Gain Scheduling Functions Research Articles

Enhancing Stability in Autonomous Control Systems Through Fuzzy Gain Scheduling (FGS) and Lyapunov Function Analysis

Enhancing Stability in Autonomous Control Systems Through Fuzzy Gain Scheduling (FGS) and Lyapunov Function Analysis

A Virtual Actuator for Advanced Individual Pitch Control (IPC)

We present a virtual actuator concept for wind turbine control, wherein rotor force and moment references from various controllers are optimally combined to compute individual blade pitch angles. The approach aims to minimize pitch bearing wear, too. The combined references can come from known control algorithms such as speed regulation, tilt-yaw control, tower dampening and helical wake control [3]. We formulate this as an optimization problem which we solve in an MPC fashion, however, instead of the usual prediction horizon over time, we use a discretized azimuth map as our finite horizon. Serving as a unified interface for all control features utilizing individual pitching, the virtual actuator replaces the plethora of multi-blade transformations and gain-scheduling functions in traditional IPC with one coherent function. Users can directly prioritize features and input constraints on actuators and structural loads. Notably, upstream control algorithms provide rotor force or moment references rather than pitch references. Simulations showcase the virtual actuator’s ability to compute intricate pitch trajectories, surpassing the capabilities of conventional IPC methods. Our method yields novel individual pitching which optimally merges conflicting IPC objectives while minimizing actuator wear.

Robust gain scheduling baseline controller for floating offshore wind turbines

AbstractThe possibility of a pitch instability for floating wind turbines, due to the blade‐pitch controller, has been discussed extensively in recent years. Contrary to many advanced multi‐input‐multi‐output controllers that have been proposed, this paper aims at a standard proportional‐integral type, only feeding back the rotor speed error. The advantage of this controller is its standard layout, equal to onshore turbines, and the clearly defined model‐based control design procedure, which can be fully automated. It is more robust than most advanced controllers because it does not require additional signals of the floating platform, which make controllers often sensitive to unmodeled dynamics. For the design of this controller, a tailored linearized coupled dynamic model of reduced order is used with a detailed representation of the hydrodynamic viscous drag. The stability margin is the main design criterion at each wind speed. This results in a gain scheduling function, which looks fundamentally different than the one of onshore turbines. The model‐based controller design process has been automated, dependent only on a given stability margin. In spite of the simple structure, the results show that the controller performance satisfies common design requirements of wind turbines, which is confirmed by a model of higher fidelity than the controller design model. The controller performance is compared against an advanced controller and the fixed‐bottom version of the same turbine, indicating clearly the different challenges of floating wind control and possible remedies.

A reconfigurable PID fault tolerant tracking controller design for LPV systems

This paper considers the design of a reconfigurable PID Fault Tolerant Tracking Controller (PID-FTTC) for Linear Parameter Varying (LPV) systems affected by actuator faults with the presence of disturbance. The LPV systems are represented through a polytopic LPV description with measurable gain scheduling functions. A new PID-FTTC scheme with a model reference, an adaptive PID controller and an Adaptive Polytopic Observer (APO), is developed. The main idea is to improve and to compare performances with this developed PID-FTTC versus previous similar FTC techniques especially about the settling time, the overshoot and integral error indices. By the way, this paper can reduce the conservatism of previous methods with more parameters design so as to avoid their disadvantages and to give better control loop performances especially in terms of accuracy and speed of trajectory tracking even when a fault occurs. So, in order to establish the stability of the reconfigured PID-FTTC, a new theoretical study is developed through the use of Linear Matrix Inequality (LMI). This new method is illustrated through a two-tank process where the results compared to previous ones, underline the improvements.

A model reference tracking based on an active fault tolerant control for LPV systems

SummaryThis work deals with the problem of a model reference tracking based on the design of an active fault tolerant control for linear parameter‐varying systems affected by actuator faults and unknown inputs. Linear parameter‐varying systems are described by a polytopic representation with measurable gain scheduling functions. The main contribution is to design an active fault tolerant controller whose control law is described by an adaptive proportional integral structure. This one requires 3 types of online information, which are reference outputs, measured real outputs, and the fault estimation provided by a model reference, sensors, and an adaptive polytopic observer, respectively. These types of information are used to reconfigure the designed controller, which is able to compensate the fault effects and to make the closed‐loop system able to track reference outputs in spite of the presence of actuator faults and disturbances. The controller and the observer gains are obtained by solving a set of linear matrices inequalities. Performances of the proposed method are compared to another previous method to underline the relevant results.

