Actuator Saturation Problem Research Articles

Test Mass Capture Control for Drag-Free Satellite Based on State-Dependent Riccati Equation Method

The drag-free satellite plays an important role in the space-based gravitational wave observatory. The capture control of test mass after release is a crucial technology that can affect the success of the mission. The test mass must be released to the center of the electrostatic suspension cage accurately. This paper presents a nonlinear dynamic model of drag-free satellites in Lagrange formalism. A capture control scheme for test mass release phase is proposed based on the state-dependent Riccati equation (SDRE) strategy. To deal with the actuator saturation problem, a nonlinear saturation model is introduced to the dynamics of satellite, while the SDRE strategy is applied to the non-affine system. The effectiveness of the proposed methodology is verified by the numerical simulation for the drag-free satellite.

An asymmetrically variable wingtip anhedral angles morphing aircraft based on incremental sliding mode control: Improving lateral maneuver capability

This paper presents the design of an asymmetrically variable wingtip anhedral angles morphing aircraft, inspired by biomimetic mechanisms, to enhance lateral maneuver capability. Firstly, we establish a lateral dynamic model considering additional forces and moments resulting during the morphing process, and convert it into a Multiple Input Multiple Output (MIMO) virtual control system by importing virtual inputs. Secondly, a classical dynamics inversion controller is designed for the outer-loop system. A new Global Fast Terminal Incremental Sliding Mode Controller (NDO-GFTISMC) is proposed for the inner-loop system, in which an adaptive law is implemented to weaken control surface chattering, and a Nonlinear Disturbance Observer (NDO) is integrated to compensate for unknown disturbances. The whole control system is proven semi-globally uniformly ultimately bounded based on the multi-Lyapunov function method. Furthermore, we consider tracking errors and self-characteristics of actuators, a quadratic programming-based dynamic control allocation law is designed, which allocates virtual control inputs to the asymmetrically deformed wingtip and rudder. Actuator dynamic models are incorporated to ensure physical realizability of designed allocation law. Finally, comparative experimental results validate the effectiveness of the designed control system and control allocation law. The NDO-GFTISMC features faster convergence, stronger robustness, and 81.25% and 75.0% reduction in maximum state tracking error under uncertainty compared to the Incremental Nonlinear Dynamic Inversion Controller based on NDO (NDO-INDI) and Incremental Sliding Mode Controller based on NDO (NDO-ISMC), respectively. The design of the morphing aircraft significantly enhances lateral maneuver capability, maintaining a substantial control margin during lateral maneuvering, reducing the burden of the rudder surface, and effectively solving the actuator saturation problem of traditional aircraft during lateral maneuvering.

Switching positive system event triggering T-S fuzzy control

This paper presents a saturation control problem with a positive switching T-S fuzzy system based on event-triggering mechanism under continuous time. Firstly, a 1-norm event triggering mechanism is designed. Then, the multilinear co-positive Lyapunov function is applied to the closed-loop positive switching system with a T-S fuzzy control strategy under continuous time. Next, we consider constructing a cone invariant set to transform the actuator saturation problem into an interval form. The designed controller with a linear programming method guarantees both the positivity and stability of the closed-loop system. Finally, an example of a communication data network proves the effectiveness of the design. The main contents are (i) The event-triggering strategy under continuous time is used in the T-S switching positive system. (ii) A controller with input saturation is introduced into controllable subsystems. (iii) When determining the attractor domain of the system state, a cone domain is considered as a potential restriction.

