Composite Nonlinear Feedback Control Law Research Articles

Robust integral controller design based on composite nonlinear feedback in uncertain systems with constrained inputs and external disturbances

AbstractIn this article, to enhance the transient performances in constrained uncertain systems, a control technique based on linear matrix inequality (LMI) is characterized to the robust integral composite nonlinear feedback (CNF) controller design. To achieve this aim, considering the inputs limitations and the uncertainties, the regulation is transformed into a minimization subjected to several LMIs. Solving an optimization in real‐time, the gains of the controller are calculated. So, the regulation and the disturbance rejection are effectively handled employing the presented control law. Compared with the existing integral methodology, the provided simulations validate the applicability of the robust integral CNF control law in uncertain systems.

Anti-disturbance sliding mode control for uncertain nonlinear systems

In this paper, the problem of disturbance-based nonlinear sliding mode observer design is investigated for uncertain time-delay repeated scalar nonlinear systems subject to quantisation output measurement. State and disturbance observers are constructed by using the quantised measured output. Then, an improved nonlinear sliding surface is developed, and sufficient conditions are obtained for the sliding mode dynamics to be asymptotically stable with the desired performance level. In addition, a composite nonlinear feedback control law is synthesised to guarantee the reachability of the nonlinear surface. Finally, examples and simulations are presented to demonstrate the effectiveness of the proposed new design techniques.

Modified composite nonlinear feedback control for output tracking of nonstep signals in singular systems with actuator saturation

SummaryThis paper considers output tracking of nonstep reference signals for multi‐input multi‐output singular systems subject to actuator saturation and external disturbances. Singularity of the system alongside the actuator saturation constraint and external disturbances adds more complexity to stability analysis and controller design than normal systems. Moreover, the problem of output tracking of nonstep reference signals in singular systems via the composite nonlinear feedback (CNF) control law is not studied so far in the literature, and this article will investigate this problem for the first time by proposing the modified CNF control law. For this purpose, first, a singular reference generator system is constructed to produce the desired nonstep reference signal. Then, the dynamical error system is obtained by defining a new state vector as the tracking error and augmenting it to the main system. Different parts of the modified CNF control law are designed afterwards. Due to complexities caused by the singularity of the system and the saturation constraint, detailed mathematical calculations are done. In this regard, a theorem is given that guarantees the tracking problem for three different cases of the saturation function. Moreover, the given theorem will investigate the uniform ultimate boundedness analysis of the tracking error in the face of external disturbances. Finally, the theoretical results are affirmed by computer simulations through three examples to verify the performance and applicability of the proposed control law.

Robust composite nonlinear feedback control for spacecraft rendezvous systems under parameter uncertainty, external disturbance, and input saturation

This paper presents a new robust composite nonlinear feedback control law for accurate, smooth, and fast regulation in the presence of parameter uncertainties, external disturbances, and input saturation for a class of spacecraft rendezvous systems. The novel proposed method consists of the original composite nonlinear feedback part for good transient performance plus a nonlinear disturbance rejection part for reducing the steady-state error stemming from variable disturbances and simultaneously producing feasible control input. The nonlinear disturbance rejection relies on sliding-mode observer for disturbance estimation. Closed-loop system stability has been proved with the Lyapunov theory. Simulation results show the closed-loop stability and superior control performance.

A robust control approach for MEMS capacitive micromachined ultrasonic transducer

An optimal composite nonlinear feedback control method with integral sliding mode is presented in this paper. The controller extends the travel range of the micro-electromechanical system capacitive micromachined ultrasonic transducer (CMUT). Moreover, enhanced transient response and precise tracking performance is achieved. It is known that CMUT is inherently unstable which results in pull-in phenomenon and it is very sensitive to small perturbations, so one of the major problems is to stabilize the CMUT beyond the pull-in limit with the external disturbances. In addition, the input saturation problem is significant to CMUT. Based on that, a robust control scheme is derived using composite nonlinear feedback control law combined with integral sliding mode control law. Then all the tuning parameters for the proposed control method are converted into a minimization problem and solved by particle swarm optimization algorithm automatically. We verified the effectiveness through extending the travel range of the CMUT gap by three control methods which are proportional integral derivative, composite nonlinear feedback and the method we proposed. The stability and small range tracking performance with three control methods is compared on the pull-in position of CMUT. The simulations show that the proposed control method has desired tracking performance and robustness to external disturbance with input saturation.

Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation

ABSTRACTThis paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.

Transient Performance Improvement in Tracking Control for a Class of Nonlinear Systems with Input Saturation

This paper addresses the composite nonlinear feedback (CNF) control for a class of singleinput single-output nonlinear systems with input saturation to track a time varying reference target with good transient performance. The CNF control law consists of a tracking control law and a performance compensator. The tracking control law is designed to drive the output of the system to track the time varying reference target rapidly, while the performance compensator is used to reduce the overshoot caused by the tracking control law. The stability of the closed-loop system is established. The design procedure and the improvement of transient performance of the closed-loop system are illustrated with a numerical example and the controlled Van del Pol oscillator.

A new continuous sliding mode control approach with actuator saturation for control of 2-DOF helicopter system

The 2-degree of freedom (DOF) helicopter system is a typical higher-order, multi-variable, nonlinear and strong coupled control system. The helicopter dynamics also includes parametric uncertainties and is subject to unknown external disturbances. Such complicated system requires designing a sophisticated control algorithm that can handle these difficulties. This paper presents a new robust control algorithm which is a combination of two continuous control techniques, composite nonlinear feedback (CNF) and super-twisting control (STC) methods. In the existing integral sliding mode (ISM) based CNF control law, the discontinuous term exhibits chattering which is not desirable for many practical applications. As the continuity of well known STC reduces chattering in the system, the proposed strategy is beneficial over the current ISM based CNF control law which has a discontinuous term. Two controllers with integral sliding surface are designed to control the position of the pitch and the yaw angles of the 2- DOF helicopter. The adequacy of this specific combination has been exhibited through general analysis, simulation and experimental results of 2-DOF helicopter setup. The acquired results demonstrate the good execution of the proposed controller regarding stabilization, following reference input without overshoot against actuator saturation and robustness concerning to the limited matched disturbances.

Semi-global output regulation for discrete-time singular linear systems with input saturation via composite nonlinear feedback control

The semi-global output regulation problem of multi-variable discrete-time singular linear systems with input saturation is investigated in this paper. A composite nonlinear feedback control law is constructed by using a low gain feedback technique for semi-global stabilisation of discrete-time singular linear systems with input saturation. The sufficient solvability conditions of the semi-global output regulation problem by composite nonlinear feedback control are established. When the composite nonlinear feedback control law is reduced to a linear control law, the solvability conditions are an exact discrete-time counterpart of the semi-global output regulation problem of continuous-time singular linear systems. With the extra control freedom of the nonlinear part in the composite nonlinear feedback control law, the transient performance of the closed-loop system can be improved by carefully choosing the linear feedback gain and the nonlinear feedback gain. The design procedure of the composite nonlinear feedback control law and the improvement of the transient performance are illustrated by a numerical example.

Output feedback composite nonlinear feedback control for singular systems with input saturation

This paper addresses the output feedback composite nonlinear feedback (CNF) controller design for a tracking control problem of single-input single-output (SISO) singular linear systems with input saturation. The output feedback CNF control law is constructed based on a state feedback CNF control law for the tracking control problem and a state observer. The stability of the closed-loop system under the output feedback CNF control law is established for an output feedback CNF control law with a singular full state observer. The design procedure and the improvement of the transient performance of the closed-loop system are illustrated with an example.

