Control Input Saturation Research Articles

Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control

This paper deals with chaos control in an arch microelectromechanical system (MEMS) from the fractional calculus perspective. There is a growing need for effective controllers in various technological fields, and it is important to consider disruptions, uncertainties, and control input limitations when designing a practical controller. To address this problem, we propose a novel disturbance-observer-based terminal sliding mode control technique for stabilizing and controlling chaos in a fractional-order arch MEMS resonator. The design of this technique takes into account uncertainty, disturbances, and control input saturation in the fractional-order system. The proposed control technique is practical for real-world applications because it includes control input saturation. The equation for a fractional-order arch MEMS resonator is presented, and its nonlinear vibration and chaotic behavior are studied. The design process for the proposed control technique is then described. The Lyapunov stability theorem is used to prove the finite-time convergence of the proposed controller and disturbance observer. The proposed controller is applied to the arch MEMS resonator, and numerical simulations are used to demonstrate its effectiveness and robustness for uncertain nonlinear systems. The results of these simulations clearly show the effectiveness of the proposed control technique.

Singularity avoidance controller design for spacecraft attitude control using double-gimbal variable-speed control moment gyro

A sub-optimal singularity avoidance large angle rest-to-rest attitude maneuver control of a rigid spacecraft actuated using a double-gimbal variable-speed control moment gyro (DGVSCMG) is proposed for avoiding the control torque saturation and the gimbal lock singularity. To achieve this objective, a modified model predictive static programming (MPSP) algorithm subject to control and state constraints is proposed and developed. A cuboid rigid spacecraft equipped with a single DGVSCMG device for the attitude control is considered to validate the proposed control algorithm. A new MPSP based control architecture for the attitude control of a spacecraft using a DGVSCMG is developed, wherein the desired gimbal angle rates and rotor spin acceleration are taken as the control input and computed directly using the MPSP algorithm without requiring the steering law. The control law ensures attitude stabilization of the spacecraft-DGVSCMG system while successfully avoiding the control input saturation and the gimbal lock singularity of the DGVSCMG, thereby enabling large angle attitude maneuvers. Multiple test cases of rest-to-rest attitude maneuvers are simulated to show the efficacy of the proposed control.

Control of spacecraft by using multiple model algorithms

Abstract. An effective scheme for fault detection and identification (FDI) and adaptive reconfigurable control (ARC) for controlling a spacecraft under conditions of actuator failures, saturation of control inputs and large external disturbances is proposed. The obtained results increase significantly the autonomy of the spacecraft. The control scheme, based on a general methodology of multiple models, switching and tuning, is designed in the context of nonlinear spacecraft dynamics. The results obtained by using the proposed scheme are illustrated by using numerical simulation algorithms. Keywords spacecraft control, multi-model approach, nonlinear dynamics of spacecraft, numerical simulation algorithm

Model Predictive Framework for Guidance and Control of a Multi-Satellite Assembly in Elliptic Orbit

In this paper, a guidance and control system for multi-satellite assembly missions in proximity operations is proposed. Utilizing the Tschauner-Hempel relative motion equations, the system is developed within the framework of model predictive control. Linear inequality constraints are employed to handle control input saturation of thrusters and to ensure collision avoidance between satellites. Additionally, a new line-of-sight constraint method is introduced to facilitate smooth docking while simplifying the optimization problem. The proposed algorithm aims to minimize a predefined cost function, which is a weighted sum of state errors and control efforts. At each sampling time, an online quadratic optimization problem is solved to determine the optimal control action that satisfies all mission constraints. Nonlinear numerical simulations in MATLAB are used to demonstrate that the proposed guidance and control system achieves the desired performance. The algorithm is tested for various multi-satellite assembly configurations (cubic and hexagonal) in elliptic orbits of arbitrary eccentricity. A comparative study is conducted between the proposed algorithm and a linear model predictive control algorithm based on the Clohessy-Wiltshire linear model. The results show that the proposed algorithm achieves superior performance in terms of constraint satisfaction and control efforts.

