reduces even more.

Subspace identification of MIMO LPV systems using a periodic scheduling sequence

A novel subspace identification method is presented which is able to reconstruct the deterministic part of a multivariable state-space LPV system with affine parameter dependence, in the presence of process and output noise. It is assumed that the identification data is generated with the scheduling variable varying periodically during the course of the identification experiment. This allows to use methods from LTI subspace identification to determine the column space of the time-varying observability matrices. It is shown that the crucial step in determining the original LPV system is to ensure the obtained observability matrices are defined with respect to the same state basis. Once the LPV model has been identified, it is valid for other nonperiodic scheduling sequences as well.

Two-Degree-of-Freedom Active Vibration Control of a Prototyped “Smart” Rotor

This paper studies the load reduction potential of a prototyped “smart” rotor. This is, a rotor where the blades are equipped with a number of control devices that locally change the lift profile on the blade, combined with appropriate sensors and controllers. Experimental models, using dedicated system identification techniques, are developed of a scaled rotating two-bladed “smart” rotor of which each blade is equipped with trailing-edge flaps and strain sensors. A feedback controller based on H∞-loop shaping combined with a fixed-structure feedforward control are designed that minimizes the root bending moment in the flapping direction of the two blades. We evaluated the performance using a number of different realistic load scenarios. We show that with appropriate control techniques the variance of the load signals can be reduced up to 90%.

Rejection of Periodic Wind Disturbances on a Smart Rotor Test Section Using Lifted Repetitive Control

A repetitive control method is presented that is implemented in real-time for periodic wind disturbance rejection for linear systems with multiple inputs and multiple outputs and with both repetitive and non-repetitive disturbance components. The novel repetitive controller can reject the periodic wind disturbances for fixed-speed wind turbines and variable-speed wind turbines operating above-rated and we will demonstrate this on an experimental “smart” rotor test section. The “smart” rotor is a rotor where the blades are equipped with a number of control devices that locally change the lift profile on the blade, combined with appropriate sensors and controllers. The rotational speed of wind turbines operating above-rated will vary around a defined reference speed, therefore methods are given to robustify the repetitive controllers for a mismatch in the period. The design of the repetitive controller is formulated as a lifted linear stochastic output-feedback problem on which the mature techniques of discrete linear control may be applied. For real-time implementation, the computational complexity can be reduced by exploiting the structure in the lifted state-space matrices. With relatively slow changing periodic disturbances it is shown that this repetitive control method can significantly reduce the structural vibrations of the “smart” rotor test section. The cost of additional wear and tear of the “smart” actuators are kept small, because a smooth control action is generated as the controller mainly focuses on the reduction of periodic disturbances.

A model-free distributed approach for wind plant control

By extracting kinetic energy from the wind flow, a wind turbine reduces the wind speed in the wake downstream of the wind turbine rotor. In a wind power plant, this wake effect reduces the power production of downstream turbines. This paper presents a control scheme for optimizing the total power output of a wind power plant by taking into account the wake effect. It is a distributed control scheme in which each wind turbine adapts its control settings based on information that it receives from neighbouring turbines. The total power optimization is performed using gradient-based optimization. The optimization is done in a model-free, data-driven manner, as the gradients are estimated from the past control actions, the measured power response of the turbine itself, and the power response of neighbouring turbines. The time-efficiency of the optimization scheme was improved by exploiting information on the locations of the turbines in the wind plant, and an estimate of the wind direction. The method is tested in a simulation of the Princess Amalia Wind Park. To be able to evaluate the time-efficiency of the scheme, in the simulation model a delay structure was included that models the wake traveling from one turbine to the next. The new control method results in a much faster convergence of the power optimization when compared with an existing model-free wind plant power optimization method that uses a game theoretic approach.

Recursive Predictor-Based Subspace Identification With Application to the Real-Time Closed-Loop Tracking of Flutter

A novel recursive predictor-based subspace identification method is presented to identify linear time-invariant systems with multi inputs and multi outputs. The method is implemented in real-time and is able to operate in open loop or closed loop. The recursive identification is performed via the subsequent solution of only three linear problems, which are solved using recursive least squares. The recursive implementation of the method is not only able to identify linear time-invariant models from measured data, but can also be used to track slowly time-varying dynamics if adaptive filters are used. The computational complexity is reduced by exploiting the structure in the data equations and by using array algorithms to solve the main linear problem. This results in a fast recursive predictor-based subspace identification method suited for real-time implementation. The real-time implementation and the ability to work with multi-input and multi-output systems operating in closed loop makes this approach suitable for online estimation of unstable dynamics. The ability to do so is demonstrated by the detection of flutter on an experimental 2-D-airfoil system.

Global Identification of Wind Turbines Using a Hammerstein Identification Method

In this brief, we present a novel methodology to obtain a nonlinear data-driven model of a wind turbine. We have previously shown that the elementary dynamics of wind turbines can be represented in the form of a multivariable closed-loop Hammerstein structure, where the nonlinear mappings consist of the torque and thrust coefficients. Hammerstein systems consist of a static nonlinearity followed by a linear, time-invariant dynamic subsystem. The dynamic subsystem is identified using a new closed-loop subspace method. The nonlinearity is described using a recently developed regression framework for multivariate splines. We further propose a separable least-squares framework for recovery of the low-rank structure between the nonlinearity and the linear time-invariant system. The method is applied to a detailed simulation of the three-bladed NREL controls advanced research turbine.

Closed-loop MOESP subspace model identification with parametrisable disturbances

A new subspace identification method for systems operating either in open-loop or in closed-loop is presented. The method obtains an estimate of the innovation sequence by performing an RQ-factorization of the measurement data, thereby avoiding explicitly solving a least-squares problem. In a second step, the estimated innovation sequence is used to perform ordinary MOESP [1] to find the system matrices up to a similarity transformation. The closed-loop identification algorithm also applies to cases where certain disturbance inputs are present that can be parametrised in terms of suitable basis functions. All computations are performed using orthogonal factorisations of the data. The method is illustrated by applying it to a system operating in closed-loop and to measurements from a real system with periodic disturbances.

Modeling of the flow in wind farms for total power optimization

In this work, the concept of total power optimization for wind farms under wake interaction is presented. A dedicated Computational Fluid Dynamic (CFD) model of the wind based on the numerical solution of the 2D Navier-Stokes equations is implemented in an efficient way by exploiting the sparsity of the involved matrices. Thus, the total power optimization over the farm is performed by incorporating the velocity field obtained from the CFD model. Finally, we show how the total power can be increased in a 2.26% with respect to the conventional optimal operation.

Closed-loop subspace identification of Hammerstein-Wiener models

In this paper we present a novel algorithm to identify MIMO Hammerstein-Wiener systems under open and closed-loop conditions.We reformulate a linear regression problem, commonly used as the first step in closed loop subspace identification, as an intersection problem which can be solved by using canonical correlation analysis (CCA). This makes it possible to utilize ideas from machine learning to estimate the static nonlinearities of Hammerstein-Wiener systems, using kernel canonical correlation analysis (KCCA). In the second step the state sequence is estimated and consequently the dynamic part can be identified. The effectiveness of the approach is illustrated with a closed-loop simulation example.