Presence Of Actuator Saturation Research Articles

Real-time motion control of robotic manipulators for safe human–robot coexistence

This paper introduces a computationally efficient control scheme for safe human–robot interaction. The method relies on the Explicit Reference Governor (ERG) formalism to enforce input and state constraints in real-time, thus ensuring that the robot can safely operate in close proximity to humans. The resulting constrained control method can steer the robot arm to the desired end-effector pose (or a steady-state admissible approximation thereof) in the presence of actuator saturation, limited joint ranges, speed limits, static obstacles, and humans. The effectiveness of the proposed solution is supported by theoretical results and numerous experimental validations on the Franka Emika Panda robotic manipulator , a commercially available collaborative 7-DOF robot arm. • Real-time predictive constrained control with Explicit Reference Governor. • Robotic arm avoids actuator saturations, limited joint and velocity constraints. • Guaranteed robot collision avoidance in static obstacle environments. • Empirical robot collision avoidance in highly dynamic environments. • Safe and performant human–robot coexistence with Franka Emika Panda.

Low gain feedback for fractional-order linear systems and semi-global stabilization in the presence of actuator saturation

Low gain feedback for fractional-order linear systems and semi-global stabilization in the presence of actuator saturation

PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.

Adaptive sliding mode control for uncertain Euler–Lagrange systems with input saturation

In this paper, the tracking control problem of uncertain Euler–Lagrange systems under control input saturation is studied. To handle system uncertainties, a leakage-type (LT) adaptive law is introduced to update the control gains to approach the disturbance variations without knowing the uncertainty upper bound a priori. In addition, an auxiliary dynamics is designed to deal with the saturation nonlinearity by introducing the auxiliary variables in the controller design. Lyapunov analysis verifies that based on the proposed method, the tracking error will be asymptotically bounded by a neighborhood around the origin. To demonstrate the proposed method, simulations are finally carried out on a two-link robot manipulator. Simulation results show that in the presence of actuator saturation, the proposed method induces less chattering signal in the control input compared to conventional sliding mode controllers.

Designing a robust controller for a lower limb exoskeleton to treat an individual with crouch gait pattern in the presence of actuator saturation

Crouch gait is a gait anomaly observed in youngsters with cerebral palsy (CP). Rehabilitation robots are useful for treating individuals with crouch gait. Multiple factors have impact on crouch, including contracture, spasticity, weak motor control, and muscle feebleness, which make the designing and controlling of these exoskeletons for this population a challenging job. A harsh kinematic trajectory enforced by an exoskeleton control strategy may place individuals with spasticity at a high risk of muscle tissue injury. Therefore, in this article, a multi-input multi-output (MIMO) control method is proposed to reduce this risk and improve crouch gait pattern. A constrained control law is used in the model since high power demands may threaten the wearer. In addition, the controller needs to be robust enough against external disturbances and uncertainties. Thus, a nonlinear disturbance observer (NDO) is presented to compute the wearer-generated muscular torque and the uncertainties in the modeling. In addition, a robust constrained MIMO backstepping sliding controller (CMBSC) based on NDO is used to deal with the effect of actuator saturation and uncertainties. A simulation test was used to validate the proposed model and controller. The results of Simulation confirmed the efficiency of the proposed control method when applied to crouch gait with subject specific gait reference. Then, some experimental tests were undertaken to validate the efficiency of the proposed controller.

Disturbance observer-based robust backstepping load-following control for MHTGRs with actuator saturation and disturbances

This paper presents a disturbance observer-based robust backstepping load-following control (DO-RBLFC) scheme for modular high-temperature gas-cooled reactors (MHTGRs) in the presence of actuator saturation and disturbances. Based on reactor kinetics and temperature reactivity feedback, the mathematical model of the MHTGR is first established. After that, a DO is constructed to estimate the unknown compound disturbances including model uncertainties, external disturbances, and unmeasured states. Besides, the actuator saturation is compensated by employing an auxiliary function in this paper. With the help of the DO, a robust load-following controller is developed via the backstepping technique to improve the load-following performance of the MHTGR subject to disturbances. At last, simulation and comparison results verify that the proposed DO-RBLFC scheme offers higher load-following accuracy, better disturbances rejection capability, and lower control rod speed than a PID controller, a conventional backstepping controller, and a disturbance observer-based adaptive sliding mode controller.

