Nonlinear State Feedback Control Research Articles

Tensor Product Alternatives for Nonlinear Field-Oriented Control of Induction Machines

The paper presents a nonlinear field-oriented control technique based on the tensor product representation of the nonlinear induction machine model and the solvability of linear matrix inequalities. The nonlinear model has 32 quasi linear parameter-varying equivalent variants, and it is shown that only half of the models result in feasible controller. Two control goals are realized: torque control and speed control. The controller is a nonlinear state feedback controller completed by integral action. A new block diagram is investigated for speed control. The controller gains are designed by the solution of linear matrix inequalities to solve the Lyapunov inequality to obtain a stable and fast response and constraints on the control signal. The presented methods are verified and compared by simulations.

Dynamics analysis of a nonlinear controlled predator–prey model with complex Poincaré map

In this paper, we propose a class of predator–prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings.

Dynamics analysis of a nonlinear controlled predator–prey model with complex Poincaré map

In this paper, we propose a class of predator–prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings.

Accurate voltage regulation for a DC microgrid using nonlinear state feedback controller

AbstractThe high penetration of distributed generation systems poses challenges in effectively managing both DC bus voltage and power‐sharing in DC microgrids (MGs). To ensure precise voltage regulation across various distributed generation systems and maintain overall system stability, this paper studies the modelling and control of an islanded DC MG described by a set of nonlinear‐nonaffine differential equations. In the proposed DC MG, a battery storage, a photovoltaic (PV) power plant, and a back‐end power converter with DC loads have been connected to a common DC bus. First, a dynamic model of a DC MG was developed. Then, to find the maximum power point of solar PV, a straightforward method based on an artificial neural net is employed. Afterward, a nonlinear local state feedback controller through output regulation theory is applied to achieve voltage stability, overcoming the drawbacks of droop‐based techniques. Moreover, partial state feedback capability simplifies controller design. To verify the effectiveness of the proposed approach, various scenarios, including sudden load variation, illumination change, and changes in the MG configuration, have been examined. Finally, numerical studies were carried out in a simulation environment to demonstrate the superiority of the proposed nonlinear control scheme over constant feedback control.

Nonlinear control algorithm for a self-excited induction generator for wind power applications

A non-linear state-feedback input-output linearizing control with tracking controllers for an isolated Induction Generator (IG) driven by a wind turbine and supplying an AC load is presented. For this purpose, an appropriate mathematical model of the IG based on the so-called stator-flux field oriented is detailed. Simulation results show that the input-output linearizing control provides an excellent control performances and a perfect tracking for both IG stator voltage magnitude and DC bus voltage. The proposed system can be directly explored for wind power generation purposes. Simulation results are curried out to demonstrate the feasibility of the proposed approach.

ADRC‐based control strategy for DC‐link voltage of flywheel energy storage system

AbstractThe direct current (DC)‐link voltage control of the flywheel energy storage system plays an important role in realizing high‐quality grid connection. With the traditional proportional‐integral control, the DC‐link voltage cannot track its reference value quickly and smoothly when the flywheel energy storage system switches from the charging stage to other working stages. Therefore, a DC‐link voltage control strategy for the flywheel energy storage system based on active disturbance rejection control is proposed in this paper to deal with this issue. The DC‐link voltage and its differential value are considered as the state variables in this strategy. The internal and external disturbances, such as load power, switching loss, and parameter uncertainty, are regarded as an expanded state. By inputting the voltage error and the observed disturbance into the nonlinear state feedback control law, the rapidity and anti‐interference of the DC‐link voltage control are ensured under different States of Charge of the flywheel energy storage system. Then, the coefficient freezing method is used to analyze the effects of the disturbance observation bandwidth by nonlinear gain and pole position changes. The DC‐link voltage can track the reference value over a wider frequency range of disturbances. By configuring the appropriate observer structure parameters, the disturbance observation bandwidth under the nonlinear function gain variation is always higher than the expected bandwidth. The effectiveness of the proposed control strategy is verified by simulation results at last.

