Linear Feedback Control Law Research Articles

A Modified ADRC Scheme Based on Model Information for Maglev Train

During the operation of maglev trains, they are subjected to various disturbances. The presence of these disturbances presents a significant challenge for attaining high-performance control and even poses the risk of system instability. To further enhance the anti-disturbance capability of maglev trains, this paper proposes a model information-assisted modified active disturbance rejection control (MADRC) approach. A mathematical model of the single-point suspension system of maglev trains is constructed for the design of the extended state observer (ESO), which is a modified extended state observer (MESO), and a nonlinear mechanism is incorporated to boost the performance of the ESO. Owing to the introduction of model information, the estimated quantity of disturbances by MESO no longer considers the system model deviation as a disturbance. Hence, the linear feedback control law is modified accordingly. The MESO is regarded as an ESO with time-varying gain using the equivalent gain method, and its stability is proven using the Lyapunov method. The tracking and anti-disturbance performances of different controllers are compared via simulation experiments. Suspension and anti-disturbance experiments are conducted on the single-point suspension experimental platform, verifying that the proposed MADRC has a more potent suppression ability for load disturbances in the suspension system.

Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems

This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on the decomposition and separation method and coordinate transformation, the DFOLCS can be transformed into an equivalent fractional-order reduced system; hence, the CSRP of the DFOLCS is equivalent to the CSRP of the reduced system. By means of positive invariant sets theory, Lyapunov stability theory, and some mathematical techniques, necessary and sufficient conditions for the polyhedral positive invariant set of the equivalent reduced system are presented. Models and corresponding algorithms for solving the CSRP of a linear feedback controller are also presented by the obtained conditions. Under the condition that the resulting closed system is positive, the given model of the CSRP in this paper for the DFOLCS is formulated as nonlinear programming with a linear objective function and quadratic mixed constraints. Two numerical examples illustrate the proposed method.

Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.

Sensorless control of permanent magnet synchronous motor based on adaptive enhanced extended state observer

SummaryThis article proposes an enhanced adaptive disturbance rejection control strategy for sensorless control of permanent magnet synchronous motor. The traditional fixed bandwidth quadrature phase‐locked loop (Q‐PLL) is insufficient to meet system dynamics in the event of sudden speed changes or motor disturbances, resulting in a significant decrease in control performance. Meanwhile, conventional extended state observers usually rely on a fixed high gain for fast convergence, which raises concerns about their sensitivity to noise. To overcome these challenges, the proposed method introduces a third‐order adaptive cascaded linear extended state observer (ACLESO) in place of the conventional PLL to accurately estimate the speed, phase, and overall disturbances, ensuring timely and accurate estimation of the total disturbance. Then, a speed controller based on linear state error feedback control law (LSEFCL) was designed to enhance the dynamic performance of the system. Based on the stability analysis using the Lyapunov function, finally, extensive experimental tests were carried out to verify the validity of the proposed method.

Local Exponential Stabilization of Rogers–McCulloch and FitzHugh–Nagumo Equations by the Method of Backstepping

In this article, we study the exponential stabilization of some one-dimensional nonlinear coupled parabolic-ODE systems, namely Rogers–McCulloch and FitzHugh–Nagumo systems, in the interval (0, 1) by boundary feedback. Our goal is to construct an explicit linear feedback control law acting only at the right end of the Dirichlet boundary to establish the local exponential stabilizability of these two different nonlinear systems with a decay e−ωt, where ω ∈ (0, δ] for the FitzHugh–Nagumo system and ω ∈ (0, δ) for the Rogers–McCulloch system and δ is the system parameter that presents in the ODE of both coupled systems. The feedback control law, derived by the backstepping method forces the exponential decay of solution of the closed-loop nonlinear system in both L2(0, 1) and H1(0, 1) norms, respectively, if the initial data is small enough. We also show that the linearized FitzHugh–Nagumo system is not stabilizable with exponential decay e−ωt, where ω > δ.

Composite adaptive control of submarine and parameter identification by integral regressor excitation

In this article, we develop a novel composite adaptive control system for the dive-plane maneuvers and parameter identification of a multi-input multi-output submarine model. The composite adaptive control system consists of (1) an input–output feedback linearizing control law and (2) an identifier formed by gradient algorithm-based two-parameter estimation laws. Unlike the existing adaptive systems for autonomous underwater vehicles and submarines, a novelty of this composite identifier lies in the use of regressor matrix integral feedback for enhancement in parameter excitation. By the Lyapunov analysis, asymptotic convergence of the depth and pitch angle tracking errors is established. Simulation results show precise depth and pitch angle control, estimation of all model parameters, and robustness to random and sinusoidal disturbance inputs.

