Feedback Linearization Method Research Articles

A Backstepping‐Based Nonlinear Controller for Glucose‐Insulin System Dynamics in Type‐1 Diabetes Patients

ABSTRACTThis paper investigates the function of the artificial pancreas, which is devised based on a dynamical backstepping approach. The Bergman's minimal model, used to describe the glucose‐insulin system, has been extended to encompass the dynamics of the insulin pump and external disturbances to closely simulate real‐world scenarios. Three techniques, namely feedback linearization, conventional backstepping, and super‐twisting sliding‐mode control, are evaluated in comparison to dynamical backstepping in the context of regulating blood glucose levels in individuals with type‐1 diabetes. In order to enhance the comparison of the controllers, we have taken into account the measurement noise and faults in the insulin pump as well. Additionally, Monte‐Carlo analysis is utilized as a practical tool to experimentally evaluate the robustness of the nonlinear controllers against measurement errors and variations in model parameters for different individuals, as would be encountered in a clinical trial. The extensive numerical simulations confirm that the dynamical backstepping method closely emulates the functionality of the natural pancreas and surpasses the super‐twisting sliding‐mode control method, the feedback linearization method, and the conventional backstepping method when faced with measurement noise, insulin pump faults, and parameter variations.

Design of a Hybrid Excitation Controller for Multimachine Infinite Bus Power System

Abstract: A significant portion of contemporary power networks is still conventional power system that uses synchronous generators to produce electricity. Conventional power systems are operated under various operating situations by means of excitation systems and turbine-governor systems of synchronous generators. This paper proposes an excitation controller for synchronous generators (SGs) in a multi machine infinite bus (MMIB) power system through combining the idea of the nonlinear backstepping (BS) and partial feedback linearization methods. The model of third-order has been linearized into a second-order linearized system that is independent of the rotor angle which is unmeasurable, using the partial feedback linearization approach. In this case, the BS is applied to the partially linearized system. The idea is to find a control input that drives the system towards a desired behaviour while ensuring the transformed states converge to their target values. Lastly, simulation research is carried out on an MMIB system to analyse how the proposed control mechanism (BS-PFLC) performs in stabilizing the system under a three phase-to-ground fault conditions of power networks. To demonstrate the effectiveness of the BS-PFLC, an existing excitation controller has been used to compare the performance.

Modeling and compensation of a hollow XY stage based on hybrid reluctance actuators

In the field of beam pointing and optoelectronic imaging, there is a growing demand for control mechanisms that offer large stroke, and high bandwidth. These are precisely the characteristics of hybrid reluctance actuator, which therefore is increasingly being used in XY stage to replace piezo-actuator and voice coil motor. This study presents a hollow XY stage utilizing hybrid resistance actuators, aiming to adapt to optical applications with inherent nonlinearity and biaxial coupling, which are further modeled and compensated to mitigate their impacts. Firstly, the basic composition and working principle of the hollow XY stage are described, and the impact of its nonlinearity and biaxial coupling characteristics is elucidated. Secondly, the sources of nonlinearity and biaxial coupling are analyzed, and an analytical model of hybrid reluctance actuators is established. The magnetic leakage coefficient of the model is determined, and the accuracy of the model is verified by Finite Element Method (FEM) and experiment, demonstrating consistency with the analytical model's results. Furthermore, based on the nonlinear and biaxial coupling model, a compensator based on feedback linearization method is established, and verified through experiment. The results show that this method has a significant suppression effect on nonlinear and biaxial coupling, and the tracking error and cross-talk is obviously reduced, which proves the effectiveness of this compensation method.

Reinforcement Learning Control of Hypersonic Vehicles and Performance Evaluations

This work presents a new framework for model-based continuous-time reinforcement learning (CT-RL) control of hypersonic vehicles (HSVs). The predominant classes of CT-RL methods for general nonlinear systems in adaptive dynamic programming (ADP) and deep RL tend to either present substantial theoretical results but lack practical synthesis capability (ADP) or show empirical promise without offering theoretical guarantees (deep RL). Meanwhile, RL control frameworks developed directly for HSVs tend to require a simplified model and complicated control structure, and they lack the substantial numerical evaluations essential for real-world flight implementation. To directly address these challenges, we propose a new decentralized excitable integral reinforcement learning framework within which the reference input-based exploration improves persistence of excitation. Together with new insights on prescaling and established decentralized control structure for HSVs, we demonstrate the resulting controller for significant performance improvement over classical Linear Quadratic Regulator (LQR) and feedback linearization methods. Additionally, we provide convergence, optimality, and closed-loop stability guarantees of the proposed method. We demonstrate these performance guarantees over a set of substantial and systematic numerical evaluations on an unstable, nonminimum phase HSV model subject to varying modeling errors and initial conditions.