Finite-Time Attitude Control of Quadrotor Unmanned Aerial Vehicle with Disturbance and Actuator Saturation

This paper introduces a nonlinear dynamic inversion control algorithm designed to address unknown disturbances and actuator saturation issues in unmanned aerial vehicle (UAV) attitude control. The algorithm is based on a combination of finite-time disturbance observer and anti-saturation auxiliary system, which ensures the rapid convergence of attitude tracking error. Firstly, based on the Newton–Euler equations, this paper establishes a model of the attitude system for quadrotor UAVs, and this paper eliminates the small-angle flight assumption. Secondly, considering the actuator saturation problem, an anti-saturation auxiliary control system is designed to shorten the time when the control volume is in the saturation interval and achieve finite-time convergence of the attitude error. And then, to improve the robustness of the controller, this paper proposes a disturbance observer based on the finite-time stability theory, which achieves a continuous smooth output of the observation results by introducing a hyperbolic tangent function in the observer, so that the observation error can be converged to zero in a finite time. Finally, it is demonstrated by Simulink simulation that the attitude error and the observation error converge quickly to zero.

Asynchronous dissipative control of time-delay singular Markovian jump systems with actuator saturation

This paper focuses on the problem of asynchronous dissipative control for time-delay singular Markovian jump systems (SMJSs) with actuator saturation. In order to describe the asynchronous phenomenon between the system and the controller, a hidden Markov model (HMM) is adopted. In addition, the problem of actuator saturation is considered. Firstly, by the mode-dependent Lyapunov function, some novel sufficient criteria for guaranteeing the stochastic admissibility with dissipative performance of the system are proposed. Secondly, according to the derived criteria, a novel approach is established to design the controller gains. Thirdly, the domain of attraction of the system is given by the optimal method. Finally, two examples are given to verify the correctness of the proposed approach.

A GOA-Based Fault-Tolerant Trajectory Tracking Control for an Underwater Vehicle of Multi-Thruster System Without Actuator Saturation

This paper proposes an intelligent fault-tolerant control (FTC) strategy to tackle the trajectory tracking problem of an underwater vehicle (UV) under thruster damage (power loss) cases and meanwhile resolve the actuator saturation brought by the vehicle’s physical constraints. In the proposed control strategy, the trajectory tracking component is formed by a refined backstepping algorithm that controls the velocity variation and a sliding mode control deducts the torque/force outputs; the fault-tolerant component is established based on a Grasshopper Optimization Algorithm (GOA), which provides fast convergence speed as well as satisfactory accuracy of deducting optimized reallocation of the thruster forces to compensate for the power loss in different fault cases. Simulations with or without environmental perturbations under different fault cases and comparisons to other traditional FTCs are presented, thus verifying the effectiveness and robustness of the proposed GOA-based fault-tolerant trajectory tracking design. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the actuator saturation problem that exists in the trajectory tracking of an underwater vehicle (UV) when encountering power loss of the thruster system. The fault-tolerance trajectory tracking performance is affected by physical constraints of the vehicle when using the traditional methods as they may deduct excessive kinematic/dynamic requirements during the control process, thus inducing the deviation of the tracking trajectory. Therefore, the refined backstepping as well as the grasshopper optimization (GOA) are combined to eliminate the excess, where the refined backstepping is used to alleviate the speed jumps (kinematic outputs) and the GOA is to control the propulsion forces (dynamic outputs) when facing thruster fault cases. This innovates the industrial practitioners that the control design of the vehicle can be improved to avoid the tracking deviation brought by unsatisfied driving commands under fault cases through embedding optimization algorithms. Moreover, for the specific type of UV studied in this paper used for dam detection, simulations regarding practical dam detection such as the 3D polygonal line trajectory tracking and the frequently occurring UV single-fault cases are chosen, which can serve as references for practitioners working in the related field. In the future, underwater experiments of the UV will be investigated, with more effects of the practical environment involved.

Model predictive cascade control for resolving actuator saturation in human‐occupied vehicle trajectory tracking

SummaryA model predictive cascade controller is proposed in this article to resolve the actuator saturation problem of underwater human‐occupied vehicle (HOV) trajectory tracking. For the kinematic model, a grasshopper optimization‐based model predictive control (MPC) is developed to obtain control velocities with small fluctuations in allowable regions. Based on the desired velocities obtained from the improved kinematic control, the HOV dynamic model is used to generate the corresponding torques and forces using sliding mode control. With the control velocities and forces given by the cascade control strategy, the elimination of actuator saturation during the HOV trajectory tracking can be realized. The proposed controller is verified by simulations using a numerical example based on a four degrees of freedom (4‐DOFs) HOV.

