Actuator Saturation Limits Research Articles

Numerical algorithm for nonlinearity compensation of hardly constrained actuation for trajectory tracking control of deadzone-included dynamic systems

This paper addresses the control of a nonlinear system affected by deadzone effects, using a constrained actuator. The system itself incorporates a second-order oscillatory dynamic actuator, with an unknown nonlinear input-output relationship. The proposed algorithm not only accommodates the deadzone constraints on control inputs but also considers the actuator's saturation limits in control input calculations. It introduces a trajectory tracking mechanism that, instead of directly following the primary trajectory, adheres to an alternative trajectory capable of stable tracking, gradually converging to the main trajectory while accounting for operational constraints. In practical control systems, the actuator's input-output relationship is often nonlinear and unknown, requiring inversion for model-based control. This paper employs an offline-trained neural network trained on synthetic data to identify and approximate the actuator's behavior. To optimize the control system's performance and ensure stability during sudden error changes, the control input operates in two modes: position and velocity control. This dual-mode control allows for continuous switching between the two, facilitated by an innovative optimization technique based on the gradient descent method with a variable step size. Simulation results validate the effectiveness of the proposed algorithm in controlling systems constrained by hard limits and featuring nonlinear oscillatory actuators, providing a valuable contribution to the field of control systems.

Hybrid Model Predictive Control with Penalty Factor Based on Image-Based Visual Servoing for Constrained Mobile Robots

For the constrained mobile robot automatic parking system, the hybrid model predictive control with a penalty factor based on image-based visual servoing (IBVS) is proposed to address the problem of feature point loss and emergency braking in dynamic obstacle scenarios caused by excessive target bias gain when using traditional IBVS control methods. The traditional IBVS control is transformed into an optimization problem with constraints in the finite time domain, by defining the optimization function based on the mobile robot’s positional deviation and image feature point deviation, while using actuator saturation and speed limit as constraints. Based on this, a convex optimization function with penalty factors is defined and combined with incremental model predictive control. This control strategy could ensure the emergency braking performance of the mobile robot when the image feature points are massively obscured by obstacles in dynamic scenes, while improving the accuracy and real-time of its trajectory tracking control. Finally, simulation comparisons are conducted to verify the effectiveness of the proposed control method.

Modelling and Control Tank Testing Validation for Attenuator Type Wave Energy Converter – Part III: Model Predictive Control and Robustness Validation

Following the tank testing results of linear passive damping control and linear non-causal optimal control (LNOC) in the Part I and Part II papers, this paper presents further tank testing results focusing on two aspects: Firstly, a model predictive controller (MPC) is designed based on the model developed by system identification in Part I to optimally handle actuator saturation limits. The MPC control is demonstrated to significantly improve the energy output by 9.86% up to 463.42% compared with a well-tuned passive damper and can also outperform the LNOC presented in Part II in a range of irregular unidirectional waves. Secondly, the robustness of the MPC controller and the LNOC controller is validated in more realistic sea conditions when directional spreading waves and side waves are superimposed onto the dominant directional waves. The test results show that both MPC and LNOC can still significantly outperform the passive damping controller in all the sea conditions. These tank testing results pave a solid way for future sea trial testing of these advanced non-causal optimal control strategies developed for wave energy converters in sea trials.

Visual-admittance-based model predictive control for nuclear collaborative robots

This paper presents a novel visual-admittance-based model predictive control scheme to cope with the problem of vision/force control and several constraints of a nuclear collaborative robotic visual servoing system. A visual-admittance model considering the desired image feature and force command in the image feature space is proposed. Moreover, a novel constraint scheme of the model predictive control (MPC) is proposed to cancel the overshoot in the interaction force control for most cases by taking the desired force command as the constraint of the proposed MPC. Via applying the robotic dynamic image-based visual servoing (IBVS) model, some other constraints, such as the actuator saturation, joint angle, and visual limits, can be satisfied simultaneously. The simulation results for the two-degrees-of-freedom (DOF) robot manipulator with an eye-to-hand camera are present to demonstrate the effectiveness of the proposed controller.