Optimal IOFL-based economic model predictive control technique for boiler-turbine system

The optimal control design of the boiler-turbine system is vital to ensure feasibility and high responsiveness over desired load variations. Using the traditional linear control techniques realization of this task is difficult, as the boiler-turbine mechanism has strong nonlinearities. Besides, environmental and economic concerns have replaced existing tracking control ones as the primary concerns of advanced power plants. Thus, this study proposes an optimal economic model predictive controller (EMPC) scheme for this unit on the basis of the input/output feedback linearization (IOFL) method. By employing the IOFL method, this unit is decoupled into a new linearized model that is utilized for developing the suggested optimal IOFL EMPC technique. The proposed control scheme is formulated in an economic quadratic programming form that considers the input-rate and input limits of the unit for optimal economic performance. In addition, an adaptive iterative algorithm is utilized for constraints mapping with guaranteeing a feasible solution in a finite number of steps without violation of original constraints over the entire predictive horizon. The outcomes of the simulation show that the suggested optimal IOFL EMPC scheme offers an improved dynamic and economic output performance over fuzzy hierarchical MPC, fuzzy EMPC, and nonlinear EMPC techniques during various load variations.

Indirect adaptive observer control (I-AOC) design for truck–trailer model based on T–S fuzzy system with unknown nonlinear function

Tracking is a crucial problem for nonlinear systems as it ensures stability and enables the system to accurately follow a desired reference signal. Using Takagi–Sugeno (T–S) fuzzy models, this paper addresses the problem of fuzzy observer and control design for a class of nonlinear systems. The Takagi–Sugeno (T–S) fuzzy models can represent nonlinear systems because it is a universal approximation. Firstly, the T–S fuzzy modeling is applied to get the dynamics of an observational system in order to estimate the unmeasurable states of an unknown nonlinear system. There are various kinds of nonlinear systems that can be modeled using T–S fuzzy systems by combining the input state variables linearly. Secondly, the T–S fuzzy systems can handle unknown states as well as parameters known to the indirect adaptive fuzzy observer. A simple feedback method is used to implement the proposed controller. As a result, the feedback linearization method allows for solving the singularity problem without using any additional algorithms. A fuzzy model representation of the observation system comprises parameters and a feedback gain. The Lyapunov function and Lipschitz conditions are used in constructing the adaptive law. This method is then illustrated by an illustrative example to prove its effectiveness with different kinds of nonlinear functions. A well-designed controller is effective and its performance index minimizes network utilization—this factor is particularly significant when applied to wireless communication systems.

Precise Obstacle Avoidance Movement for Three-Wheeled Mobile Robots: A Modified Curvature Tracking Method

This paper proposes a precise motion control strategy for a three-wheeled mobile robot with two driven rear wheels and one steered front wheel so that an obstacle avoidance motion task is able to be well implemented. Initially, the motion laws under nonholonomic constraints are expounded for the three-wheeled mobile robot in order to facilitate the derivation of its dynamic model. Subsequently, a prescribed target curve is converted into a speed target through the nonholonomic constraint of zero lateral speed. A modified dynamical tracking target that is aligned with the dynamic model is then developed based on the relative curvature of the prescribed curve. By applying this dynamical tracking target, path tracking precision is enhanced through appropriate selection of a yaw motion speed target, thus preventing speed errors from accumulating during relative curvature tracking. On this basis, integral sliding mode control and feedback linearization methods are adopted for designing robust controllers, enabling the accurate movement of the three-wheeled mobile robot along a given path. A theoretical analysis and simulation results corroborate the effectiveness of the proposed trajectory tracking control strategy in preventing off-target deviations, even with significant speed errors.