An improved compact-form antisaturation model-free adaptive control algorithm for a class of nonlinear systems with time delays.

To solve the time-delay problem and actuator saturation problem of nonlinear plants in industrial processes, an improved compact-form antisaturation model-free adaptive control (ICF-AS-MFAC) method is proposed in this work. The ICF-AS-MFAC scheme is based on the concept of the pseudo partial derivative (PPD) and adopts equivalent dynamic linearization technology. Then, a tracking differentiator is used to predict the future output of a time-delay system to effectively control the system. Additionally, the concept of the saturation parameter is proposed, and the ICF-AS-MFAC controller is designed to ensure that the control system will not exhibit actuator saturation. The proposed algorithm is more flexible, has faster output responses for time-delay systems, and solves the problem of actuator saturation. The convergence and stability of the proposed method are rigorously proven mathematically. The effectiveness of the proposed method is verified by numerical simulations, and the applicability of the proposed method is verified by a series of experimental results based on double tanks.

Fixed‐time disturbance observer based distributed cooperative containment control with fixed‐time anti‐saturation compensator for multi‐unmanned aerial vehicles

AbstractThis article proposes a fixed‐time backstepping distributed cooperative containment control scheme for multiple unmanned aerial vehicles (UAVs). A fixed‐time compensator is designed for the fixed‐wing UAVs actuator saturation problem. Based on this, an improved fixed‐time disturbance observer is proposed for the problem of the excessive initial peak. The problem of “complexity explosion” is solved by the fixed‐time differential filter. For the distributed containment control of multiple UAVs, a cooperative control architecture based on a fixed‐time anti‐saturation compensation system is proposed. The proposed algorithm can be shown practicable by using Lyapunov stability theory and graph theory. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.

Decentralized fault-tolerant control of modular robot manipulators with actuator saturation: neural adaptive integral terminal sliding mode-based control approach

A novel neural adaptive integral terminal sliding mode control for decentralized fault-tolerant control strategy, including the integral terminal sliding mode surface, the nonlinear disturbance observer, the radial basis neural network and robust controller, is presented in this paper to achieve fault-tolerant control of modular robot manipulators. First, the integral terminal sliding mode is designed for the fault-tolerant controller. Then, to boost the performance of the controlled system, the radial basis neural network and disturbance observer are introduced to approximate the nonlinear terms and disturbances. The reconstructed approximate uncertainty term is applied as compensation. Next, the super-twisting technique is employed to compensate for estimation errors to ensure stability. In addition, for the actuator saturation problem, the radial basis function neural network-based compensation control is proposed. Finally, the stability of the closed-loop robotic system is demonstrated based on Lyapunov theory. Computer simulations verified the efficiency and advantages of the presented approach.

High Minimum Inter-Execution Time Sigmoid Event-Triggered Control for Spacecraft Attitude Tracking With Actuator Saturation