Real-Time Implementation and Control of Multi-Source Electric Vehicle Traction Motor under Various Drive Conditions

The hybridization of multiple energy sources is crucial for electric vehicles to deliver the same performance as modern fossil fuel-based automobiles. This paper presents a torque and speed control strategy for an electric vehicle DC traction motor by regulating the power flow from two energy sources, namely battery and supercapacitor systems, to resist unpredictable disturbances. A control system with three control loops is applied to regulate the speed of the traction motor. The outer speed control loop is a nonlinear state feedback controller with a disturbance observer, which is capable of handling non-linear systems with unpredictable disturbances. The inner voltage and current control loop are precisely tuned PI controllers. Using an adaptive energy management method that varies depending on the state of charge of the source, the total reference current needed to support the load demand is split between two sources. A laboratory prototype system model is generated, and the performance is analyzed under motoring and regenerative braking conditions. For monitoring and controlling the system, the dSPACE DS1202 real-time simulator is employed. The performance of the proposed control system is evaluated and it is found that the settling time to settle within a tolerance band of 1% is 0.75 s.

Nonlinear control design for walking assistance training robotic systems

AbstractIn this paper, the control problem for a novel walking assistance training robot is considered where the main objective is utilizing the robot to control the tilt angle and the position of a user. First, the novel walking assistance training robot together with a user is modeled as a nonlinear dynamical system in state space form with control input where the control input includes two elements standing for pulling forces on two straps which attach to the chest and back, respectively, of the user. Then, based on the nonlinear dynamical system and some results proposed in this paper, a feedback control system is developed, and a nonlinear state feedback control algorithm is designed where the control input includes two parts, namely, a dynamical part and a constant part. By doing this, it is ensured that the feedback control system is stable, and achieves the main objective under some limits for the control input. A simulation example is given to illustrate the effectiveness and performance of the proposed nonlinear state feedback control algorithm.

Synchronization of time-varying fractional-order chaotic systems in the presence of unknown disturbance using a fast disturbance identification

This paper studies the synchronization of fractional-order chaotic systems in the presence of unknown external disturbances. A new disturbance identification method using fractional-order algebraic identification is proposed to handle unknown disturbances. In order to guarantee system stability, the nonlinear state-feedback controller is designed based on the Lyapunov theory. All system parameters and orders, as well as the external disturbances, are considered time-varying in this paper. The simulation results show that the estimation of unknown disturbance is executed more quickly and accurately using the proposed method, which also leads to fast and precise synchronization of the chaotic systems. A circuit implementation is also performed to identify the unknown disturbances in a fractional-order electronic chaotic oscillator system to evaluate the practicability of the proposed approach.

Tree-structured neural networks: Spatiotemporal dynamics and optimal control

How the network topology drives the response dynamic is a basic question that has not yet been fully answered in neural networks. Elucidating the internal relation between topological structures and dynamics is instrumental in our understanding of brain function. Recent studies have revealed that the ring structure and star structure have a great influence on the dynamical behavior of neural networks. In order to further explore the role of topological structures in the response dynamic, we construct a new tree structure that differs from the ring structure and star structure of traditional neural networks. Considering the diffusion effect, we propose a diffusion neural network model with binary tree structure and multiple delays. How to design control strategies to optimize brain function has also been an open question. Thus, we put forward a novel full-dimensional nonlinear state feedback control strategy to optimize relevant neurodynamics. Some conditions about the local stability and Hopf bifurcation are obtained, and it is proved that the Turing instability does not occur. Moreover, for the formation of the spatially homogeneous periodic solution, some diffusion conditions are also fused together. Finally, several numerical examples are carried out to illustrate the results’ correctness. Meanwhile, some comparative experiments are rendered to reveal the effectiveness of the proposed control strategy.