Model Simplification for Asymmetric Marine Vehicles in Horizontal Motion—Verification of Selected Tracking Control Algorithms

This paper addresses a trajectory tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North–East–Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method, for which the application condition was that the vehicle was symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Adaptive PMSM Control of Ship Electric Propulsion with Energy-Saving Features

Electric ship propulsion is considered one of the most promising alternatives to conventional combustion systems. Its goal is to reduce the carbon footprint and increase a ship’s maneuverability, operational safety, and reliability. The high requirements for ship propulsion make permanent magnet synchronous motors (PMSMs) an attractive solution due to their characteristics. This paper discusses the control problem of a PMSM based on the input–output feedback linearization method combined with the optimal and adaptive control techniques. The method presented here integrates the parameter tuning process with the optimal design of the baseline controller. Since the load disturbances are treated as an additional unknown parameter, there is no need to introduce an integral action to deal with the resulting steady-state error. An important feature of the designed controller is the so-called energetic optimization of the system; i.e., in addition to the aforementioned adaptive and optimal controller, it has a feature of ensuring zero reactive power consumed by the system. The performed simulations of the machine speed stabilization process confirmed the high efficiency of the proposed controller despite the assumed uncertainty of the system parameters and environmental (load) disturbances. Besides achieving high-quality control, an essential feature of this approach is the elimination of the tuning problem.

Communication topology for AUV formation consensus based on optimal cost control under time-varying communication and input delays

This study investigates the optimal communication topology for consensus in autonomous underwater vehicle (AUV) formations, considering both leader-following and leaderless scenarios. Initially, a second-order dynamic model of the AUV is established using the feedback linearization method. To address time-varying delays, a universal predictor-based consensus protocol is introduced, capable of operation with or without a designated leader. Subsequently, two global quadratic cost functions are formulated based on distinct consensus errors. Utilizing linear quadratic regulator (LQR) theory and matrix theory, the optimal communication topologies and associated gain matrices are deduced. Specifically, for leader-following AUV formations, the optimal communication topology is identified as an unevenly weighted star-shaped directed spanning tree. Conversely, for leaderless formations, the optimal topology adopts a complete digraph, which indicates high interaction requirements. To accommodate practical constraints, a suboptimal topology is devised, featuring a directed spanning tree. These findings offer a theoretical framework for selecting communication topologies in AUV formations, with numerical examples provided to validate the proposed approaches.

Robust Direct Power Control of Three-Phase PWM Rectifier with Mismatched Disturbances

To effectively eliminate the impacts of both matched and mismatched power disturbances in a three-phase PWM rectifier, this paper proposes a robust direct power control (RDPC) method with a single-loop control structure. Firstly, a nonlinear power model of the three-phase PWM rectifier is established. Then, using the exact feedback linearization method, a linearized power model including matched and mismatched power disturbances is derived and achieves the decoupling of active and reactive power. Secondly, to regulate the DC bus voltage, a sliding-mode controller (SMC) combined with a nonlinear disturbance observer (NDO) is proposed. The proposed SMC combined with an NDO (SMC + NDO) method features a single-loop control structure, which enables a faster response and simpler structure compared to the dual-loop DPC method. By incorporating estimated mismatched power disturbance into the sliding-mode surface, it overcomes the SMC’s defect in incompletely suppressing mismatched disturbances and enables the simultaneous regulation of voltage and active power. Additionally, it effectively reduces sliding-mode chattering. To regulate reactive power, a sliding-mode controller based on the exponential convergence law is designed to suppress matched reactive power disturbances. Finally, the simulation and experimental comparative results demonstrate that the proposed controller exhibits stronger robustness against matched and mismatched power disturbances, as well as a better performance under the constant power load (CPL).

Generalized predictive control application scheme for nonlinear hydro-turbine regulation system: Based on a precise novel control structure

Generalized predictive control (GPC), which has excellent control performance and robustness, is only applicable to the control object that can be expressed in the transfer function and is difficult to be directly applied to the hydraulic turbine regulation system (HTRS) that contain extremely complex nonlinearity. Therefore, considering the practical application of GPC in a hydropower station containing the Francis turbine, the double models, real-time feedback linearization module, and a nonlinear characteristic compensator are designed, and a generalized predictive control strategy combining these modules (GPC-DM-RFLM-NCC) is proposed. Firstly, the salp swarm algorithm (SSA) is improved based on the chaotic mapping and Levy flight, an accurate nonlinear hydraulic turbine model is constructed based on the backpropagation neural network (BPNN) and improved SSA (ISSA), and an HTRS simulation platform with nonlinear characteristics is built by combining modules such as water diversion system, servo system, and generator. Then, the irrationality of the commonly used linear hydraulic turbine models in HTRS dynamic process simulation is verified through quantitative calculation. Furthermore, by combining the real-time feedback linearization method and ISSA-based nonlinear characteristic compensator, the GPC-DM-RFLM-NCC is proposed. Finally, the HTRS simulation platform, which consists of GPC, double models, real-time feedback linearization module, and nonlinear characteristic compensator, is built, and the applicability, reliability, and excellent robustness of the proposed GPC-DM-RFLM-NCC are verified by the real data of a hydropower station.