This paper investigates the attitude tracking problem for spacecraft with limited communication, network congestion, unknown model parameters, actuator saturation, and external disturbances. To alleviate communication load, a novel sigmoid event-triggered mechanism is proposed with the special ability to guarantee a high minimum inter-execution time to avoid network congestion like package loss or time delay effectively. A neural network-based adaptive control algorithm is designed to deal with unknown model parameters. Besides, the problem of actuator saturation is tackled by introducing a dynamic loop gain function-based approach. System stability is proved by Lyapunov stability analysis and the high minimum inter-event time is substantiated by Zeno Behavior analysis with explanatory remarks. Numerical simulation results also show that a high minimum inter-event time and a high average inter-event time can be realized on the premise of high attitude tracking accuracy. Compared with all the previous studies, the ratio of the minimum inter-execution time to the average minimum inter-execution time has been improved by nearly 10 times with the proposed approach. Note to Practitioners—This paper was motivated by the problem of spacecraft attitude takeover control, but it also applies to other aperiodic discrete-time control systems. Existing event-triggered control methods have solved the problem of limited communication for attitude takeover control of spacecraft by reducing the number of times wireless communication is required. This paper proposes a new method for realizing quasi-periodic control with a large time gap between any two consistent control impulses using a hyperbolic tangent function or another sigmoid function in an event-triggered mechanism. The proposed sigmoid event-triggered mechanism (ETM) can magnify the event-triggered threshold dozens of times in a short time to avoid unnecessary frequent triggering without decreasing the precision of control. It’s feasible to employ the proposed sigmoid ETM to deal with limited communication and network congestion in other network control systems that are constructed with similar dynamic structures. Furthermore, it would be marvelous if we could transform this sigmoid ETM into a high-efficiency decision-making mechanism in some control systems without using a wireless network. Now we are studying how to realize orbital-attitude (maneuver) control with a relatively average time interval and fewer times of orbit transfer by using the proposed sigmoid ETM. Besides, to further improve the system performance, we are also seeking to further increase the ratio of the minimum inter-execution time to the average inter-execution time. For the purpose of a more even distribution of the triggering events on the time axis, we may modify the proposed sigmoid event-triggered method or associate it with other methods.

Robust saturated fault-tolerant control for active suspension system via partial measurement information

This paper proposes a robust output feedback-fault tolerant control approach associated with the vibration suppression problem for active suspension subject to actuator fault and saturation, unavailable velocity signals, model uncertainty and external disturbance simultaneously. In this paper, an auxiliary system is introduced to solve the actuator saturation problem. The actuator fault, model uncertainty and external disturbance are treated as lumped disturbance. A novel estimator with finite-time convergence characteristics is proposed to estimate the unavailable velocity signals and lumped disturbance, and the disturbance compensation-based controller is designed with the reconstructed signals. In the process of controller design, a nominal controller is designed without lumped disturbance, and the nominal controller and finite-time estimator can be designed independently, so the controller gains can be selected flexibly. Rigorous theoretical analysis is carried out to confirm that all states of the closed-loop system are bounded. In the end, some experimental studies are conducted to show that the active suspension can be controlled effectively, and the efficacy and superiority of the designed method are verified.

A Safety Planning and Control Architecture Applied to a Quadrotor Autopilot

This letter presents a safety trajectory planning and tracking architecture for a quadrotor autopilot. Motor saturation constraints are explicitly considered in obstacle avoidance mission. Two challenging cases are covered: agile flight with a short task time and stable flight with actuator degradation. By explicitly considering the real physical constraints, the proposed method can make better use of the quadrotor maneuverability. Specifically, from control aspect, a sliding mode observer (SMO) based safety controller is implemented on the autopilot. Subsequently, the actuator saturation problem is analyzed and modeled as axis-coupled constraints. The B-spline curve is used to deal with the constraints due to its convex hull property. As a result, the planning problem can be transformed into a quadratically constrained quadratic programming (QCQP) problem with the proposed minimum energy cost function. Experiments show that the resulting trajectories can yield improvements in tracking accuracy in comparison of conventional planning method.