Containment control of multi-agent systems with input saturation and unknown leader inputs

This paper investigates the containment control problem for multi-agent systems (MASs) with multiple leaders which have non-zero control inputs. Agents’ tracking errors are described by a linear system with an external disturbance. The containment control problem is then solved by applying a distributed observer-based output feedback controller. Anti-windup (AW) compensation is designed by convex conditions, to improve the performance in the presence of actuator saturation. Finally, simulations are presented to illustrate the effectiveness of the proposed method.

Design and Validation of Disturbance Rejection Dynamic Inverse Control for a Tailless Aircraft in Wind Tunnel

This paper focuses on the design of a disturbance rejection controller for a tailless aircraft based on the technique of nonlinear dynamic inversion (NDI). The tailless aircraft model mounted on a three degree-of-freedom (3-DOF) dynamic rig in the wind tunnel is modeled as a nonlinear affine system subject to mismatched disturbances. First of all, a baseline NDI attitude controller is designed for sufficient stability and good reference tracking performance of the nominal system. Then, a nonlinear disturbance observer (NDO) is supplemented to the baseline NDI controller to estimate the lumped disturbances for compensation, including unmodeled dynamics, parameter uncertainties, and external disturbances. Mathematical analysis demonstrates the convergence of the employed NDO and the resulting closed-loop system. Furthermore, an anti-windup modification is applied to the NDO for control performance preserving in the presence of actuator saturation. Subsequently, the designed control schemes are preliminarily validated and compared via simulations. The baseline NDI controller demonstrates satisfactory attitude tracking performance in the case of nominal simulation; the NDO augmented NDI controller presents significantly improved ability of disturbance rejection when compared with the baseline NDI controller in the case of robust simulation; the anti-windup modified scheme, rather than the baseline NDI controller nor the NDO augmented NDI controller, can preserve the closed-loop performance in the case of actuator saturation. Finally, the baseline NDI scheme and the NDO augmented NDI scheme are implemented and further validated in the wind tunnel flight tests, which demonstrate that the experimental results are in good agreement with that of the simulations.

Relative Position Model Predictive Control of Double Cube Test-Masses Drag-Free Satellite with Extended Sliding Mode Observer

The drag-free satellites, being space-borne ultrahigh precise measurement platforms, have played irreplaceable roles in a great number of space science missions such as navigation, earth science, fundamental physics, and astrophysics. Most of these missions have to be performed based on the satellites placed with double cube test-masses, which makes the satellite layout and control strategy be more complex. This paper investigates the orbit keeping control problem of a class of low Earth orbit drag-free satellites with double cube test masses. A disturbance observer-based composite control method is proposed, which consists of an extended sliding mode observer and the tube-based robust model predictive control approach. In this design, the observer is proposed to estimate the relative position and velocity of the satellite and the external space disturbance force. A tube-based robust model predictive control scheme is then developed to stabilize the satellite orbit control systems in the presence of actuator saturation, state constraints, and additive stochastic noises. Finally, a simulation example is presented to demonstrate the efficacy and superiority of the proposed orbit control method.