Adaptive fault‐tolerant tracking control for nonlinear systems with unknown control coefficient and input saturation

SummaryIn this article, the tracking control problem is investigated for a class of nonlinear systems in the presence of unknown disturbance, input saturation, actuator fault, and unknown control coefficient. A novel disturbance observer‐based adaptive fault‐tolerant tracking control strategy is proposed with regard to nonlinear systems. Based on the Gaussian error function, the auxiliary dynamic system is designed to offset effects caused by the input saturation. Moreover, the Nussbaum‐type function is employed to avert control singularity and deal with the unknown control coefficient. A theoretical analysis indicates that the boundedness of all signals in the closed‐loop system can be guaranteed. Finally, two examples with one concerning the dynamic point‐the‐bit rotary steerable drilling tool system are given to confirm the validity of the method.

FUZZY SLIDING-MODE CONTROL OF FRACTIONAL-ORDER CHAOTIC SYSTEMS SUBJECT TO UNCERTAIN CONTROL COEFFICIENTS AND INPUT SATURATION

In this paper, a novel fuzzy sliding-mode backstepping control approach is put forward to tackle the tracking control issue of fractional-order chaotic nonlinear systems subject to uncertain control coefficient and input saturation. First, a kind of sliding surface with nonlinear term of exponential monotonic attenuation is introduced to facilitate the fast error convergence and the chaos effect suppression. Subsequently, fuzzy logic systems and Nussbaum gains are synthesized to cope with the entire uncertainties including unknown control coefficients. Furthermore, dynamic surface technique is utilized to circumvent the occurrence of “complexity explosion” during the overall backstepping control procedure. By means of the proposed control scheme, system state is guaranteed to maintain close to the sliding surface without any reaching phrase, and whereafter the tracking error converges to a sufficiently small residual set containing the origin. Finally, the comparison between the proposed control scheme and an alternative existing chaos control approach is given through numerical simulation, which further confirms the validity of the obtained results and the superiority of the proposed strategy.

Feedback control of actuation‐constrained moving structure carrying Timoshenko beam

AbstractThis article deals with tracking control and active vibration suppression of a hybrid rigid‐elastic vibrational mobile system with a nonlinear elastic foundation in the presence of actuator bandwidth limitation and control input saturation. The system consists of a rigid rectilinearly mobile frame on an elastic foundation, and a flexible Timoshenko beam clamped to it with a heavy attached concentrated mass. The hybrid partial differential equation (PDE)‐ordinary differential equation (ODE) system of the plant is obtained using Hamilton's principle and then is converted to a system of ODEs using the assumed mode method (AMM). Next, the model will be discretized in the time domain using the two‐step Adams‐Bashforth technique. Considering the first‐order dynamics to cover the bandwidth limitation of the actuator, a discrete‐time sliding mode controller (DSMC) is designed based on a positive definite Lyapunov functional. Following that, an innovative optimal predictive algorithm is proposed to compensate for the effects of input saturation. The proposed algorithm is based on a positive definite cost function and using an intelligent regime of optimizations and decisions, minimizes the cost function in a predefined prediction horizon. The vibratory behavior of the system also is included in the mentioned cost function. Consequently, the overall control scheme called optimal rigid‐elastic interaction control (OREIC) will be able to follow the desired tracking trajectory, suppress the beam vibrations, and compensate for the effect of bandwidth limitation as well as the effect of input saturation. The performance of the OREIC algorithm is compared with a saturated DSMC controller and the simulation results demonstrate the efficiency of the method in vibration control of mobile rigid‐elastic systems subjected to actuator bandwidth frequency and saturation limitations.

Fault tolerant control of a permanent magnet synchronous machine using multiple constraints Takagi-Sugeno approach

Introduction. Fault diagnosis, and fault tolerant control issues are becoming very important to ensure a good supervision of systems and guarantee the safety of human operators and equipments even if system complexity increases. Problem. In fact, the presence of faults in actuators, sensors and processes can lead to system performance degradation, system breakdown, economic loss, and even disastrous situations. Furthermore, Actuator saturation or control input saturation is probably the most usual nonlinearity encountered in control engineering because of the physical impossibility of applying unlimited control signals and/or safety constraints. Purpose. This article is dedicated to the problem of fault tolerant control for constrained nonlinear systems described by a Takagi-Sugeno model. One of the interests of this type of models is the possibility of extend some tools and methods from linear system case to the nonlinear one. The novelty of the work consists in developing a fault tolerant control algorithm for a nonlinear Permanent Magnet Synchronous Machine model using an observer based state-feedback control technique in order to enhance fault and state estimation despite actuator saturation and system disturbances. Methods. Indeed a sensor fault detection observer based residual generator is synthesized with a guaranteed L2 performance to attenuate the external disturbances effect from one side and to maximize the residual sensitivity to faults from the other side. Based on Lyapunov function, design conditions are formulated in terms of Linear Matrix Inequalities to ensure stability of the global system. Practical value. A detailed study concerning nonlinear permanent magnet synchronous machine model, which is consolidated by simulation results, is conducted to show the used algorithm’s effectiveness guarantying fault estimation and reconfiguration of the control law to maintain stable performance even in the presence of actuator faults, external perturbation and the phenomenon of actuator saturation.