An Extension of the Feedback Linearization Method in the Control Problem of an Inverted Pendulum on a Wheel

This paper continues previous studies on designing stabilizing control laws for a mechanical system consisting of a wheel and a pendulum suspended on its axis. The control objective is to simultaneously stabilize the vertical position of the pendulum and a given position of the wheel. The difficulty of this problem is that the same control is used to achieve two targets, i.e., stabilize the pendulum angle and the wheel rotation angle. Previously, the output feedback linearization method was applied to this problem. The sum of the pendulum angle and the wheel rotation angle was taken as the output. For the closed loop system to be not only asymptotically stable in the output but also to have asymptotically stable zero dynamics, a dissipative term was added to the output-stabilizing control law. Below, a two-parameter modification of this law is described. Along with the dissipative term, we introduce a positive factor. The more general parameterization allows stabilizing this system in the cases where the control law proposed previously appeared ineffective. The properties of the new control law are investigated, and the attraction domain is estimated. The estimation procedure is reduced to checking the feasibility of linear matrix inequalities.

An Extension of the Feedback Linearization Method in the Control Problem of an Inverted Pendulum on a Wheel

Продолжается исследование синтеза стабилизирующих законов управления для механической системы, состоящей из колеса и маятника, подвешенного на его оси. Цель управления состоит в одновременной стабилизации вертикального положения маятника и заданного положения колеса. Трудность этой задачи состоит в том, что одно управление используется для достижения двух целей – стабилизации угла отклонения маятника и угла поворота колеса. Ранее предлагалось использовать метод линеаризации обратной связью по выходу. Вкачестве выхода берется сумма угла отклонения маятника и угла поворота колеса. Для того, чтобы замкнутая система была не только асимптотически устойчивой по выходу, но и обладала асимптотически устойчивой нулевой динамикой, предлагалось к закону управления, стабилизирующему по выходу, добавлять диссипативное слагаемое. Вданной работе предложена двухпараметрическая модификация этого закона. Наряду с диссипативным слагаемым предлагается ввести положительный множитель. Более общая параметризация позволяет стабилизировать данную систему в случаях, когда использование ранее предложенного закона не давало результата. Исследуются свойства нового закона управления и строится оценка области притяжения. Построение оценки сводится к задаче о разрешимости линейных матричных неравенств.

An Extension of the Feedback Linearization Method in the Control Problem of an Inverted Pendulum on a Wheel

An Extension of the Feedback Linearization Method in the Control Problem of an Inverted Pendulum on a Wheel

Hopf bifurcation control of a modified continuum traffic flow model

The stability of the transportation system refers to the structural stability of the system. When the system structure is unstable, local or global bifurcation phenomena will occur, which is one of the main reasons for nonlinear traffic phenomena such as congestion. To truly understand the internal mechanism of the formation of these phenomena, it is necessary to analyze the bifurcation of traffic flow. In this paper, the Hopf bifurcation control of a modified viscous macroscopic traffic flow model is studied by using the linear state feedback method, which changes the characteristics of the bifurcation phenomenon of the dynamic system and obtains the required dynamic behavior of the system. First, we can convert the original traffic model into the nonlinear ordinary differential form suitable for bifurcation analysis, solve the equilibrium point of the system, and carry out phase plane analysis. Then, the linear state feedback term is added and the corresponding controlled system is generated, the existence and type of Hopf bifurcation and the existence of saddle node bifurcation are proved. Numerical simulation results show that the analysis and control of Hopf bifurcation in the traffic model are well realized in this paper.