Composite anti-unwinding attitude control of spacecraft under actuator saturation and angular velocity limits

Spacecraft attitude control employs quaternion representation to avoid singularity issues and obtain global maneuver stability. However, it has redundancy associated, resulting in dual equilibrium points. The attitude control may confront the unwinding phenomenon due to the presence of the equilibria. In this paper, an anti-unwinding controller for spacecraft stabilization in the presence of external disturbances and inertial uncertainties, angular velocity limit, actuator saturation and faults is presented. Specifically, a modified extended state observer (ESO) is designed to obtain total disturbance estimates of the rigid-body spacecraft. Auxiliary parameters are added in the design to avoid initial high estimates in the proposed ESO design resulting in faster convergence. The proposed disturbance observer is to release the assumption that requires the estimated disturbance to be constant or varying at slow rates. Using the ESO estimates, a particular back-stepping-SMC (ESO-BTSMC) controller is devised to formulate anti-unwinding control law for spacecraft stabilization. Lyapunov stability theory is employed to prove closed-loop stability of system and estimation error convergence. Comparative simulations are performed to demonstrate the performance of the proposed control scheme. It is found that the proposed control scheme gives smooth and precise control performance along with faster transient response. Additionally, it also alleviates the chattering phenomenon.

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.

Formation control of multiple wheeled mobile robots based on model predictive control

AbstractThis paper considers the problem of formation control for a team of nonholonomic wheeled mobile robots considering obstacle avoidance. A new control algorithm based on the model predictive control (MPC) and the nonlinear dynamics of the system is presented here. The control algorithm is applied to the nonlinear system using two different controllers including linear MPC and nonlinear MPC. The virtual structure formation approach and artificial potential field method are employed to determine the reference trajectories of the robots and to solve the problem of obstacle avoidance. A control algorithm consisting of two parts is proposed to track the trajectories and maintain the team’s formation. Two advantages of using MPC techniques are the ability to consider control and state constraints which are of high importance in practical applications. The main contribution of this paper is the design of two robust control systems to disturbance with respect to actuator saturation limits. Simulation results demonstrate the effectiveness and robustness of the proposed control algorithm in trajectory tracking and formation maintenance in the presence of disturbance and actuator limits.

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. If the plasma temperature were to inadvertently rise in this burning regime, the positive correlation between temperature and the fusion reaction rate would establish a destabilizing positive feedback loop. Careful regulation of the plasma’s temperature and density, or burn control, is required to prevent these potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. An adaptive estimator manages destabilizing uncertainties in the plasma confinement properties and the particle recycling conditions (caused by plasma–wall interactions). The controller regulates the plasma density with requests for deuterium and tritium particle injections. In ITER-like plasmas, the fusion-born alpha particles will primarily heat the plasma electrons, resulting in different electron and ion temperatures in the core. By considering separate response models for the electron and ion energies, the proposed controller can independently regulate the electron and ion temperatures by requesting that different amounts of auxiliary power be delivered to the electrons and ions. These two commands for a specific control effort (electron and ion heating) are sent to an actuator allocation module that optimally maps them to the heating actuators available to ITER: an electron cyclotron heating system (20 MW), an ion cyclotron heating system (20 MW), and two neutral beam injectors (16.5 MW each). Two different actuator allocators are presented in this work. The first actuator allocator finds the optimal mapping by solving a convex quadratic program that includes actuator saturation and rate limits. It is nonadaptive and assumes that the mapping between the commanded control efforts and the allocated actuators (i.e. the effector model) contains no uncertainties. The second actuator allocation module has an adaptive estimator to handle uncertainties in the effector model. This uncertainty includes actuator efficiencies, the fractions of neutral beam heating that are deposited into the plasma electrons and ions, and the tritium concentration of the fueling pellets. Furthermore, the adaptive allocator considers actuator dynamics (actuation lag) that contain uncertainty. This adaptive allocation algorithm is more computationally efficient than the aforementioned nonadaptive allocator because it is computed using dynamic update laws so that finding the solution to a static optimization problem is not required at every time step. A simulation study assesses the performance of the proposed adaptive burn controller augmented with each of the actuator allocation modules.