A predictive approach to adaptive fuzzy sliding-mode control of under-actuated nonlinear systems with input saturation

In this paper, a computationally efficient robust predictive control method is proposed for continuous-time under-actuated SISO systems in the presence of actuator saturation and state-dependent uncertainties. The proposition of this research is to employ the idea of model prediction together with the Adaptive Fuzzy Sliding-Mode Control (AFSMC) for tuning the sliding surface parameters by predicting the anticipated effects of uncertainties. In the proposed scheme, only after the trigger conditions are met, the coefficients of the sliding surface are updated and the AFSMC is applied. Hence, computational complexity can be controlled by adjusting the switching rule. In the AFSMC, a fuzzy system is used to approximate a nonlinear function, and a robust term to compensate for any possible mismatches. An adaptively tuned gain is also applied to the control signal to prevent instability caused by the actuator saturation. Based on the updating sliding surface, fuzzy singletons, the upper bound of the fuzzy approximation error, and the saturation gain are adaptively tuned. Closed-loop stability is shown to be guaranteed using the multiple Lyapunov functions theorem and the Barbalat’s lemma. Finally, the method is applied for the depth control of an Autonomous Underwater Vehicle (AUV), depicting the excellent performance of the proposed method.

Energy-based design of dynamic allocation in the presence of saturating actuators

This paper addresses the design of dynamic allocation functions for systems with saturating actuators. The novelty of the proposal relies on the use of an anti-windup loop to drive the state of the allocator, which in some sense dynamically compensates the difference between the computed control signal and the plant input. Furthermore, the co-design of the allocator and anti-windup loop is presented, allowing to deal with the multiple objective of reducing the allocator error and increasing the closed-loop region of stability. Theoretical conditions are derived in terms of linear matrix inequalities (LMIs) and an optimization scheme consisting in the minimization of the energy of the allocator error is proposed. Two examples borrowed from the literature illustrate the proposed technique and show its effectiveness.

Safety‐guaranteed constraint‐oriented modelling and control for bidirectional vehicular platoons

The safety of a vehicular platoon is seriously threatened in the presence of actuator saturations, (possibly fast) time-varying non-linear uncertainties. Meanwhile, the string stability and the strong string stability cannot eliminate the potential safety hazard caused by large initial error conditions. This study focuses on safety-guaranteed distributed control of the vehicular platoon with a bidirectional communication topology and the constant time headway policy. The authors formulate bilateral inequality constraints on the spacing error between adjacent vehicles to represent the collision-avoidance and compact formation performance. A novel state transformation technique is proposed to convert the bounded spacing error space to an unconstrained state space. On the basis, Comprehensive equality constraints for the transformed states are established by integrating the information of proximal (preceding and following) vehicles. In addition, an anti-windup compensation method is utilised to handle actuator saturations. Then an adaptive constraint-following controller is designed to render the uniform boundedness and uniform ultimate boundedness performance of the transformed state. As a result, the string stability, the strong string stability, the collision-avoidance and compact formation are guaranteed despite the presence of actuator saturations and complex uncertainties. Numerical simulations are performed to validate the effectiveness of the proposed control scheme.

Global consensus of multi‐agent systems with intermittent directed communication in the presence of actuator saturation

SummaryWe consider the problem of global leader‐following consensus of a multi‐agent system with intermittent directed communication in the presence of actuator saturation. The dynamics of the follower agents are represented by a chain of integrators of an arbitrary length. The leader agent possesses the same internal dynamics of the follower agents. For each follower agent, a bounded consensus algorithm utilizing the information obtained intermittently through the communication network is constructed. It is shown that these consensus algorithms achieve global leader‐following consensus as long as the communication topology among all agents, when the communication is active, contains a spanning tree rooted at the leader agent. Numerical examples are given to show the theoretical results.

Low-conservative robust composite nonlinear feedback control for singular time-delay systems

A low-conservative composite nonlinear feedback controller is proposed for singular time-delay systems with time-varying delay. The proposed composite nonlinear feedback controller not only improves the transient responses of the closed-loop system but it also has less conservatism than other composite nonlinear feedback controllers. The gain of the linear part of the composite nonlinear feedback controller is obtained by precise mathematical calculation to depend not only on the upper bound of the delay but also on the delay range and rate of its changes. More advantages of the proposed composite nonlinear feedback controller are its accurate operation in the presence of actuator saturation, model uncertainties, and system singularities. The linear and nonlinear parts of the proposed controller are designed by solving a linear matrix inequality problem confirmed through a theorem using Lyapunov stability analysis. The theoretical achievements are endorsed by computer simulation through numerical and practical examples.

