Linear Control Law Research Articles

Research on Control Strategy of Oscillating Continuous-Wave Pulse Generator Based on ILADRC

To achieve fast and precise position servo control in a continuous-wave pulse generator and address issues such as internal and external disturbances and significant overshoot, this paper proposes an improved linear active disturbance rejection control strategy. First, a mathematical model of the permanent magnet synchronous motor is established, and a second-order linear active disturbance rejection controller is designed based on this model. To address the issue of large errors in disturbance estimation by the traditional extended state observer, a cascaded extended state observer is introduced. By designing an additional state observer to estimate the system’s residual disturbances, the impact of disturbances on system performance is further reduced. Through an in-depth analysis of the motion characteristics of the continuous-wave pulse generator, the trade-off between system overshoot and response speed is revealed. To address this, a new adaptive law is proposed. This law, based on the system’s periodic wave response and tracking error, adjusts the parameters of the linear state error feedback control law in real time, reducing system overshoot while improving response speed. To validate the effectiveness of the proposed control strategy, a simulation model of the position servo control system for the continuous-wave pulse generator was developed. The comparative analysis of the simulation results for the different control strategies shows that the improved linear active disturbance rejection control strategy significantly enhances the system’s dynamic response performance.

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.

Nonlinear Attitude and Altitude Trajectory Tracking Control of a Bicopter UAV in Geometric Framework

In this paper, we deal with a Bicopter drone that has two thrusters and two tilting servos. Both the position and attitude dynamics of Bicopter are globally expressed on the Special Euclidean group SE3. A simple control allocation method is proposed to map between the control wrench and actuator inputs for the Bicopter. A geometric nonlinear attitude and altitude tracking controller is developed for the Bicopter and the asymptotic stability analysis is performed using the Lyapunov method for the closed-loop nonlinear system. The performance of the proposed altitude and attitude stabilization controller is validated through experimental hardware developed in-house. The attitude controller performance is validated through simulations and shown to be comparable against an linear matrix inequality-based control law.

Coordinated management of oxygen excess ratio and cathode pressure for PEMFC based on synthesis variable-gain robust predictive control

In this research endeavor, a novel synthesis variable-gain robust model predictive control (SVGRPC) method using the min-max technique with parameter dependent Lyapunov functions is introduced to achieve the desired trajectory tracking of oxygen excess ratio (OER) and cathode pressure in the polymer electrolyte membrane fuel cells (PEMFCs) system. Initially, a simplified control-oriented model of the air supply system is developed and then transformed into a polytopic form to accommodate the inherent uncertainties in the PEMFC. Subsequently, the polytopic model is integrated with the reference trajectory to construct an augmented state-space model for deriving an error state representation. In the framework of robust model predictive control (RPC) utilizing a parameter-dependent Lyapunov function, a series of variable feedback gains are employed to mitigate conservatism. Additionally, the online solution process imposes a significant computational burden, presenting challenges for the real-time implementation of RPC-based control strategy. Therefore, the offline computing is introduced to significantly reduce the computational burden, resulting in the development of the SVGRPC strategy proposed in this paper. Subsequently, the SVGRPC strategy computes explicit linear state-feedback control laws by solving linear matrix inequalities (LMIs) using an offline control algorithm. The effectiveness of the proposed controller is then validated through assessments conducted under three distinct operating conditions of the PEMFC system. The outcomes of this study affirm that the proposed controller improves the requirements of control performance when compared to the online RPC with a quadratic Lyapunov function while significantly alleviating the computational workload.

SPACECRAFT RELATIVE ON-OFF CONTROL VIA REINFORCEMEN T LEARNING

The article investigates the task of spacecraft relative control using reactive actuators, the output of which has two states, “on” or “off”. For cases where the resolution of the thrusters does not provide an accurate approximation of linear control laws using a pulse-width thrust modulator, the possibility of applying reinforcement learning methods for direct finding of control laws that map the state vector and the on-off thruster commands has been investigated. To implement such an approach, a model of controlled relative motion of two satellites in the form of a Markov decision process was obtained. The intelligent agent is presented in the form of “actor” and “critic” neural networks, and the architecture of these modules is defined. It is proposed to use a cost function with variable weights of control actions, which allows for optimizing the number of thruster firings explicitly. To improve the control performance, it is proposed to use an extended input vector for the “actor” and “critic” neural networks of the intelligent agent, which, in addition to the state vector, also includes information about the control action on the previous control step and the control step number. To reduce the training time, the agent was pre-trained on the data obtained using conventional control algorithms. Numerical results demonstrate that the reinforcement learning methodology allows the agent to outperform the results provided by the linear controller with the pulse-width modulator in terms of control accuracy, response time, and number of thruster firings.

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.

Steering control and stability analysis for an autonomous bicycle: part II experiments and a modified linear control law

Steering control and stability analysis for an autonomous bicycle: part II experiments and a modified linear control law

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.