Combined control algorithm based on synchronous reinforcement learning for a self-balancing bicycle robot

In this paper, balance control of a bicycle robot is studied without either a trail or a mechanical regulator when the robot moves in an approximately rectilinear motion. Based on the principle of moment balance, an input nonaffine nonlinear dynamics model of the bicycle robot is established. A driving velocity condition is proposed to maintain the robot balance. The nonaffine nonlinear system is transformed into an affine nonlinear system by defining the equivalent control. Subsequently, a feedback linearization controller is designed for the equivalent control. We design a combined control algorithm of synchronous policy iteration based on the actor–critic architecture. The actor neural network (NN) is designed based on the feedback linearization control law. Weight tuning laws for the critic and actor NNs are proposed. The system closed-loop stability and convergence of the NN weights are guaranteed based on the Lyapunov analysis. The optimality of the equivalent control policy is guaranteed. To satisfy the driving velocity condition, the values of the steering angle and driving velocity are determined based on the optimal equivalent control. The effectiveness of the proposed algorithm is verified through simulations and real experiments.

Local stabilization of the Burgers–Fisher equation via boundary control

AbstractLocally exponential stabilization for the Burgers–Fisher system is addressed by boundary control in this paper. For the nonlinear partial differential equation, a linear boundary feedback control law is applied to control the Burgers–Fisher system. Locally exponential stabilization of the closed loop system is established based on the relationship between operator theories and relations of different norms. Finally, the theory is validated through numerical simulations.

An Objective Holographic Feedback Linearization Based on a Sliding Mode Control for a Buck Converter with a Constant Power Load

As a typical load, the constant power load (CPL) has negative impedance characteristics. The stability of the buck converter system with a mixed load of CPL and resistive load is affected by the size of the CPL. When the resistive load is larger than the CPL, the buck converter with the output voltage as an output function is a non-minimum phase nonlinear system, because its linear approximation has a right-half-plane pole. The non-minimum phase characteristic limits the application of many control techniques, but the objective holographic feedback linearization control (OHFLC) method is a good control strategy that can bypass the non-minimum phase system and make the system stable. However, the traditional OHFLC method, in designing the controller, generally uses a linear optimal quadratic design method to obtain a linear feedback control law. It requires a state quantity component with a one-order relative degree to the system. But it is not easy to find such a suitable state quantity with a one-order relative degree to the system. In this paper, an improved OHFLC method is proposed for Buck converters with a mixed loads of CPL and resistive loads, using the sliding mode control (SMC) theory to design the controller, so that the output state quantity components with different relative degrees to the system can be used in the holographic feedback linearization method. Finally, the simulation and experimental results also demonstrate that this method has the same, or even better, dynamic response performance and robustness than the traditional OHFLC method.

Optimization of the model predictive control meta-parameters through reinforcement learning

Model predictive control (MPC) is increasingly being considered for control of fast systems and embedded applications. However, MPC has some significant challenges for such systems, such as its high computational complexity. Further, the MPC parameters must be tuned, which is largely a trial-and-error process that affects the control performance, the robustness, and the computational complexity of the controller to a high degree. This paper presents a multivariate optimization method based on reinforcement learning (RL) that automatically tunes the control algorithm’s parameters from data to achieve optimal closed-loop performance. The main contribution of our method is the inclusion of state-dependent optimization of the meta-parameters of MPC, i.e. parameters that are non-differentiable wrt. the MPC solution. Our control algorithm is based on an event-triggered MPC, where we learn when the MPC should be re-computed, and a dual-mode MPC and linear state feedback control law applied in between MPC computations. We formulate a novel mixture-distribution RL policy determining the meta-parameters of our control algorithm and show that with joint optimization we achieve improvements that do not present themselves with univariate optimization of the same parameters. We demonstrate our framework on the inverted pendulum control task, reducing the total computation time of the control system by 36% while also improving the control performance by 18.4%.

A Robust Model Predictive Control for a Photovoltaic Pumping System Subject to Actuator Saturation Nonlinearity

In this paper, a new robust model predictive control (RMPC) for uncertain nonlinear systems subject to actuator saturation is designed to regulate the terminal voltage of a photovoltaic generator (PVG) that feeds a DC motor-pump via a buck DC–DC converter. The considered system is a combination of a PVG-converter and DC motor-pump, which possesses nonlinear behavior along with under a saturating control signal highly dependent on the operation point and climate conditions of solar radiation and temperature. As a result, the control task is complex due to the nonlinearity of the system and its dependence on climate conditions. Based on the dead-zone property, the presented paper introduces a new RMPC technique to provide an innovative and efficient solution to ensure the closed-loop system’s robust stability in the presence of actuator nonlinearity. In this paper, the nonlinear system is described in polytypic form, and an appropriate linear feedback control law is designed and used to minimize an infinite horizon cost function under the framework of linear matrix inequalities (LMIs). Furthermore, sufficient state-feedback control law conditions are synthesized to guarantee the robust stability of the closed-loop system in the presence of polytypic uncertainties. Simulation results are provided, in which the results illustrate the effectiveness of the proposed method.

