Saturated Output Feedback Research Articles

Saturated output feedback control of free-floating space manipulator with fragility-avoidance prescribed performance

Saturated output feedback control of free-floating space manipulator with fragility-avoidance prescribed performance

Saturated Output Feedback Control for Robot Manipulators With Joints of Arbitrary Flexibility

Abstract This paper proposes a saturated output feedback controller for flexible-joint robot manipulators with joints of arbitrary flexibility. First, under the framework of singular perturbation theory, a saturated flexible compensator is introduced in the dynamics model to enlarge the joint stiffness and achieve a united control for the robot with joints of arbitrary flexibility. Meanwhile, the saturation problem of torque control is also addressed. Second, an extended Kalman filter (EKF) with adaptive high gain that combines the noise filter of EKF with global convergence of high-gain observer is presented to enable the output feedback tracking control without the velocity of the link side or the motor side. Third, explicit but strict stability analyses of the whole system in both full-state feedback and output feedback are given. Finally, simulation comparisons are provided to verify the effectiveness of the proposed approach.

Additional Cover

The back cover image is based on the Research Article Inertia-free saturated output feedback attitude stabilization for uncertain spacecraft by Chuang Liu et al., https://doi.org/10.1002/rnc.5044.

Velocity-free friction compensation for motion systems with actuator constraint

This paper concerns on the output feedback problem of fast and precise positioning for uncertain motion systems subject to friction and actuator constraint by position measurement only. A simple model-independent saturated robust output feedback nonlinear proportional-derivative (PD) control is proposed by adding relay action driven by position error. Lyapunov’s direct method is employed to prove global asymptotic positioning stability. The appealing advantages of the proposed approach are that it is fairly easy to construct with simple and intuitive structure and without reference to modeling parameter and velocity measurement and has the ability to ensure that the actuator constraint is not violated. This is accomplished by selecting control gains a priori. Numerical simulations and real-time experimental validations demonstrate that the proposed approach provides an easy-going model-free solution for high performance positioning of uncertain motion systems subject to unknown friction and actuator constraint with position measurement only.

Saturated output feedback control for finite-time attitude stabilization of spacecraft

The finite-time attitude stabilization of spacecraft subject to actuator constraints and attitude measurements only is investigated. A saturated output feedback finite-time proportional-derivative control is proposed. Lyapunov stability theory and homogeneous method are employed to show the finite-time stabilization. Advantages of the proposed control include the finite-time stabilization featuring faster transient and higher precision and the absence of the modelling information and the velocity measurements in the control law formulation, and thus, it offers an easy-going solution for high-quality motion control of spacecraft. An additive feature is that the actuator saturation will not be reached by selecting the control gains a priori. Simulations are presented to illustrate the effectiveness of the proposed control.

Globally Asymptotic Output Feedback Tracking of Robot Manipulators With Actuator Constraints

This paper revisits the problem of asymptotic tracking for robot manipulators with actuator constraints and position measurements only. A new dynamic nonlinear filter is first proposed and then a saturated output feedback proportional-derivative (PD) control is constructed. Lyapunov’s direct method is employed to show global asymptotic stability (GAS). Explicit conditions on control gains ensuring GAS and avoidance of actuator constraints are obtained. This is accomplished by selecting control gains a priori. Advantage of the proposed approach is that it can assure GAS and satisfy actuator constraints. Numerical simulations are presented to demonstrate the improved performance of the proposed approach.

High Gain Observer-Based Saturated Controller for Feedback Linearizable System

The presence of pulse width modulation driven components, limiters, and electronic switches constrain the magnitude of control input in electrical and electro-mechanical systems. The presence of nonlinearities in these system models and unavailability of full state measurements, further complicate the controller design process. This brief introduces a novel saturated output feedback design to solve the tracking problem for a class of feedback linearizable circuits. The feedback scheme comprises of a modified approximate dynamic inversion controller in conjunction with a standard high gain observer. Unlike the Lyapunov-based approaches, the proposed contraction theory-based methodology details a quantitative framework for the convergence analysis of closed loop trajectories. This, in turn, serve the dual purpose of proving ultimate boundedness and quantifying the convergence bounds in terms of known parameters.

Reduced-order observer-based saturated finite-time stabilization of high-order feedforward nonlinear systems by output feedback

This paper is concerned with the problem of global finite-time stabilization by output feedback for a class of feedforward (upper-triangular) nonlinear systems in p-normal form. Remarkably, both the high order powers and the saturated input are involved in the system under consideration, that renders the existing output feedback control methods are inapplicable. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a reduced order observer-based saturated finite-time output feedback control scheme is successfully developed. With choosing appropriate design parameters, the proposed controller ensures that the states of the closed-loop system are regulated to zero in a finite time without violation of the input constraint. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed method.