Multi-Objective Finite-Frequency H ∞/GH 2 Static Output-Feedback Control Synthesis for Full-Vehicle Active Suspension Systems: A Metaheuristic Optimization Approach

In this paper, the problem of multi-objective control for active suspension systems with polytopic uncertainty is addressed via <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GH</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> static output feedback with a limited-frequency characteristic. For the overall analysis of the performance demanding both vehicle-ride comfort related to vertical- and transversal-directional dynamics and the time-domain constraints related to the driving maneuverability, a seven-degree-of-freedom full-vehicle model with an active suspension system is investigated. The robust static output-feedback control strategy is adopted because some state variables may not be directly measured in a realistic implementation. In designing this control, the finite-frequency H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance using the generalized Kalman—Yakubovich—Popov lemma is optimized to improve the passenger’s ride comfort, while the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GH</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance is optimized to guarantee the constraints concerning the suspension deflection limitation, road-holding ability, and actuator saturation problem. This control synthesis problem is formulated as nonconvex bilinear matrix inequalities and requires simultaneous consideration of different finite-frequency domain ranges for vertical and transversal motions for evaluating the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. These design difficulties are overcome by the proposed multi-objective quantum-behaved particle swarm optimizer, which efficiently explores the relevant trade-offs between the considered multiple performance objectives and eventually provides the desired Pareto-optimal control set. Further, the numerical simulation cases of a full-vehicle active suspension system are presented to illustrate the effectiveness of the proposed control synthesis methodology in frequency and time domains.

A novel controller based on the sum of squares relaxation for the uncertain model of the PEMFC considering external disturbances and actuator saturation

The current paper aims to model the uncertainties of the proton exchange membrane fuel cell system and control its main parameters, such as compressor speed and oxygen excess ratio, in the presence of external disturbances and actuator saturation using the improved controller, which is designed based on the sum of squares relaxation for nonlinear models. The open-loop nonlinear system is considered in state-dependent polynomial equations. The state feedback method is used to obtain the appropriate control responses. To numerically solve the state-dependent Linear Matrix Inequalities, semi-definite programming based on the sum of squares decomposition is also used. First, the transient response of the system is improved in the design phase of the controller. Then, the actuator saturation problem of PEMFC is considered for the state feedback controller proposed in polynomial systems, and the obtained results are expanded for the uncertain system. Results are also validated in the presence of external disturbances. The results are compared with those of the robust and adaptive control methods. The proposed controller not only has good agreement with the results of robust and adaptive control methods but also outperforms the previous controllers in terms of accuracy, rise time, fluctuation, and overshoot.

A Fuzzy Logic-based Cascade Control without Actuator Saturation for the Unmanned Underwater Vehicle Trajectory Tracking

An intelligent control strategy is proposed to eliminate the actuator saturation problem that exists in the trajectory tracking process of unmanned underwater vehicles (UUV). The control strategy consists of two parts: for the kinematic modeling part, a fuzzy logic-refined backstepping control is developed to achieve control velocities within acceptable ranges and errors of small fluctuations; on the basis of the velocities deducted by the improved kinematic control, the sliding mode control (SMC) is introduced in the dynamic modeling to obtain corresponding torques and forces that should be applied to the vehicle body. With the control velocities computed by the kinematic model and applied forces derived by the dynamic model, the robustness and accuracy of the UUV trajectory without actuator saturation can be achieved.

Hypersonic tracking control under actuator saturations via readjusting prescribed performance functions

Prescribed performance control (PPC) has been shown to be an effective tool in pursuing prescribed transient and steady-state specifications. Unfortunately, the existing PPC is incapable of handling the peaking of errors caused by actuator saturations, which is due to the short of the ability of readjusting the prescribed performance functions. In this article, we propose a novel PPC scheme, namely the readjusting-performance-function-based approach, for hypersonic flight vehicles subject to actuator saturations. A new sort of performance functions containing readjusting terms are developed to impose prescribed constraints on the velocity tracking error and the altitude tracking error. More specially, the prescribed performance functions can be adaptively readjusted to guarantee that tracking errors are always within them. This eliminates the singular problem that is usually encountered by traditional PPC. To deal with the actuator saturation problem, a novel compensated system (CS) is exploited for the velocity dynamics. Then, the CS is further extended to the altitude subsystem by reforming it as a high-order formulation. Besides the aforementioned baseline controllers, optimal control protocols are also addressed based on adaptive dynamic programming. Finally, comparison simulation results are given to verify the advantages.

