Output-feedback control for switched linear systems subject to actuator saturation

This article is devoted to the output-feedback ?_∞ control problem for switched linear systems subject to actuator saturation. We consider both continuous- and discrete-time switched systems. Using the minimal switching rule, nonlinear output feedbacks expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional ?₂ (?₂)-gains over a class of energy-bounded disturbances. The conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation. A spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach.     

Switching control of linear systems subject to asymmetric actuator saturation

In this paper, we study the saturation control problem for linear time-invariant (LTI) systems subject to asymmetric actuator saturation under a switching control framework. The LTI plant with asymmetric saturation is first transformed to an equivalent switched linear model with each subsystem subject to symmetric actuator saturation, based on which a dwell-time switching controller augmented with a controller state reset is then developed by using multiple Lyapunov functions. The controller synthesis conditions are formulated as linear matrix inequalities (LMIs), which can be solved efficiently. Simulation results are also included to illustrate the effectiveness and advantages of the proposed approach.     

Adaptive actuator fault compensation control for a rigid-flexible manipulator with ODEs-PDEs model

In this paper, the actuator fault problem is studied for a two-link rigid-flexible manipulator system in the presence of boundary disturbance and state constraint. The system consists of a rigid beam, a flexible beam and a payload at the end, which are described by hybrid ordinary differential equations–partial differential equations. The novel controller includes a proportional-derivative feedback structure, a disturbance observer and a fault-tolerant algorithm, which can regulate the joint positions and eliminate vibration of flexible beam, on circumstance of boundary disturbance and actuator fault. With the help of Barrier Lyapunov Function, the states will not be violated. It is proved that the closed-loop system has asymptotic stability by LaSalle Invariance Principle. Simulations are provided to demonstrate the effectiveness of the proposed controller.     

Robust robot manipulator control with autonomous consideration algorithm of torque saturation

As each joint actuator of a robot manipulator has a limit value of torque, the motion control system should consider the torque saturation. Conventional motion control based on robust acceleration controller cannot consider the torque saturation and it often causes an oscillated or wrong response. This paper proposes a new autonomous consideration method of joint torque saturation for robust manipulator motion control. The proposed method consists of three on-line autonomous algorithms. These algorithms are the torque limitation algorithm in joint space, the adjustment algorithm of motion control in Cartesian space, and the adjustment algorithm of motion reference in Cartesian space. The robot motion control using the proposed algorithms realizes smooth and robust robot motion response.     

Dissipative control for singular time-delay system with actuator saturation via state feedback and output feedback

This paper is devoted to the problem of dissipative control for a class of singular time-delay systems with actuator saturation via state feedback and output feedback. First, by tuning the Wirtinger-based integral and the double integral inequality, a sufficient condition is derived to guarantee that the singular time-delay system is regular, impulse free, asymptotically stable and strictly (Q,S,R)-dissipative. Then, based on the derived condition, and applying linear matrix inequality techniques, the dissipative state feedback and output feedback controller are synthesised. Moreover, the maximal estimate of the domain of attraction is proposed by an optimisation problem. Finally, some simulation examples are provided to verify the effectiveness of the obtained theoretic results.     

Finite-time tracking control for robot manipulators with actuator saturation

This paper addresses the finite-time tracking of robot manipulators in the presence of actuator saturation. The commonly-used proportional-derivative (PD) plus dynamics compensation (PD+) scheme is extended by replacing the linear errors in the PD+ scheme with saturated non-smooth but continuous exponential-like ones. Advantages of the proposed controller include semi-global finite-time tracking stability featuring faster transient and high-precision performances and the ability to ensure that actuator constraints are not violated. This is accomplished by selecting control gains a priori, removing the possibility of actuator failure due to excessive torque input levels. Lyapunov's direct method and finite-time stability are employed to prove semi-global finite-time tracking. Simulations performed on a three degree-of-freedom (DOF) manipulator are provided to illustrate the effectiveness and the improved performance of the formulated algorithm.     