On Output Feedback Trajectory Tracking Control of an Omni-Mobile Robot

Abstract This paper presents the solution to the trajectory tracking control problem of an omnidirectional mobile robot without velocity measurements. Lyapunov function-based control design strategy is developed via an application of a quasi-invariance principle for non-autonomous systems of differential equations. The global uniform asymptotic stability property of the set of all equilibrium points of the closed-loop system has been proved by constructing a saturated position output feedback controller.

Saturated output-feedback nonlinear control of a 3-continuous exothermic reactor train

The problem of controlling with saturated output-feedback (OF) temperature control a six-state (concentration-temperature) bistable train of three continuous stirred tank reactors with recycle is addressed. The closed-loop system must operated about the unstable steady-state (SS) by manipulating the coolant temperature on the basis of one of the tank temperatures. The aim is to attain robust closed-loop stability with a control scheme as simple as possible. The constructive combination of advanced and industrial control ideas yields a the behavior of a passive nonlinear state-feedback (NLSF) stabilizing controller can be recovered with an industrial-type proportional-integral (PI) control with anti-windup protection plus criteria to choose the sensor location as well as control gains and limits.

Quadratic boundedness of LPV systems via saturated dynamic output feedback controller

SummaryFor the linear parameter varying systems with bounded disturbance, a saturated dynamic output feedback controller is designed by specifically considering input saturation, to stabilize the closed‐loop system. The controller parameters and the corresponding region of attraction are calculated by solving an off‐line optimization problem with respect to input saturation, state constraints, and robust stability. In the off‐line optimization problem, both the unknown and available scheduling parameters are considered for the linear parameter varying systems. When the unknown scheduling parameters are considered, the off‐line optimization problem is nonconvex and can be solved by the cone complementary linearization method. When the available scheduling parameters are considered, the off‐line optimization problem can be reformulated as convex optimization due to the parameter dependent form of controller parameters. In the both cases, input saturation is specifically handled by introducing a set of linear matrix inequalities into the off‐line optimization problem, which can reduce the conservatism of the controller design and fully exploit the controller capability. Based on the real‐time estimated state, system output, and scheduling parameters, the actual input can be obtained by saturating the dynamic output feedback controller, and steer the augmented state quickly converge to the neighborhood of the origin. Two numerical examples are provided to illustrate the proposed approaches.

Output Feedback Control for Asymptotic Stabilization of Spacecraft with Input Saturation

This paper investigates the attitude stabilization problem of rigid spacecraft subject to actuator constraints, external disturbances, and attitude measurements only. An output feedback control framework with input saturation is proposed to solve this problem. The general saturation function is utilized in the proposed controller design and a unified control method is developed for the asymptotic stabilization of rigid spacecraft without velocity measurements. Asymptotic stability is proven by Lyapunov stability theory. Moreover, a new nonlinear disturbance observer is designed to compensate for external disturbances. Then, a composite controller is presented by combining a unified saturated output feedback control with a nonlinear disturbance observer. Desirable features of the proposed control scheme include the intuitive structure, robustness against external disturbances, avoidance of model information and velocity measurements, and ability to ensure that the actuator constraints are not violated. Finally, numerical simulations have been carried out to verify the effectiveness of the proposed control method.

Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation

ABSTRACTThis paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.

Dynamic output feedback control of saturated switched delay systems under the PDT switching

SummaryThis paper is devoted to saturated control of switched delay systems. The main focus is to find a suitable switching law and saturated output feedback controllers such that the closed‐loop systems are asymptotically stable and have the disturbance tolerance/rejection capacity. A mixed slow/arbitrary switching approach, so‐called persistent dwell time (PDT) switching, is used to design the switching law. Compared with the slow switching, it is more general and leads to more flexibility in the process of constructing switching signals. More importantly, the proposed PDT is dependent on state delay, which includes the previous delay‐independent PDT. Next, time‐varying ellipsoids and a prescribe l2‐gain are introduced to characterize the disturbance tolerance and rejection capacities of systems, respectively. Based on the proposed results, the relation between delay‐dependent PDT and level of disturbance tolerance/rejection is shown. Finally, saturated controllers working in time‐varying hull controllable regions are designed. Thus, the considered problem is solved. An example is exploited to illustrate the effectiveness of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.