Impedance Control of a Delta Robot

A delta robot is an attractive platform for robotic applications involving contacts and collisions, such as object assembly, because of its low mass and inertia (for low impedance and high speed), low link and joint compliance (for precision), and mechanical simplicity (for low cost). For these types of applications, impedance control is desirable, enabling a task-level controller to modulate the manipulator impedance to minimize the transfer of energy, momentum and force between the manipulator and the environment or task. In this paper, a feedback linearizing control law in task space is derived and used to construct an impedance controller for a three degree of freedom delta robot. Because the robot is a complex closed chain, neither the forward kinematics nor the feedback linearizing control law can be expressed analytically, in closed form. However we show that both can be computed algorithmically. We also show how tactile sensors, integrated into the gripper, may be used in an outer loop feedback to modify, and specifically reduce, the robot impedance. This is useful for manipulating objects of relatively low mass, or where transfer of energy, momentum or force from the robot to an object to be grasped must be minimized. We demonstrate the controller in simulation for a soft grasping primitive, and also in a laboratory experiment, where it plays speed chess.

Safe Learning-Based Control of Elastic Joint Robots via Control Barrier Functions

Ensuring safety is of paramount importance in physical human-robot interaction applications. This requires both adherence to safety constraints defined on the system state, as well as guaranteeing compliant behavior of the robot. If the underlying dynamical system is known exactly, the former can be addressed with the help of control barrier functions. The incorporation of elastic actuators in the robot's mechanical design can address the latter requirement. However, this elasticity can increase the complexity of the resulting system, leading to unmodeled dynamics, such that control barrier functions cannot directly ensure safety. In this paper, we mitigate this issue by learning the unknown dynamics using Gaussian process regression. By employing the model in a feedback linearizing control law, the safety conditions resulting from control barrier functions can be robustified to take into account model errors, while remaining feasible. In order to enforce them on-line, we formulate the derived safety conditions in the form of a second-order cone program. We demonstrate our proposed approach with simulations on a two-degree-of-freedom planar robot with elastic joints.

Delay-dependent and order-dependent conditions for stability and stabilization of fractional-order memristive neural networks with time-varying delays

The stability and stabilization problems of fractional-order memristive neural networks with time-varying delays are addressed. Based on Jensen-based integral inequalities, novel delay-dependent and order-dependent stability conditions for fractional-order memristive neural networks with time-varying delays are established. The proposed stability criterion is in terms of linear matrix inequalities and is easy to be verified and applied. Then, a linear feedback control law that stabilizes fractional-order memristive neural networks with time-varying delays is designed by utilizing the obtained stability conditions. Two numerical examples are used to illustrate the effectiveness and less conservativeness of the proposed results.

Design and Analysis of Longitudinal Controller for the Platoon With Time-Varying Delay

The communication topologies between vehicles in a platoon substantially impact the platoon’s stability. This study provides a distributed linear feedback control law that considers time-varying delay with guaranteed internal and string stability of the platoon system under various communication topologies. Firstly, the vehicle dynamics linearized model was derived using the precise feedback linearization technology. Different types of communication topologies, such as vehicle-to-vehicle communication and sensor-based communication, were described using directed graphs. Secondly, the linear feedback control law was designed to establish the stable zone of the linear controller gain under the effect of different communication topologies using directed graphs and the Routh-Hurwitz stability theorem. The Lyapunov-Razumikhin theorem determines the upper bound of the time-varying delay of various communication topologies. Additionally, the string stability of leader-predecessor following topology was studied, and the results were combined with the internal stability to determine the upper bound of time-varying delay. Finally, the results were verified by conducting two numerical simulations.

Unified Control Parameterization Approach for Finite-Horizon Feedback Control With Trajectory Shaping

This article presents control parameterization as a unifying framework for designing a linear feedback control law that achieves the finite-time transfer of output as well as trajectory shaping. Representing control input as a linear combination of independent basis functions allows wide variability in the resultant feedback control laws through the selection of the number and types of basis functions. Given an array of basis functions that meets the trajectory shaping necessities, the unified design approach proceeds with the determination of the coefficients so that the predicted trajectory attains the desired output at the final time. The input evaluated with the coefficients found at each instance essentially turns out to be a linear state feedback policy with an additional feedforward term and time-dependent gains, which is appropriate for practical use. The unified control parameterization approach lends itself well to missile guidance applications with the expandability and direct trajectory shaping capability that it provides. To emphasize the expandability of the framework, this study revisits the trajectory shaping guidance laws from the control parameterization viewpoint and shows how the notion of specifying input basis functions not only generalizes various existing methods but also enables further extensions. Furthermore, an application to integrated guidance and control illustrates the strength of the design process in handling the shaping requirements more directly through the construction of appropriate basis.