Event-triggered control for semi-global stabilisation of systems with actuator saturation

This paper investigates the problem of event-triggered control for semi-global stabilisation of null controllable systems subject to actuator saturation. First, for a continuous-time system, novel event-triggered low-gain control algorithms based on Riccati equations are proposed to achieve semi-global stabilisation. The algebraic Riccati equation with a low-gain parameter is utilised to design both the event-triggering condition and the linear controller; a minimum inter-event time based on the Riccati ordinary differential equation is set a priori to exclude the Zeno behaviour. In addition, the high–low gain techniques are utilised to extend the semi-global results to event-based global stabilisation. Furthermore, for a discrete-time system, novel low-gain and high–low-gain control algorithms are proposed to achieve event-triggered stabilisation. Numerical examples are provided to illustrate the theoretical results.     

具有执行器饱和特性的不确定系统预测控制器设计

针对具有执行器饱和特征的不确定系统,提出了一种带有状态观测器的新型预测控制器设计方法.该方法在滚动优化的每一步,采用带有饱和特性的反馈控制结构得到一个最优控制律.使无穷时域性能指标最小.考虑在状态不完全已知的情况下,设计了带有状态观测器的预测控制器,并通过观测器参数调整使闭环系统渐近稳定.通过仿真实验验证了所设计控制器的有效性.     

Analysis and design of delta operator systems with nested actuator saturation

In this paper, the problem of estimating the domain of attraction is considered for delta operator systems subject to nested actuator saturation. A set invariance condition is established for the delta operator system with nested actuator saturation in terms of auxiliary feedback matrices. Based on the set invariance condition, an optimisation approach is proposed to estimate the domain of attraction for the delta operator system. Thereby, the partial results of nested actuator saturation for both continuous-time systems and discrete-time systems are extended to delta operator system framework. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

Low-and-high gain design technique for linear systems subject to input saturation —a direct method

The low-and-high gain design technique, which was initiated for a chain of integrators and completed for general linear asymptotically null controllable with bounded controls systems, was conceived for semi-global control problems beyond stabilization and was related to the performance issues such as semi-global stabilization with enhanced utilization of the available control capacity and semi-global disturbance rejection. Although the low-and-high gain design technique, as initiated for a chain of integrators, is based on an explicit eigenstructure assignment algorithm, its full development is based on the solution of an algebraic Riccati equation (ARE) which is paramterized in an arbitrarily small scalar, called low gain, parameter. In this paper, we develop a new complete low-and-high gain design procedure which is based on an explicit eigenstructure assignment algorithm. The new design approach avoids the solution of the numerically stiff parametrized ARE. © 1997 by John Wiley & Sons, Ltd.     

Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation

In this paper, the problem of robust fault tolerant control for a class of singular systems subject to both time-varying state-dependent nonlinear perturbation and actuator saturation is investigated. A sufficient condition for the existence of a fixed-gain controller is first proposed which guarantees the regularity, impulse-free and stability of the closed-loop system under all possible faults. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. An adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online. Both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart. An example is included to illustrate the proposed procedures and their effectiveness.     

Supervisory control of production-distribution systems with saturation decisions

In this paper, the supervisor implementation which guarantees good performance for saturation operation and prevents reset windup is presented. Moreover, the bounded-input bound-output (BIBO) stability for saturated systems using supervisory control with a dynamic controller is provided in the time domain.     