Model-Free Saturated PD-SMC Method for 4-DOF Tower Crane Systems

In this article, we design a novel saturated proportional-derivative (PD) with sliding-mode control (SMC) method or saturated PD-SMC in short for 4-DOF tower crane systems under uncertain dynamics, external disturbances, as well as saturated control input constraints. The designed control method is model free, which can achieve accurate positioning and rapid swing suppression and elimination using only jib/trolly position/velocity and payload swing feedback with limited control inputs. Different from the existing control methods, the designed control method takes the advantages of simple structure and being easily realized in practical applications of the PD control, strong robustness of the SMC method with respect to model uncertainties and external disturbances, avoiding the requirements of accurate model knowledge associated with the SMC method, as well as rapid payload swing reduction of the swing suppression control. The stability of the controlled system is ensured by rigorous Lyapunov-based analysis. To the best of our knowledge, this is the first model-free control method without any linearization operations for tower crane systems with uncertain dynamics, external disturbances, and saturated control input constraints. Several experimental results are given to validate the superior control performance and strong robustness of the designed control method.

Suboptimal attitude tracking control law and eigenvalue analysis for a near-space hypersonic vehicle based on Koopman operator and stable manifold method

This paper proposes a novel strategy to design a suboptimal attitude tracking control law for a near-space hypersonic vehicle (NSHV) based on the Koopman operator and stable manifold theory. The nonlinear vector field of the NSHV attitude model is locally Lipschitz continuous and can be approximated by a high-dimensional linear system over a compact set. Linear and nonlinear parts of the attitude dynamics are determined based on this system. Subsequently, the stable manifold theory is applied to determine the unconstrained approximated optimal control law that is used to further consider the control input constraints of the NSHV attitude model. The suboptimality of the control law is analyzed, and the local exponential stability of the closed-loop system with input constraints is proven. Furthermore, the eigenvalues for the closed-loop nonlinear attitude error dynamics are analyzed. After the control input saturation, the nonlinear closed-loop error dynamics of the NSHV can be approximated by a high-dimensional linear system with a minimal dimension. The eigenvalues of this linear system indicate the stability and time response characteristics of the attitude error dynamics of the NSHV. The numerical simulation results demonstrate the effectiveness and suboptimality of the proposed attitude tracking control law and workflow of the eigenvalue analysis.

Full‐state prescribed performance pose tracking of space proximity operations with input saturation

AbstractThis paper investigates the relative position tracking and attitude synchronization control for spacecraft close‐range proximity missions with input saturation and model uncertainties. A robust saturated relative motion controller is proposed for this purpose. Prescribed performance functions are designed to guarantee the transient and steady‐state response of the system and the full‐state constraints. Then, a nonlinear disturbance observer is developed to estimate the lumped disturbance that comprises the effects of parametric uncertainties and kinematic couplings. At the same time, a linear compensator system is incorporated into the controller design to deal with the control input saturation. Finally, it can be proved via the Lyapunov theory that the closed‐loop system is uniformly ultimately bounded stable. Simulation results on the spacecraft close‐range rendezvous and docking mission validate the effectiveness of the proposed control approach.

Effect of saturation structure on finite-time stabilization of nonlinear systems with impulsive disturbance

This paper studies the finite-time stabilization (FTS) of nonlinear systems with impulsive disturbance, where the effect of saturation structure on the control input is fully considered. By establishing a potential relationship between saturation structure and impulsive disturbance, some FTS criteria are presented via a class of saturated control input, where estimations of domain of attraction and settling-time are derived. Compared with the control input without saturation structure, the constraints on impulse time sequence are strengthened to guarantee that the saturated control input has an effective stabilizing effect on the system. Based on such constraints, the system subjected to impulsive disturbance can still achieve FTS. Then theoretical results are applied to finite-time synchronization for a class of impulsive dynamical networks. Finally, two examples and their simulations are given to illustrate the effectiveness of the proposed results.