Combining Augmented Error Modeling Technique and Block-Pulse Functions Method for Tracking Control Design of Nonlinear Polynomial Systems with Multiple Time-Delayed States Subject to Nonsymmetric Input Saturation

The present research work is intended to synthesize a novel tracking control strategy for a class of nonlinear polynomial systems characterized by multiple well-defined delays in state variables under the presence of nonsymmetric input saturation. The design strategy makes full use of an associate’s memory nonlinear state feedback control with integral-based actions. An original control scheme joining block-pulse functions method combined with the augmented error modeling technique is used to infer the controller’s tracking gains. The objective is to convert the investigated nonlinear algebraic problem governed by specifying constraints into a constrained linear one that can be solved in the constrained least square methodology. Detailed novel sufficient conditions proving the closed-loop augmented system’s practical stability are elaborated. The instance of a twofold inverted pendulums benchmark is considered so as to exhibit the benefits of the proposed control approach.

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system.

Hybridization of battery and ultracapacitor for electric vehicle application with dynamic energy management and non-linear state feedback controller

• Proposed a dynamic energy management system for hybrid sources in an electric vehicle. • Buck-boost H-bridge converters are introduced for bidirectional power flow control. • System non-linearities are addressed using a nonlinear state feedback controller. • The proposed system accurately delivers instantaneous vehicle speed and torque. This paper describes a methodology to control a multi-source battery-capacitor hybrid EV incorporating a dynamic power splitting strategy. Considering the requirement for precise speed control characteristics of the EV and the non-linear behavior of traction motor with system disturbances, a non-linear state feedback controller (NLSFC) with a disturbance observer is suggested as the speed control technique for the EV traction motor. To interface a parallel configured multi-source system, a non-inverted buck-boost H-bridge is proposed as the source side converter for effective recovery of the braking energy. Detailed control design for traction motor and converter is also presented for efficient control of EV. Besides, an adaptive energy management strategy considering power profile and dynamic source characteristics is incorporated into the overall control system. The simulation results from various case studies indicate that the proposed system can follow the required vehicle speed and torque despite the sudden change in EV load torque. Furthermore, the comparative analysis between NLSFC and PI controller shows improvement with steady-state error reduction from 0.43 to 0.0014 and peak overshoot drop from 12.07% to 3.51% during acceleration of the system when proposed NLSFC is adopted. The proposed solutions will be implemented in a prototype EV system in the future.

Towards a Taylor-Carleman bilinearization approach for the design of nonlinear state-feedback controllers

The Carleman bilinearization is an approach that performs an exact conversion of a finite-dimensional nonlinear system into an infinite-dimensional bilinear system. A finite-dimensional system is later obtained through a truncation for analysis and control purposes. This paper investigates the linear matrix inequality (LMI)-based design of a switched state-feedback control law for the model obtained via Carleman bilinearization of a first-order nonlinear system. It is shown that in order to obtain feasible design conditions, the performance requirements must be relaxed in a neighborhood of the zero equilibrium point, so that problems arising from the uncontrollability of the linear part of the model can be avoided. The effectiveness of the proposed approach is shown using a numerical example and experimental results using a multi-input tank system.

Global asymptotic stability of input-saturated one degree-of-freedom Euler–Lagrange systems with Rayleigh dissipation under nonlinear control

ABSTRACT In this manuscript, the regulation of one degree-of-freedom Euler–Lagrange systems subject to input saturation is addressed. In particular, the design and analysis of a nonlinear static state feedback controller is presented. As a result, it is proven via Lyapunov's direct method that, in the presence of Rayleigh dissipation, the closed-loop equilibrium point is globally asymptotically stable with a strict Lyapunov function. Since saturation occurs in the system which contains the actuator model, the proposed control law is unconstrained and can be simplified to a proportional-derivative with desired gravity compensation algorithm. As a by-product global asymptotic stability is also proven for the case where Rayleigh dissipation is null. Numerical simulations on a crank-slider mechanism are presented. Moreover, experimental results on a DC-DC buck power converter are also shown and confirm the viability of our approach.