Quaternion-based attitude synchronisation for multiple rigid bodies in the presence of actuator saturation

This paper concentrates on the quaternion-based attitude synchronisation problems of networked rigid bodies under fixed and undirected communication topology without relative angular measurements in the presence of actuator saturation. We first consider the leaderless attitude synchronisation problem with zero final angular velocity. In this case, we not only discuss the performance under the acyclic communication topology with the proposed bounded control algorithm, but also analyse that if there exist cycles in the topology, the proposed bounded algorithm guarantees that all equilibrium points are unstable except that the attitudes of networked rigid bodies achieve synchronisation. We also expand the result to the case of attitude tracking synchronisation with a static leader in the presence of actuator saturation. Next, the tracking synchronisation problem with the desired time-varying attitude is addressed in the presence of actuator saturation. Numerical examples are provided to validate the effectiveness of the proposed bounded schemes and illustrate the performances of multiple rigid bodies.     

Robust stabilisation and L2 -gain analysis for switched systems with actuator saturation under asynchronous switching

Robust stabilisation and L₂-gain analysis for a class of switched systems with actuator saturation are studied in this paper. The switching signal of the controllers lags behind that of the system modes, which leads to the asynchronous switching between the candidate controllers and the subsystems. By combining the piecewise Lyapunov function method with the convex hull technique, sufficient conditions in terms of LMIs for the solvability of the robust stabilisation and weighted L₂-gain problems are presented respectively under the dwell time scheme. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed results.     

Adaptive fault-tolerant control of linear systems with actuator saturation and L_2-disturbances

This paper studies the problem of designing adaptive fault-tolerant H-infinity controllers for linear timeinvariant systems with actuator saturation.The disturbance tolerance ability of the closed-loop system is measured by an optimal index.The notion of an adaptive H-infinity performance index is proposed to describe the disturbance attenuation performances of closed-loop systems.New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compe...     

Fault-tolerant control of linear systems using adaptive virtual actuator

In this paper, design and development of fault-tolerant control (FTC) is investigated for linear systems subject to loss of effectiveness and time-varying additive actuator faults as well as an external disturbance using the fault-hiding approach. The main aim of this approach is to keep the nominal controller and to design a virtual actuator that is inserted between the faulty plant and the nominal controller in order to hide actuator faults and disturbances from the nominal controller, and consequently the performance of the system before and after the occurrence of actuator faults is kept to be the same. The proposed adaptive virtual actuator does not require a separated fault detection, isolation and identification (FDII) unit and both state and output feedback cases are considered. An illustrative example is given to demonstrate the effectiveness of the proposed adaptive virtual actuator in both cases.     

Adaptive-like control methodologies for a CSTR system with dynamic actuator constraints

This paper deals with a catalytic continuous stirred tank reactor example, modeled as a two-input constrained nonlinear system. Under the Lyapunov-based linearization strategy, the saturation-type parameterized control design can reduce the effect of actuator subject to amplitude and rate constraints. Using the two-input control framework, it turns out to be robust against unknown disturbances, and it also ensures the asymptotic output regulation. For the purpose of practical implementation, the adaptive-like control methodology is developed. A reduced-order nonlinear observer plus the integration of both controllers is synthesized. Our results are illustrated via numerical simulation.     

Anti-windup control design for exponentially unstable LTI systems with actuator saturation

In this paper, a new saturation control technique in the framework of anti-windup compensation is developed for exponentially unstable linear time-invariant systems subject to input nonlinearities. The proposed control algorithm guarantees regional stability in the existence of input saturation, and provides less conservative performance than most existing anti-windup schemes. Moreover, an explicit form of anti-windup controller with its order no more than the order of the plant is derived. An inverted pendulum example is used to demonstrate the advantages of the newly proposed anti-windup control technique.     

Distributed model predictive control for polytopic uncertain systems subject to actuator saturation

In this paper, we present a distributed model predictive control (MPC) algorithm for polytopic uncertain systems subject to actuator saturation. The global system is decomposed into several subsystems. A set invariance condition for polytopic uncertain system with input saturation is identified and a min–max distributed MPC strategy is proposed. The distributed MPC controller is designed by solving a linear matrix inequalities (LMIs) optimization problem. An iterative algorithm is developed for making coordination among subsystems. Case studies are carried out to illustrate the effectiveness of the proposed algorithm.