Quadrotor control in complex manoeuvres using a hybrid backstepping and feedback linearisation control strategy

In this article, a novel control algorithm called the combined backstepping and feedback linearisation method, along with an uncertainty estimator, is presented for quadrotors. The objective is to develop a robust control algorithm capable of handling various flight conditions, compensating for uncertainties and disturbances, and effectively controlling high-speed manoeuvres. To accomplish this, the quadrotor dynamics model is first derived using the Newton–Euler method. Subsequently, a backstepping control algorithm is designed for the quadrotor's internal control layer, followed by the application of the feedback linearisation method to the external control layer. An estimator is also designed to mitigate the effects of disturbances and uncertainties. A comparison is made between the proposed combined backstepping and feedback linearisation algorithm and the backstepping method, revealing that the combined backstepping and feedback linearisation algorithm outperforms the backstepping method across different aspects. Notably, the combined backstepping and feedback linearisation algorithm achieves faster trajectory tracking and demonstrates fewer steady-state errors. Additionally, the integration of the uncertainty estimator into the combined backstepping and feedback linearisation algorithm effectively mitigates the detrimental effects of disturbances and uncertainties. Comparative results for tracking control are presented to evaluate the performance of the proposed algorithm across various scenarios and case studies.

Finite-time attitude tracking control of stratospheric airship in the presence of multiple disturbances

AbstractThis paper proposes a composite non-singular fast terminal sliding mode attitude control scheme based on a reduced-order extended state observer for the stratospheric airship’s attitude system affected by multiple disturbances. First, the feedback linearisation method is applied to address the nonlinearity of the attitude motion model and achieve decoupling of the model in three channels. Second, the overall disturbances, encompassing airship parameter perturbations and external disturbances, are treated as an aggregate. A reduced-order extended state observer is designed for each channel to formulate a composite non-singular fast terminal sliding mode surface. In the control design phase, the hyperbolic sine function is adopted as replacement for the sign function to ensure the continuity of the control signal. The estimated disturbances are incorporated in the control law design to directly offset the effects of multiple disturbances on the attitude motion of the airship. Third, based on Lyapunov theory, it has been proven that the control law can drive the attitude tracking error to converge to zero within a finite time. Simulation results demonstrate that the proposed control scheme exhibits favorable disturbance rejection capability, as well as higher tracking accuracy and faster response speed.

Maximum Power Point Tracking Control of Offshore Hydraulic Wind Turbine Based on Radial Basis Function Neural Network

A maximum power point tracking control strategy for an affine nonlinear constant displacement pump-variable hydraulic motor actuation system with parameter uncertainty, used within an offshore hydraulic wind turbine, is studied in this paper. First, we used the feedback linearization method to solve the affine nonlinear problem in the system. However, offshore hydraulic wind turbines have strong parameter uncertainty characteristics. This conflict was resolved through the further application of RBF neural network adaptive control theory. So, we combined feedback linearization with RBF adaptive control as the control theory, and then two control laws were compared by setting the pump rate and rating as outputs, respectively. It is shown by the MATLABR2016a/Simulink emulation results that power control is smoother than speed and friendlier for electric networks. It is also shown by the emulation results, in terms of the undulatory wind speed condition, that the feedback linearization–RBF neural network adaptive control strategy has perfect robustness. According to the simulation results, the feedback linearization–RBF neural network adaptive control strategy adopts the RBF neural network to approach complex nonlinear models and solve the parameter uncertainty problem. This control law also avoids the use of feedback linearization control alone, which can result in the system becoming out of control.

Secure Event-Triggered Sliding Control for Path Following of Autonomous Vehicles Under Sensor and Actuator Attacks

Sensor and actuator attacks, which propagate the injected false data through CAN bus, make real threats to the security of the control of autonomous vehicles. This paper attempts to solve the secure event-triggered path following control problem of autonomous vehicles subject to both sensor and actuator attacks. Firstly, a more general physical security model is established to characterize the impacts of sensor and actuator attacks on measurements and control actions. Then, feedback linearization method based on Lie derivative is exploited to linearize the established nonlinear attacked model. Thus, the nonlinear path following control is transformed into a linear case which will facilitate to the following networked-based analysis and design. Based on the established secure model, the event-triggered control scheme is utilized to alleviate communication burden under sampled-data control framework. Furthermore, the sliding control design is augmented to mitigate the malicious impacts caused by such false data injection attacks due to its inherent robustness to abnormal attack signal. Remarkably, the proposed secure sliding control can be plugged into the original control scheme rather than changing its existing control structure. Criteria for formal stability analysis and controller design are also provided and expressed in terms of some numerically tractable linear matrix inequalities. Finally, both simulation and experimental verification cases are shown to verify the composite control scheme.