A numerical algorithm to find optimum parameters of a flexible-link manipulator arm for performing payload launching

PurposeThe aim of the current study is proposing a novel framework to attain the optimum value of a flexible arm manipulator parameters for payload launching missions.Design/methodology/approachThe proposed scheme is based on optimal control approach and combines direct and indirect search methods while considering the actuator capacity.FindingsThree nonlinear parameter-optimization problems will be solved to illustrate how the proposed algorithm can be exploited. Employing variational based nonlinear optimal control within the suggested framework, the answer of these problems is highly intertwined to the solution of a set of differential equations with split boundary values. To solve the obtained boundary value problem (BVP), the related solver of MATLAB® software, bvp6c, will be employed. The achieved simulation results support the worth of the developed procedure.Originality/valueFor the first time, the optimal parameters of a flexible link robot for object launching are found in the current research. In addition, the actuator saturation limits are considered which enhances the applicability of the suggested method in the real world applications.

Robust output tracking for the non-minimum phase over-actuated systems

Typically, if the system is right-invertible only, then this implies that the number of inputs is more than that of outputs as well as states of the system. Over-actuated systems belong to such class. In this paper, a systematic design of a reduced-order super-twisting control is proposed to track arbitrary reference signals for uncertain non-minimum phase over-actuated systems. The proposed method involves the transformation that resolves the redundancy in the control inputs so that system can be represented as a normally-actuated system with virtual control inputs. Further, unstable zero dynamics are virtually stabilized through one more transformation so that stable and virtually stable zero dynamic states can be excluded from the super-twisting control design. Finally, the computed virtual control magnitude is spread across all the actuators via a redistributed pseud-inverse type of control allocation so that the system can be operated within the actuator saturation limits.

Model-Independent Formation Tracking of Multiple Euler-Lagrange Systems via Bounded Inputs.

This article addresses two kinds of formation tracking problems, namely: 1) the practical formation tracking (PFT) problem and 2) the zero-error formation tracking (ZEFT) problem for multiple Euler-Lagrange systems with input disturbances and unknown models. In these problems, the bounded input constraint, which can be possibly caused by actuator saturation and power limitations, is taken into consideration. Then, the two classes of model-independent distributed control approaches, in which the prior information (i.e., the structures and features) of the system model is not used, are proposed correspondingly. Based on the nonsmooth analysis and Lyapunov stability theory, several novel criteria for achieving PFT and ZEFT of multiple Euler-Lagrange systems are derived. Finally, numerical simulations and comparisons are presented to verify the validity and effectiveness of the proposed control approaches.

Fault and Failure Tolerant Model Predictive Control of Quadrotor UAV

This paper presents fault tolerance control (FTC) of a quadrotor under actuator faults. A complete FTC design approach with fault detection and diagnosis (FDD) is addressed. The proposed FTC is based on the model predictive control, which can be applied to nonlinear systems using the so-called successive convexification algorithm, which converts a nonconvex function to a convex function in a successive manner through linearization. The faults are parameterized in the form of loss of effectiveness (LOE) of a quadrotor actuator and estimated using a two-stage Kalman filter. Compared with other FTC, the proposed FTC is capable of controlling not only partial loss of actuator effectiveness defined as a fault but also a complete loss of actuator effectiveness defined as failure. Controller switching is not required, while an actuator saturation limit is also considered. The proposed FTC approach has been validated under various actuator fault conditions through nonlinear simulation studies.

