Efficient Nonlinear Model Predictive Control via quasi-LPV representation

Cisneros, Pablo S. G.; Voss, Sophia; Werner, Herbert

doi:10.1109/cdc.2016.7798752

Cited by 53 publications

(61 citation statements)

References 9 publications

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“…For the considered case, a predefined quadratic performance criterion specifies the trade‐off between energy production maximization and resonance excitation minimization, and the optimizer finds the optimal corresponding control signal in the prediction horizon. However, as for each time step, the scheduling sequence over the prediction horizon is unknown, and the nonlinear MPC control problem is solved by an iterative method . The method solves subsequent QPs minimizing the predefined cost and uses the resulting predicted scheduling sequence as a warm‐start for the next iteration.…”

Section: Quasi‐lpv Model Predictive Controlmentioning

confidence: 99%

“…However, when the system is scheduled on state variables and/or input signals, the model is referred to as a quasi‐LPV (qLPV) system. Recently, an efficient MPC scheme for such qLPV systems is proposed by solving subsequent quadratic programs (QPs) …”

Section: Introductionmentioning

confidence: 99%

“…This paper subjects a tower model to the earlier introduced demodulation transformation and augments it with a simplified wind turbine model, such that a qLPV model is obtained. The result is combined with the efficient MPC method, exploiting the beneficial properties of qLPV systems . The proposed qLPV‐MPC framework provides a methodology for performing an optimal trade‐off between produced energy and tower loads is presented and thereby presents the following contributions: •Providing the derivation results of a model demodulation transformation, for moving the magnitude and phase content at the excitation frequency to a quasi steady‐state contribution. •Applying the transformation to a second‐order tower model and showcasing its working principles by an illustrative example. •Combining the transformed tower model with a simplified wind turbine model and linearizing at below‐rated operating points, for obtaining a qLPV state‐space system description. •Discretizing and converting the qLPV model to its affine form. •Formally deriving the efficient MPC approach for affine qLPV model structures. •Showcasing the proposed approach in closed‐loop high‐fidelity simulations with different wind profiles, to clearly show its effectiveness and practical applicability. …”

Section: Introductionmentioning

confidence: 99%

“…Recently, an efficient MPC scheme for such qLPV systems is proposed by solving subsequent quadratic programs (QPs). 25 This paper subjects a tower model to the earlier introduced demodulation transformation and augments it with a simplified wind turbine model, such that a qLPV model is obtained. The result is combined with the efficient MPC method, exploiting the beneficial properties of qLPV systems.…”

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Preventing wind turbine tower natural frequency excitation with a quasi‐LPV model predictive control scheme

et al. 2019

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With the ever increasing power rates of wind turbines, more advanced control techniques are needed to facilitate tall towers that are low in weight and cost-effective but in effect more flexible. Such soft-soft tower configurations generally have their fundamental side-side frequency in the below-rated operational domain. Because the turbine rotor practically has or develops a mass imbalance over time, a periodic and rotor-speed dependent side-side excitation is present during below-rated operation. Persistent operation at the coinciding tower and rotational frequency degrades the expected structural life span. To reduce this effect, earlier work has shown the effectiveness of active tower damping control strategies using collective pitch control. A more passive approach is frequency skipping by inclusion of speed exclusion zones, which avoids prolonged operation near the critical frequency. However, neither of the methods incorporates a convenient way of performing a trade-off between energy maximization and fatigue load minimization. Therefore, this paper introduces a quasi-linear parameter varying model predictive control (qLPV-MPC) scheme, exploiting the beneficial (convex) properties of a qLPV system description. The qLPV model is obtained by a demodulation transformation and is subsequently augmented with a simple wind turbine model. Results show the effectiveness of the algorithm in synthetic and realistic simulations using the NREL 5-MW reference wind turbine in high-fidelity simulation code. Prolonged rotor speed operation at the tower side-side natural frequency is prevented, whereas when the trade-off is in favor of energy production, the algorithm decides to rapidly pass over the natural frequency to attain higher rotor speeds and power productions. KEYWORDS model demodulation transformation, model predictive control, quasi-linear parameter varying, tower natural frequency skipping INTRODUCTIONThe tower makes up a substantial part of the total turbine capital costs, and therefore finding an optimum between its mass and manufacturing expenses is a critical trade-off. 1 For conventional towers, diameters are limited because of land-based transportation constraints. This aspect dictates the increase of wall thickness for the production of taller towers and consequently leads to increased weight and costs. Conventional tower designs are soft-stiff to locate the tower fundamental frequency outside the turbine variable-speed operational range and thereby eliminate the possibility of exciting a tower resonance by the rotor rotational or blade-passing frequency. However, with the ever increasing wind turbine power rates, a combination of technical solutions should enable future, low-cost, tall towers, by relaxing this frequency constraint. Soft-soft tower configurations form an opportunity for tall towers by their smaller tower diameters and reduced wall thickness. As a result, soft-soft towers are