Active Attitude Control of Ground Vehicles with Partially Unknown Model

We present a novel solution to the attitude control problem of ground vehicles by means of the Active Front Steering (AFS) system. The classical feedback linearization method is often used to track a reference yaw dynamics while guaranteeing vehicle stability and handling performance, but it is difficult to apply because it relies on the exact knowledge of the nonlinearities of the vehicle, in particular the tire model. In this work, the unknown nonlinearities are real-time learnt on the basis of the universal approximation property, widely used in the area of neural networks. With this approximation method, the Uniform Ultimate Boundedness (UUB) property with respect to tracking and estimation errors can be formally proven. Preliminary simulation results show good tracking capabilities when model and parameters are affected by uncertainties, also in presence of actuator saturation.

Adaptive Sliding Mode Control of Vehicular Platoons With Prescribed Tracking Performance

This paper investigates a vehicular platoon control problem with prescribed tracking performance in the presence of actuator saturation, uncertain parameters, and unknown disturbances. Two adaptive sliding mode control schemes based on leader–predecessor and leader–bidirectional information flows are presented to ensure string stability and strong string stability, respectively, with a prescribed tracking performance. The actuator saturation nonlinearity is addressed by approximating it with a smooth hyperbolic tangent function. The effects of uncertain parameters and exogenous disturbances are dealt with by introducing a set of adaptation laws. The effectiveness of the proposed control schemes is demonstrated via numerical simulation results.

Stabilization of Discrete-Time Delayed Systems in Presence of Actuator Saturation Based on Wirtinger Inequality

This paper examines the stability analysis of discrete-time control systems particularly during the event of actuator saturation and time-varying state delay. With the help of Wirtinger inequality along with Lyapunov-Krasovskii functional gain of state feedback controller is determined for stabilization of above system. The saturation nonlinearity is represented in the terms of convex hull. A new linear matrix inequality (LMI) criterion is settled with reciprocally convex combination based inequality which is dependent on delay. The proposed criterion is less conservative in concern to increase the delay bound and a controller is also simulated for real time problem of missile control system in this paper. It is also attained that projected stability criterion is less conservative compared to other outcomes. Furthermore, an optimization procedure together with LMI constraints has been proposed to maximize the attraction of domain.

Force Sensorless Admittance Control With Neural Learning for Robots With Actuator Saturation

In this paper, we present a sensorless admittance control scheme for robotic manipulators to interact with unknown environments in the presence of actuator saturation. The external environment is defined as linear models with unknown dynamics. Using admittance control, the robotic manipulator is controlled to be compliant with external torque from the environment. The external torque acted on the end-effector is estimated by using a disturbance observer based on generalized momentum. The model uncertainties are solved by using radial basis neural networks (NNs). To guarantee the tracking performance and tackle the effect of actuator saturation, an adaptive NN controller integrating an auxiliary system is designed to handle the actuator saturation. By employing Lyapunov stability theory, the stability of the closed-loop system is achieved. The experiments on the Baxter robot are implemented to verify the effectiveness of the proposed method.

Tube-based Model Predictive Control for Dynamic Positioning of Marine Vessels

This paper focuses on the design of a robust model predictive control law for dynamic positioning (DP) of marine vessels in the presence of actuator saturation and environmental disturbances. The proposed solution is a tube-based MPC ensuring robustness and constraint fulfillment. Formulation of the tube-based MPC relies on a sufficient robust invariant set condition, along with a linear matrix inequality (LMI) synthesis procedure, and an efficient analytical Pontryagin set difference computation. Simulation results show the effectiveness and satisfactory behaviour of the proposed controller.

Control design in the presence of actuator saturation: from individual systems to multi-agent systems

Control design in the presence of actuator saturation: from individual systems to multi-agent systems