Robust dynamic heading tracking control for wave gliders

Heading control plays an essential role in improving accuracy of all kinds of navigations for wave gliders. However, the performance will exhibit large heading errors and oscillations caused by weak maneuverability and large ocean current disturbance when the wave glider is gliding at a time-varying velocity. A robust dynamic heading tracking control integrated a modified active disturbance rejection controller (MADRC) and an improved anti-windup (IAW) compensator was put forward in this paper, which could extremely guarantee heading tracking accuracy with appropriate actuator power consumption in real time. Focused on dynamically tracking a time-varying desired heading, a reduced-order extended state observer (RESO) was designed to estimate and compensate uncertain disturbance and reduce the computational complexity. The IAW was applied to deal with actuator saturation problem, which could further reduce convergence time and power consumption in the heading control. Following this, a closed-loop control was put forward with a dynamic model of “Black Pearl” wave glider and a given heading control. The proposed control was verified by simulations and sea trials compared with conventional heading controls, which demonstrated its effectiveness and practicability.

A Novel Anti-Saturation Model-Free Adaptive Control Algorithm and Its Application in the Electric Vehicle Braking Energy Recovery System

In this work, a novel anti-saturation model-free adaptive control (AS-MFAC) algorithm is proposed for the problem of pure electric vehicle’s braking energy recovery with the uncertain dynamic external factors. In the process of energy recovery during vehicle braking, actuator saturation and error accumulation occur due to various external conditions. In AS-MFAC, the non-linear dynamics of the vehicle braking energy recovery process is firstly linearized via a novel dynamical linearization technique with a time-varying parameter pseudo partial derivative (PPD). Then, by proposing the concept of the saturation parameter, the AS-MFAC controller is designed. Consequently, the stability and safety of the braking system are guaranteed while ensuring energy recovery. The major advantages of the AS-MFAC algorithm are that the controller uses only input and output data from the regenerative braking control system and this approach addresses the actuator saturation problem as well as provides a feasible solution. Moreover, the stability of the AS-MFAC algorithm is proven by rigorous mathematical theory and its effectiveness is verified by a series of experimental simulations. Remarkably, the proposed AS-MFAC controller has the property of symmetry since the controller structure and the corresponding parameter (time-varying PPD) estimator are both inferred based on the project algorithm. Consequently, the structures of the controller and the parameters of AS-MFAC have a symmetric similarity.

Robust gain-scheduling [formula omitted] control of uncertain continuous-time systems having magnitude- and rate-bounded actuators: An application of full block S-procedure

This paper addresses a novel robust gain-scheduling(GS) state-feedback (SF) H∞ (induced L2) control method for uncertain continuous-time(CT) systems having actuators with hard rate and magnitude bounds. The proposed method relies on acceleration form representation of the uncertain CT system. The technique enables the user to represent the control signal and its slew rate as auxiliary outputs along with the main controlled output. Two different norms, namely the induced L∞ and L2 are used to control the system effectively. While the L∞ gain from the exogenous disturbance inputs to the control signal related outputs is used to deal with actuator saturation problem, L2 gain from the disturbance inputs to the performance outputs is utilised in attenuation of the effects of the disturbances. To achieve these goals with minimal conservatism, we develop new forms of dilated Matrix Inequality (MI) conditions for peak-to-peak gain and L2 gain with no additional conservatism. Then, we propose a novel robust GS control methodology to deal with the problem via dilated MIs and a modified full block S-procedure method (MFBSPM). The utilisation of MFBSPM ensures that the robust control design method of this note applies to any uncertain system having rational parameter dependence. Finally, the efficiency of the presented method is portrayed through extensive simulations of the responses of a marine vessel to wave excitations in which the vessel model is assumed to have magnitude and rate limited active fin stabiliser.