Adaptive control allocation for constrained systems

This paper proposes an adaptive control allocation approach for uncertain over-actuated systems with actuator saturation. The proposed control allocation method does not require uncertainty estimation or persistency of excitation. Actuator constraints are respected by employing the projection algorithm. The stability analysis is provided for two different cases: when ideal adaptive parameters are inside and when they are outside of the projection boundary which is chosen consistently with the actuator saturation limits. Simulation results for the Aerodata Model in Research Environment (ADMIRE), which is used as an example of an over-actuated aircraft system with actuator saturation, demonstrate the effectiveness of the proposed method.

Control Law Design for MISO System in the Presence of Actuator Position Limit Constraint

This article is about including the actuator position limit constraint while designing PD controller based on output feedback pole placement methodology for a multi-input-single-output (MISO) system. While designing control law for MISO system, designer has additional degrees of freedom which can be utilized in many ways to achieve different time and frequency domain specifications. One such goal can be to maximize the control availability at any instant of time in the presence of growing disturbance moment. In the paper it is shown that if the proportional path gains of all the loops are constrained to be in the ratio of the maximum value (actuator saturation limit) of control input of respective loops, then at steady state, total control demand will always be distributed to different control power plants in the ratio of their maximum control availability. Designing control law with the inclusion of actuator saturation limit, as constraint on proportional path gains, helps in ensuring the stability of the whole closed loop system by postponing saturation to higher disturbance values. Efficacy of the proposed method is demonstrated on a real life problem of attitude control law design for a typical launch vehicle.

On the optimization of actuator saturation limits for LTI systems: an LMI-based invariant ellipsoid approach

This paper considers the problem of optimal actuator dimensioning for LTI systems, in the sense of choosing appropriate saturation limits for a given set of admissible initial conditions and for a predefined integral state-feedback control law. By using an invariant ellipsoid argument, it is shown that this problem can be described as a linear matrix inequality (LMI)-based optimization that can be solved efficiently. Moreover, the paper shows that the optimal actuator dimensioning is connected to the choice of the initial conditions of the integral states of the controller, which can be included in the overall optimization to improve further the results. Two different methods are described and analyzed by means of numerical simulation.

Adaptive Control and Optimization of Mobile Manipulation Subject to Input Saturation and Switching Constraints

In this paper, a hierarchical hybrid motion/force control architecture for the manipulation and grasping of mobile manipulators is presented, where the systems are subject to varieties of physical constraints such as Coulomb friction cones, nonholonomic/holonomic constraints, and actuator saturation limits. The incorporation of a projection-based operation space control and an adaptive controller based on the neural networks used in this paper formulates a novel control scheme, so the system stability is further guaranteed and the uncertain dynamics is handled without redesigning the minimal-order dynamics model. Considering the effects of these constraints, the actuator saturation limits are handled by an auxiliary designed system, and the neural dynamics optimization is applied for the quadratically constrained programing problem of the optimal robotic grasping. The dynamic uncertainties can be estimated online by using the developed motion/force control strategy, and the application of a novel disturbance observer is explored to ensure the good tracking performance. The experimental results are presented to verify the performance and the efficiency of the proposed method. Note to Practitioners —This paper is motivated by the problems of robotic grasping, the trajectory tracking of mobile manipulation, which are with time-varying topology (e.g., actuator saturation limits, switching constraints). Traditional approaches tackling such problems mainly use multiple-models switching control architecture; however, these methods are not suitable for the switching conditions. Therefore, it is necessary to develop a novel control approach dealing with these issues together. In this paper, a unified hierarchical hybrid motion/force control architecture is proposed using the notion of projection operator, and the control inputs are decomposed into the null space, which produces the motion complement of the system and the orthogonal complement space constructing physical constraints, respectively. In addition, an auxiliary system is also designed to solve the limits from the actuator saturation. The feasibility of the system is demonstrated by the extensive experiment results including trajectory tracking and the switching constraints in the developed mobile manipulator.