Finite-time output feedback stabilisation of chained-form systems with inputs saturation

ABSTRACTThis paper investigates the problem of finite-time stabilisation by output feedback for a class of non-holonomic systems in chained form with input saturation. Rigorous design procedure for saturated output feedback control is presented by using the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Finite‐time output feedback attitude stabilisation for rigid spacecraft with input constraints

This study deals with finite-time output feedback attitude stabilisation problem for rigid spacecraft systems subject to input constraints. First, a continuous saturated state feedback controller is proposed based on the homogeneous method, after which can guarantee the closed-loop system is global finite-time stable. Then, a switched saturated output feedback controller is developed under a state observer, after which can guarantee the closed-loop system is semi-global finite-time stable. Simulation results are given to demonstrate the effectiveness of the proposed method.

Dynamic Output Feedback Robust MPC with Input Saturation Based on Zonotopic Set-Membership Estimation

For quasi-linear parameter varying (quasi-LPV) systems with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with the consideration of input saturation is investigated. The saturated dynamic output feedback controller is represented by a convex hull involving the actual dynamic output controller and an introduced auxiliary controller. By taking both the actual output feedback controller and the auxiliary controller with a parameter-dependent form, the main optimization problem can be formulated as convex optimization. The consideration of input saturation in the main optimization problem reduces the conservatism of dynamic output feedback controller design. The estimation error set and bounded disturbance are represented by zonotopes and refreshed by zonotopic set-membership estimation. Compared with the previous results, the proposed algorithm can not only guarantee the recursive feasibility of the optimization problem, but also improve the control performance at the cost of higher computational burden. A nonlinear continuous stirred tank reactor (CSTR) example is given to illustrate the effectiveness of the approach.

L2-Gain analysis and output feedback control for switched delay systems with actuator saturation

This paper is concerned with the l2-gain analysis and control problems for switched delay systems subject to actuator saturation. The proposed technical framework consists of a switching law and the output feedback controllers. The switching law obeys the mode-dependent average dwell time (MDADT), which allows each subsystem of the switched system has its own average dwell time (ADT). More important, the switching law is dependent on the state delay. In special case, it can include the existing switching laws satisfying MDADT or ADT. Further, it allows more switching numbers in slow switching framework, which leads to more freedom for constructing switching signals. Hence, the proposed delay-dependent switching law is more general and applicable. The saturated output feedback controllers with the form of quasi-linear parameter-varying (QLPV) are then designed such that the closed-loop system under the switching law is with the disturbance tolerance capacity and a weighted l2-gain. Sufficient conditions for the existence of the switching law and the controllers are developed based on the linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is illustrated through a numerical example.

$$L_{2}$$ L 2 -gain analysis and control of saturated switched systems with a dwell time constraint

This paper investigates the \(L_{2}\)-gain analysis and control problem for switched systems with actuator saturation. A minimal dwell time constraint is first introduced, which avoids possible arbitrarily fast switching. Then, to satisfy the mentioned constraint, a switching strategy depending only on a lower bound of the dwell time and partial measurable states of the closed-loop system is developed in output feedback framework, which extends previous results in state feedback framework. Further, under the proposed switching strategy, time-varying hull controllable regions and saturated output feedback controllers working on them are constructed such that the closed-loop system has a prescribed \(L_{2}\)-gain. Meanwhile, the states of the system starting from the origin will remain inside a time-varying ellipsoid determined by a discretized Lyapunov matrix function. In addition, the resulting ellipsoid is also proven to be between two time-invariant ellipsoids. A solution of the considered problem is given via a linear matrix inequality formulation. Finally, an example is exploited to illustrate the effectiveness of the theoretical results.

A Saturating Extension of an Output Feedback Controller for Internally Damped Euler‐Lagrange Systems

AbstractIn this research, a novel extension of the passivity‐based output feedback trajectory tracking controller is developed for internally damped Euler‐Lagrange systems with input saturation. Compared with the previous output feedback controllers, this new design of a combined adaptive controller‐observer system will reduce the risk of actuator saturation effectively via generalized saturation functions. Semi‐global uniform ultimate boundedness stability of the tracking errors and state estimation errors is guaranteed by Lyapunov stability analysis. An application of the proposed saturated output feedback controller is the stabilization of a nonholonomic wheeled mobile robot with saturated actuators towards desired trajectories. Simulation results are provided to illustrate the efficiency of the proposed controller in dealing with the actuator saturation.