Tracking control for a class of fractional order uncertain systems with time-delay based on composite nonlinear feedback control

<abstract><p>In this paper, we dealt with the tracking control problem of a class of fractional-order uncertain systems with time delays. In order to handle the effects brought by the uncertainties, external disturbances, time-delay terms, and to overcome the obstacles caused by inputs saturation, the tracking controller, which consisted of linear control law, nonlinear law, and robust control law proposed in this paper, was designed by combining the composite nonlinear feedback control method and the properties of fractional order operators. Furthermore, the validation of this tracking controller was proved.</p></abstract>

Minimum Data-Rate for Emulating a Linear Feedback System

In this work, we ask what the minimum data-rate is for a possibly nonlinear control law acting on a linear system to emulate the closed-loop behavior of a desired linear control law. This result gives an implicit estimate for the information flow in the feedback path of the closed-loop linear system. We formally introduce the notion of emulation and control law, and we present a data-rate theorem. Remarkably, we note that the minimum data-rate varies discontinuously with the parameters of the open and closed-loop systems. This feature is new since the usual data-rate theorem, which only requires stabilization instead of emulation, gives a continuously varying minimum data-rate.

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

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.

Integral sliding mode control design for uncertain impulsive systems with delayed impulses

This paper addresses the integral sliding mode control (ISMC) problem of uncertain impulsive systems with delayed impulses. Firstly, an integral sliding surface with embedded impulse information is constructed, which is able to counteract the intermittent impact of delayed impulses. Then an ISMC law is designed to guarantee the finite-time reachability of the predefined sliding surface without special restriction on system dynamics. Secondly, two different types of linear control laws with switching gains are proposed to robustly stabilize the sliding mode dynamics. The first type is independent of the size of impulse delays, and is used to tackle the impulses with unknown bounded delays. The second type aims at providing impulse-delay-dependent stabilization algorithms under the assumption that the delays are smaller than the impulse intervals. In the situation where the upper bounds of the uncertainties are characterized by two unknown constants, an adaptive ISMC law is proposed to ensure the existence of sliding mode. Switching Lyapunov functions and the state augmentation technique are introduced to exploit the positive/negative effects of delayed impulses. Several tractable conditions for designing the switching gains and the sliding surfaces are derived in terms of linear matrix inequalities. Finally, three numerical examples are presented to show the effectiveness of the proposed control algorithms and highlight their merits.

Nonlinear impedance matching control for a submerged wave energy converter

AbstractThe impedance matching control, also known as approximate complex conjugate control (ACC), is one of the main strategies for improving the capture of energy by point absorber wave energy converters. Such a strategy shapes the mechanical impedance related to the floater dynamics via the control law. Since the traditional ACC is given by a linear control law, this work proposes a generalization denoted as nonlinear complex conjugate control (NCC) that considers the presence of nonlinear viscous damping in addition to the usual linear damping and stiffness. The energy maximization conditions for the proposed NCC are derived in the frequency domain through the describing function method. These conditions show that the ACC is a special case of the NCC when the total damping on the floater is approximated as a linear function of its velocity. From numerical simulations of a point absorber wave energy converters with nonlinear damping, which is based on the Archimedes wave swing prototype, it is shown that the NCC provides greater energy conversion than the ACC, as well as a robust performance in the presence of variations of the damping coefficient and the excitation force peak frequency.

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.

Bifurcation and stability analysis of a high-speed rail vehicle with active yaw dampers

Active yaw dampers (AYDs) show promise in addressing the carbody and bogie hunting issues of high-speed rail vehicles. However, the bifurcation behaviour under active control and the control law for hunting instability still require investigation. This study presents a comprehensive description of the linear control law, which can be simplified to various schemes, including skyhook damping, groundhook stiffness, modal, and blended schemes. The bifurcation behaviour under active control was analysed using a simplified lateral-dynamics-intended seven DOFs vehicle model and verified using a 3D full DOFs model in SIMPACK. Besides the well-known Hopf bifurcation, results also revealed a branching point (BP) and two new stable asymmetric equilibria. Although the asymmetric equilibria born through BP are stable, BP bifurcation should still be avoided for wheel flange contact and derailment concerns. Possible control laws are explored for two hunting scenarios: carbody hunting and bogie hunting. For carbody hunting cases, the control force can be either a linear function of bogie yaw displacement or a linear weighting function of bogie lateral and carbody roll velocity. The dominant frequency of the actuated force falls below 2 Hz, with a peak of 1.6 kN, and the allowable time delay is 70 ms. For bogie hunting cases, the control force can be a linear function of either bogie yaw displacement or velocity. In other words, both the groundhook stiffness and damping strategy are applicable. However, the actuated force contains several relatively high-frequency components (6∼13 Hz), which poses challenges to the control system and actuators, and the allowable time delay is relatively small.