Sliding‐mode fault‐tolerant control using the control allocation scheme

SummaryThis paper is devoted to the design of a novel fault‐tolerant control (FTC) using the combination of a robust sliding‐mode control (SMC) strategy and a control allocation (CA) algorithm, referred to as a CA‐based sliding‐mode FTC (SMFTC). The proposed SMFTC can also be considered a modular‐design control strategy. In this approach, first, a high‐level SMC, designed without detailed knowledge of systems' actuators/effectors, commands a vector of virtual control signals to meet the overall control objectives. Then, a CA algorithm distributes the virtual control efforts among the healthy actuators/effectors using the real‐time information obtained from a fault detection and reconstruction mechanism. As the underlying system is not assumed to have a rank‐deficient input matrix, the control allocator module is visible to the SMC module resulting in an uncertainty. Hence, the virtual control, in this scheme, is designed to be robust against uncertainties emanating from the visibility of the control allocator to the controller and imperfections in the estimated effectiveness gain. The proposed CA‐based SMFTC scheme is a unified FTC, which does not need to reconfigure the control system in the case of actuator fault or failure. Additionally, to cope with actuator saturation limits, a novel redistributed pseudoinverse‐based CA mechanism is proposed. The effectiveness of the proposed schemes is discussed with a numerical example.

False-Data Injection Attack in Electricity Generation System Subject to Actuator Saturation: Analysis and Design

The secure operation of electricity generation system (EGS) is essential to the quality of electricity and the security of energy Internet. In order to design secure control strategy for EGS, the behavior and capacity of adversary and possible attack should be studied. From this point of view and considering the actuator saturation and the false-data injection attack in control input channel of EGS, we analyze the behavior and stealthiness of adversary and design stealthy attack strategies in this paper. First, we prove that the magnitude of effective attack signal is smaller than the magnitude of injected attack signal because of actuator saturation. Second, we find that smaller actuator saturation limit makes the adversary easier to be detected. Finally, two stealthy attack strategies are designed for EGS which incorporates a $\chi ^{2}$ attack detector, and the effectiveness of them are illustrated through simulation.

Active Fault-Tolerant Control System Design for Spacecraft Attitude Maneuvers with Actuator Saturation and Faults

This paper designs an active fault-tolerant control system for spacecraft attitude control in the presence of actuator faults, fault estimation errors, and control input constraints. The developed fault-tolerant control system is able to detect the actuator fault without false alarms caused by external disturbances, and also estimate the total fault effects accurately through an indirect fault identification approach, in which an auxiliary variable is utilized to build the relation between fault and system states. Once the fault identification is completed with certain degree of reconstruction accuracy, a fault-tolerant backstepping controller using the nonlinear virtual control input is reconfigured to accommodate the detected actuator faults effectively, in spite of actuator saturation limitations and fault estimation errors. Numerical simulation is carried out to demonstrate that the proposed active fault-tolerant control system is successful in fault detection, identification, and controller reconfiguration for handling actuator faults in attitude control systems.

Prescribed performance fixed-time tracking control for a class of second-order nonlinear systems with disturbances and actuator saturation

This paper investigates the prescribed performance fixed-time tracking control problem for a class of second-order nonlinear systems with bounded disturbance and actuator saturation limit. In order to facilitate the controller development, we introduce the performance function and output error transformation technique to transform the tracking error dynamics with inequality performance constraints to an equivalent unconstrained error one. Different from the existing work on the guaranteeing prescribed performance control, we incorporate the fixed-time sliding mode surface into the control design procedure to cope with the disturbances and actuator saturation limit. Specifically, a robust adaptive fixed-time tracking controller, which requires no upper bound of the disturbance, is designed to solve the prescribed performance fixed-time tracking control problem. The rigorous mathematical stability proof is given. Finally, numerical simulations for the attitude tracking control are presented to demonstrate the effectiveness and robustness of the proposed controller.