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Section: Quasi‐lpv Model Predictive Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Preventing wind turbine tower natural frequency excitation with a quasi‐LPV model predictive control scheme

et al. 2019

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“…Capturing nonlinear systems using linear relationships leads to development of quasi-LPV model [3]- [4] where the scheduling signals can be the states, inputs or outputs of the system. Polytopic LPV approach [5]- [6] is also a popular technique to synthesize the linear controllers by interpolating LMIs at different vertices of the polytope.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of pan-tilt systems using acceleration based LMI-LQR controller

Han

Ünel

2017

2017 11th Asian Control Conference (ASCC)

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Abstract-This paper extends the previous work on LPV modeling of a pan-tilt system [1] and tackles the robust stabilization problem by employing angular acceleration feedback in an LMI based optimal LQR controller. The state vector of the LPV model is augmented to include the integral of the position errors in addition to joint angles and velocities. Therefore, an extended polytopic quasi-LPV model of the pantilt system is derived. The LMI based optimal LQR controller that utilizes acceleration feedback is synthesized based on the extended LPV model. Since the time varying parameter vector is 4 dimensional, the proposed controller is synthesized by interpolating LMIs at 16 vertices of the polytope. A cascaded nonlinear high gain observer is also designed to estimate reliable positions, velocities and accelerations from noisy encoder measurements. Simulation results show that the proposed LMI based optimal LQR controller outperforms the classical LMI based LQR controller.

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Data‐driven safe gain‐scheduling control

Modares

Sadati

Modares

2023

Asian Journal of Control

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Data‐based safe gain‐scheduling controllers are presented for discrete‐time linear parameter‐varying systems (LPV) with polytopic models. First, ‐contractivity conditions are provided under which the safety and stability of the LPV systems are unified through Minkowski functions of the safe sets. Then, a data‐based representation of the closed‐loop LPV system is provided, which requires less restrictive data richness conditions than identifying the system dynamics. This sample‐efficient closed‐loop data‐based representation is leveraged to design data‐driven gain‐scheduling controllers that guarantee ‐contractivity and, thus, invariance of the safe sets. It is also shown that the problem of designing a data‐driven gain‐scheduling controller for a polyhedral (ellipsoidal) safe set amounts to a linear program (a semi‐definite program). The motivation behind direct learning of a safe controller is that identifying an LPV system requires satisfying the persistence of the excitation (PE) condition. It is shown in this paper, however, that directly learning a safe controller and bypassing the system identification can be achieved without satisfying the PE condition. This data‐richness reduction is of vital importance, especially for LPV systems that are open‐loop unstable, and collecting rich samples to satisfy the PE condition can jeopardize their safety. A simulation example is provided to show the effectiveness of the presented approach.

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Efficient Nonlinear Model Predictive Control via quasi-LPV representation

Cited by 53 publications

References 9 publications

Preventing wind turbine tower natural frequency excitation with a quasi‐LPV model predictive control scheme

Preventing wind turbine tower natural frequency excitation with a quasi‐LPV model predictive control scheme

Stabilization of pan-tilt systems using acceleration based LMI-LQR controller

Data‐driven safe gain‐scheduling control

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