State feedback control assisted by a gain scheduling scheme for three-level NPC VSC-HVDC transmission systems

In this work, a feedback linearization controller together with a gain scheduling function is proposed in order to control a high-voltage direct-current transmission system (VSC-HVDC), composed by two three-phase three-level neutral point clamped converters. The described dq0 model has the advantage of simplifying the mathematical analysis and does not disregard the zero-dynamics, against other reported solutions. In addition, based on the input-output linearization a direct current control (DCC) for the whole VSC-HVDC system is presented, where the control tasks are distributed between both converters. Moreover, a control loop to balance, in an independent way the voltage between capacitors at each converter is designed. Additionally, to the unbalance compensator, a gain scheduling scheme is proposed to assigning new tuning parameters for the PI controller, considering the system states as scheduling variables. The real-time simulator OPAL-RT® is employed as rapid prototyping and test the performance of the proposed DCC scheme.

Robust H−/H∞ fault detection observer design for descriptor-LPV systems with unmeasurable gain scheduling functions

This paper addresses a design of a fault detection observer (FDO) for descriptor linear parameter varying (D-LPV) systems. In contrast with the conventional approach for D-LPV systems, the gain scheduling functions (GSF) are considered unmeasurable. The FDO is investigated in the H−/H∞ index framework in order to minimise the effects of the disturbance and maximise the effect of faults on the residuals, and minimise the error caused by the unmeasurable GSF. The stability is guaranteed based on a Lyapunov approach. Sufficient conditions for the existence of the FDO are established in terms of linear matrix inequalities. The effectiveness of the proposed method is illustrated by means of a simulation example.

Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

Abstract This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.

Robust state and fault estimation observer for discrete-time D-LPV systems with unmeasurable gain scheduling functions. Application to a binary distillation column

This paper deals with the problem of robust jointly state and fault estimation (actuator and sensor) observer design for discrete-time Descriptor-Linear Parameter Varying (D-LPV) with unmeasurable gain scheduling. The proposed approach is based on the H∞ synthesis applied to the state estimation error. Sufficient conditions are given by a set of Linear Matrix Inequalities (LMIs), which ensures robustness to disturbances/noise and the error given by the unmeasurable gain scheduling functions. Thus, the main contribution is to develop a conceptually simple integrated procedure to estimate states, sensor or actuator faults. In order to illustrate the methodology, simulations based on a realistic model of binary distillation column are considered.

Fuzzy Logic Scheduling in PI Control of the Servo System Under High Stiction Torque

This paper is concerned with a controller design for a servo system with a high stiction torque. A complete friction model is adopted that caters for a dynamic stiction torque. A classical cascaded control structure that is composed of the inner velocity and outer position control loops is employed. The PI controllers are used in this loops. Due to a high stiction torque a high accuracy of servo tracking in the steady-state and a high dynamic performance cannot be simultaneously achieved by fixed parameter controller under uncertainty in the friction model parameters. High gains of the controller needed to reject friction in order to obtain required steady-state error would lead to a loss of stability. Gain scheduling is proposed based on the servo speed measurements. The gain scheduling functions cannot be derived using classical techniques due to the uncertainty and nonlinearities. A fuzzy logic approach is then applied that easily utilises available qualitative representation of the functions. Performance of the controller is illustrated by simulation results.

Mixed H2/ H∞ multi-channel linear parameter-varying control in discrete time

This paper develops a new method for the synthesis of linear parameter-varying (LPV) controllers in discrete time. LPV plants under consideration have a linear fractional transformation (LFT) representation. In contrast to earlier results which are restricted to single-objective LPV problems, the proposed method can handle a set of H 2/ H ∞ specifications that can be defined channel-wise. This practically attractive extension is derived by using specific transformations of both the Lyapunov and scaling/multiplier variables in tandem with appropriate linearizing transformations of the controller data and of the controller scheduling function. It is shown that the controller gain-scheduling function can be constructed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameter, hence is easily implemented on line. Finally, these manipulations give rise to a tractable and practical LMI formulation of the multi-objective LPV control problem.