An Improved Extended State Observer-Based Composite Nonlinear Control for Permanent Magnet Synchronous Motor Speed Regulation Systems

This paper addresses the problems of an improved extended state observer (ESO)-based composite nonlinear control for the permanent magnet synchronous motor (PMSM) speed regulation systems, which is primarily constituted by a linear ESO-based feedforward compensation and nonlinear proportional feedback (NPF) control law. Firstly, by taking the parametric perturbations and external disturbances into account, a novel linear ESO is designed and analyzed to estimate the lumped disturbance, such that the system anti-disturbance performance is preserved. Meanwhile, the estimation of system state is also performed. Then, an optimal control synthesis function-based tracking differentiator (TD) is developed to arrange the transition dynamic for the reference velocity value, while its high quality differential signal is facilitated. Furthermore, an adaptive proportional control law is proposed, resulting in the eventual composite nonlinear strategy by incorporating the estimate values into the designed NPF controller. Finally, a PMSM servo system is studied to demonstrate the advantages and effectiveness of the proposed approaches.

Active Disturbance Rejection and Ripple Suppression Control Strategy With Model Compensation of Single-Winding Bearingless Flux-Switching Permanent Magnet Motor

The speed and radial displacement of the rotor have the obvious ripples due to the strong coupling between torque and suspension force of a single-winding bearingless flux-switching permanent magnet motor, and the traditional PID/PI controller is difficult to suppress the disturbance of the unbalanced magnetic force. A linear active disturbance rejection control method based on model compensation is proposed in this article. First, the topology and operation principle of the motor are described, and then the dynamic model of the rotor and flux linkage model of the motor are analyzed. Accordingly, the integral-series standard mathematical models of the displacement and speed are deduced, and then the mathematical expressions of the controller gain and radial disturbance are obtained. Second, the linear extended state observer with known model perturbation information and the linear feedback control law are designed, and the parameters tuning method is given. Finally, the simulation and experimental results verified that the proposed method can significantly reduce the rotor displacement and torque ripples, and it has better disturbance rejection performance than the traditional PID/PI control method in the same stability margin.

Disturbance Observer Based Sensorless Predictive Control for High Performance PMBLDCM Drive Considering Iron Loss

The control of motor drive without considering iron loss affects the phase back electromotive force and the torque performance. This article investigates the performance of permanent magnet brushless direct current motor (PMBLDCM) modeling taking impact of iron loss into account. A disturbance observer based sensorless scheme is proposed for PMBLDCM model with precise estimation of the rotor angular position. The effect of unmodeled nonlinear parameters on iron loss of PMBLDCM are regarded as disturbances for the proposed sensorless approach. A linear feedback control law with optimal current vector formulation is introduced to minimize the current ripple and torque ripple resulting in reduced copper loss. In order to select optimum switching vector considering the effect of iron loss, a model predictive control technique is proposed for the three-phase three-level neutral point clamped voltage source inverter driven PMBLDCM. The proposed sensorless predictive control (SPC) algorithm is verified both by simulation and experiments. The SPC approach demonstrates improved performance compared to the conventional approach in which the effect of iron loss is not taken into account.

On interval observer design for active Fault Tolerant Control of Linear Parameter-Varying systems

This paper proposes an active Fault Tolerant Control (FTC) scheme for polytopic uncertain Linear Parameter-Varying (LPV) systems subject to uncertainties and actuator faults. First, a fault estimation interval observer is designed to estimate the system state and the actuator fault. A novel approach is developed using the L ∞ norm to attenuate the effects of the uncertainties and to improve the accuracy of the proposed observer. Then, based on the fault estimation information, the FTC strategy is designed using a linear state feedback control law and H ∞ technique to compensate actuator faults and maintain system performance and stability, even under faulty conditions. Finally, the effectiveness of the proposed method is demonstrated by its application to a vehicle lateral dynamic nonlinear model. • Fault Tolerant Control using interval state estimation and robust stabilization. • Set-membership framework for the design of Linear Parameter Varying systems. • Fault estimation observer design for descriptor system. • L ∞ norm-based design method to attenuate the effect of fault and uncertainties and to improve the estimation performance.