An Output Feedback Discrete-Time Controller for the DC-DC Buck Converter

This paper presents a discrete-time output feedback controller to regulate the output voltage of a DC-DC buck converter. The proposal’s main feature is the application of a discrete-time equivalent of the robust exact filtering differentiator. First, the document exposes a theoretical analysis of the closed-loop system, where it is considered the problem of implementing a real-time differentiator with a good relationship between exactness and noise filtration performance. Hence, secondly, the controller in a laboratory setup is presented. The first experimental results suggest that the proposed controller exhibits good robustness against noise and maintains the asymptotic accuracy, even with saturated control inputs, as in the case of the DC-DC buck converter. Consequently, aiming to verify the features of the proposed method, the controller is validated through multiple experiments, showing satisfactory voltage tracking accuracy, good suppression of instantaneous load and supply voltage disturbances, and robustness against bounded measurement noise.

Higher-Order Sliding Mode design with Bounded Integral Control generation

In this paper uncertain continuous-time nonlinear systems affine in the control variable and with saturated actuators are considered. The finite-time regulation problem of the system output to zero is then solved by proposing a generic Higher-Order Sliding Mode (HOSM) controller equipped with a novel mechanism to encounter the saturation limits, thus extending previous results on saturated control inputs valid only in case of specific r-order sliding mode algorithms. The so-called Bounded Integral Control (BIC) method is reformulated into the framework of continuous HOSM, so as to replace the traditional integrator used to generate the continuous signal directly fed into the plant. Stability conditions for tuning the proposed algorithm are provided, and a numerical example finally assesses the effectiveness of the proposed technique.

Saturated PD-SMC method for suspension systems by exploiting beneficial nonlinearities for improved vibration reduction and energy-saving performance

In this paper, through purposely employing beneficial nonlinear stiffness and damping with a constructed bioinspired reference model, a novel saturated PD with sliding mode control method (referred to as saturated PD-SMC method), is designed for active suspension systems under saturated control input constraints. The designed control method has several distinct benefits, including the simple structure of PD control method, strong robustness of SMC method with respect to model uncertainties and external disturbances, without requirements of exact system parameters associated with traditional SMC method, as well as taking input constraints into consideration. In the designed control method, the PD part is employed to stabilize the controlled active suspension system, the SMC part is applied to provide strong robustness, and the saturation functions are introduced to prevent the violation of control input constraints. The corresponding stability analysis is provided by Lyapunov techniques. Several experimental results show that, the proposed control method dramatically improves transient performance in comparison with some existing methods, including significantly decreasing control energy by 30% for sinusoidal road profile, and decreasing control energy up to 66% for random road profile, which achieve a satisfactory trade-off between costs and results for suspension system control. As far as we know, it is the first time to combine PD control, SMC method, and saturation structures together, to achieve obvious performance improvements for suspension systems, and simultaneously, complete stability analysis is given.

Safety control using barrier certificates for multiagent systems with input saturation and formation constraints

Maintaining the given operational area is critical in guaranteeing the safety of nonlinear second-order multiple autonomous agents. The properties of multiagent systems and several physical constraints, including bounded modeling error and actuator saturation, dramatically affect the maneuverability of multiagent systems inside the specified operational area. Moreover, the existing safety control algorithms heavily rely on the boundaries of the operational area. To overcome this issue, by constructing a novel scalable control technique, the safety area for multiagent systems can be transformed into input-constrained control barriers along each coordinate of motion for agents. It is shown that the safety of each agent and the global asymptotic stability are guaranteed under the proposed distributed control algorithm. The asymmetrical closed-form scheme for the agent's safety rule is built by applying the adjustable low and high bounds of the control signals associated with the actual control inputs, which are repeatedly computed by using new local measurements as the agents move, and the saturated control inputs with asymmetrical constraints are ensured. The absolute values of the modeling errors and external disturbances can be tracked by the proposed safety controller. Super-twisting control (STC) is employed to address the formation constraint problem of multiagent systems, where the effect that arises from uncertain nonlinear complexity of the agents and external disturbances is eliminated. Moreover, finite-time convergence, a desirable robust behavior of multiagent systems, and the formation constraint are simultaneously achieved. Furthermore, the stability of the proposed integrated control strategy for multiagent systems is analyzed, which reveals that the proposed distributed safety control can seamlessly integrate with the robust control protocol with minimum modification under the directed information interaction topology. Safety formation control calibration and tuning are carried out, and comparative simulation results are provided to illustrate the effective performance of the obtained theoretical results.