Nonlinear State Dependent Riccati Equation Controller for 3-DOF Airfoil with Cubic Structural Nonlinearity

In this paper, Limit Cycle Oscillations (LCOs) of a Two-Dimensional (2-D) airfoil with cubic structural nonlinearity in the plunge Degree of Freedom (DOF) are investigated. The aerodynamic loads are modelled using the unsteady Theodorsen’s theory. Wagner function and Jones’ approximation are used to transform the unsteady aerodynamic loads from frequency domain into time domain. The aeroelastic differential equations are solved using the routine ODE45 in MATLAB to get the system response. Both subcritical and supercritical LCOs are observed in the 3-DOF airfoil with structural nonlinearity in the plunge DOF. Such LCOs are undesirable phenomena and should be suppressed within the flight envelope. A nonlinear state feedback controller is designed to minimize the amplitude of LCOs presented in the considered nonlinear aeroelastic system. The State-Dependent Riccati Equation (SDRE) approach in combination with Kalman filter technique is used to design a controller for the 2-D airfoil with trailing edge control surface (flap). The forces and moments produced by this flap’s action are used to stabilize the system and suppress the existence of LCOs. The efficiency of the proposed nonlinear controller by the SDRE and Kalman filter in suppressing the existence of subcritical and supercritical LCOs are verified by the numerical simulation results.

Theoretical Study of the Unconstrained and Constrained Nonlinear Optimal Discrete Time State Feedback Control

Abstract Majority of the optimal control techniques can only be applied successfully if the model of the controlled process is known and it is linear. If the system model is nonlinear, then this nonlinear model can be approximated with different simple, linear models. However, these models are valid only in the neighbourhood of the operating points. The success of the control algorithms is highly dependent on the used linearization methods. The aim of the paper is to compare different optimal control algorithms and linearization methods. The presented optimal control algorithms have been also tested in constrained and unconstrained versions.

Nonlinear state feedback controller combined with RBF for nonlinear underactuated overhead crane system

This paper proposes a robust control scheme for an underactuated crane system. The presented scheme contains two control strategies, feedback control term and corrective control term, based on Radial Basis Function (RBF) neural networks. A feedback control term is deigned based on the nominal dynamic model of the controlled system. RBF neural networks have been used as adaptive control term to compensate for the system uncertainties and external disturbance. Lyapunov stability theorem has been used to derive updating laws for the weights of the RBF neural networks. To illustrate the robustness and effectiveness of the proposed controller, Matlab program is used to simulate the model of the nonlinear overhead crane system with the proposed control method, taking into account system uncertainties and external disturbance. Simulation results indicated superior control performance of the proposed control method compared to the other control methods used in the test.

Nonlinear Optimal Feedback Control of the Two-Level Open Non-Markovian Stochastic Quantum System

In this paper, a nonlinear optimal feedback control based on the nonlinear state estimator for a two-level open non-Markovian stochastic quantum system is proposed. The proposed nonlinear state estimator is designed by using the state-dependent differential Riccati equation and constructed to optimally estimate the state. The estimated state is updated by the output data of continuous weak measurement of the controlled quantum system and used to design the nonlinear state feedback controller to track the output of the reference model. The output state of reference model is chosen as the desired performance. The numerical simulation results verify the achievability of the proposed state feedback control strategy, and the capability to steer the state of system from any arbitrary initial state to the final reference target state with high state transfer success rate.

Global feedback stabilization of discrete‐time bilinear systems

AbstractThis paper studies the stabilization of the discrete‐time bilinear system , where A and B are bounded linear operators on a pre‐Hilbert space H, by means of a new nonlinear state feedback control which is uniformly bounded. First, sufficient conditions for uniform exponential stabilization are given, and the decay rate of the state is estimated. Then global weak stabilization is investigated under less stringent assumptions. In the case of the finite dimension, easily verified conditions for uniform stabilization are given. Moreover, a decomposition method allows additional stabilization results. Finally, illustrative examples are provided.