Decentralized formation trajectory tracking control of multi-AUV system with actuator saturation

This paper focuses on the three-dimensional (3-D) formation tracking of multiple autonomous underwater vehicle (multi-AUV) system in complex ocean environments. An observer-controller scheme based on decentralized estimation and control is designed. Develop an observer for each AUV to estimate the overall state of the system, then integrate it with collective task variables to produce the control inputs. It enables the multi-AUV system to perform formation trajectory tracking tasks that depend on global information. In the design stage, utilizing hyperbolic tangent function reduces the risk of actuator saturation, and the measurement noise and nonlinearities of the system are addressed. Next, under the connected undirected topology, as well as for the cases of unsaturated and saturated control inputs, the stability analysis based on the Lyapunov method proves the convergence of estimation errors and task errors. Simultaneously, sufficient conditions for the formation tracking convergence are given. Finally, the simulation results in different cases demonstrate the effectiveness of the proposed method.

A Predictive Control Approach for Cooperative Transportation by Multiple Underwater Vehicle Manipulator Systems

This article addresses the problem of cooperative object transportation for multiple underwater vehicle manipulator systems (UVMSs) in a constrained workspace involving static obstacles. We propose a nonlinear model predictive control (NMPC) approach for a team of UVMSs in order to transport an object while avoiding significant constraints and limitations, such as kinematic and representation singularities, obstacles within the workspace, joint limits, and control input saturation. More precisely, by exploiting the coupled dynamics between the robots and the object and using certain load sharing coefficients, we design a predictive controller for each UVMS in order to cooperatively transport the object within the workspace’s feasible region. Moreover, the control scheme adopts load sharing among the UVMSs according to their specific payload capabilities. In addition, the feedback relies on each UVMS’s onboard measurements and no explicit data are exchanged online among the robots, thus reducing the required communication bandwidth. Finally, realistic simulation results conducted in the UwSim dynamic simulator running in robot operating system (ROS) environment as well as real-time experiments employing two small UVMSs and demonstrated the effectiveness of the proposed control strategy.

Command filtering‐based adaptive neural network control for uncertain switched nonlinear systems using event‐triggered communication

AbstractIn this article, a command filtering‐based adaptive event‐triggered neural network control scheme is proposed for a class of uncertain switched nonlinear systems with unknown control coefficient and input saturation. First, radial basis function neural networks are used as function approximators to estimate unknown nonlinear functions. Then, an event‐triggering mechanism based on the tracking error is introduced to avoid the over‐consumption of communication resources. Furthermore, command filters are employed to solve the problem of complexity explosion that exists in conventional backstepping control design, and the error compensation signals are designed to reduce the errors caused by the filters. Considering that the unknown control gain and input saturation exist in many practical applications, a Nussbaum‐type function is thus introduced into the controller design to address these challenging issues. Finally, stability of the closed‐loop system is strictly proven under a standard Lyapunov stability analysis framework. The effectiveness of the proposed control scheme is illustrated by a simulation example.

Event-triggered adaptive consensus for stochastic multi-agent systems with saturated input and partial state constraints

This paper is concerned with the consensus tracking problem of stochastic multi-agent systems with both output, partial state constraints, and input saturation via event-triggered strategy. To handle with the saturated control inputs, the saturation function is transformed into a linear form of the control input. By using radial basis function neural network to approximate the unknown nonlinear function, the unmeasurable states are acquired by an adaptive observer. To ensure that the constraints of system outputs and partial states are never violated, an appropriate time-varying barrier Lyapunov function is constructed. The control scheme is event-triggered in order to save communication resources. The proposed distributed controller can guarantee the boundedness of all system signals, the consensus tracking with a small bounded error, and the avoidance of the Zeno behavior by using backstepping techniques. The validity of the theoretical results is verified by computer simulation.