An Observer-Based Mode Switching Control Scheme for Improved Position Regulation in Servomotors

A mode switching control scheme is proposed to achieve fast and precise set-point tracking in motor servo systems. The control scheme incorporates a composite nonlinear feedback (CNF) control law into the framework of proximate time-optimal servomechanism (PTOS). The CNF control law consists of a linear feedback part for achieving fast response and a nonlinear feedback part for suppressing the overshoot, so as to improve the transient performance in short span positioning, while the PTOS control law is responsible for fast acceleration and deceleration when the tracking error is large. A reduced-order extended state observer is designed to estimate the unmeasured velocity and unknown disturbance for feedback and compensation. The closed-loop stability is analyzed theoretically. The control scheme is then applied to the position-velocity control loop in a permanent magnet synchronous motor servo system. Experimental studies have been carried out using the TMS320F2812 digital signal controller board. The results verify that the controlled system is capable of tracking a wide range of target positions fast, smoothly, and accurately, with some degrees of performance robustness against disturbance and uncertainty.

Integral sliding mode based optimal composite nonlinear feedback control for a class of systems

This paper presents an optimization method of designing the integral sliding mode (ISM) based composite nonlinear feedback (CNF) controller for a class of low order linear systems with input saturation. The optimal CNF control is first designed as a nominal control to yield high tracking speed and low overshoot. The selection of all the tuning parameters for the CNF control law is turned into a minimization problem and solved automatically by particle swarm optimization (PSO) algorithm. Subsequently, the discontinuous control law is introduced to reject matched disturbances. Then, the optimal ISM-CNF control law is achieved as the sum of the optimal CNF control law and the discontinuous control law. The effectiveness of the optimal ISM-CNF controller is verified by comparing with a step by step designed one. High tracking performance is achieved by applying the optimal ISM-CNF controller to the tracking control of the micromirror.

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.

Composite nonlinear feedback controller design for an overhead crane servo system

This paper investigates the design of a composite nonlinear feedback (CNF) control law for an overhead crane servo system to improve the transient performance of both displacement tracking of the trolley and anti-sway of the payload. To address the property of underactuation of the overhead crane system, a novel nonlinear function of the CNF control law is specifically proposed to compromise the tracking performance of the trolley and the anti-sway performance of the payload. The performance improvement in both tracking of the trolley and anti-sway of the payload is illustrated with a complete comparison between the CNF control method and the trajectory planning method, which has been proposed in recent literature. The simulation results show that this well-tuned CNF control law can significantly shorten the settling time of the trolley displacement tracking and reduce the sway of the payload.

Relative position keeping in satellite formation flying with input saturation

This paper studies a relative position keeping problem in satellite formation flying with input saturation. The relative motion dynamics is designed with polytopic-type uncertainties by considering elliptic and noncoplanar formation, and unknown angular rate and acceleration within some boundary. A composite nonlinear feedback control law is developed by using a low-and-high gain control scheme with an algebraic Riccati inequality (ARI). In the presence of input saturation and disturbances, finite-gain L∞ stability of the relative motion dynamics is ensured using the proposed control law. Additionally, the domain of attraction for the stability is evaluated by formulating an optimization problem. Through numerical simulations, the validity of the proposed scheme is illustrated.

Improving transient performance for output regulation problem of linear systems with input saturation

SUMMARYThis paper addresses the transient performance of output regulation problem for general linear system with input saturation. To improve the transient performance, the composite nonlinear feedback (CNF) control technique is introduced to solve the output regulation problem. On the basis of the linear feedback control law that solves the output regulation problem, a state feedback CNF control law and an output feedback with feedforward CNF control law are constructed, respectively. The CNF control law consists of a linear feedback part and a nonlinear feedback part. Introducing the nonlinear feedback part does not change the solvability condition of the output regulation problem, but the transient performance can be improved significantly by appropriately choosing the linear feedback gain and the nonlinear feedback gain in the CNF control law. The effectiveness of the CNF control is illustrated by a disturbance rejection problem.Copyright © 2012 John Wiley & Sons, Ltd.

Precise control of linear systems subject to actuator saturation using tracking differentiator and reduced order composite nonlinear feedback control

Aiming at the actuator saturation problem and the system performance requirement, this article proposes a new control scheme, i.e. a newly developed tracking differentiator-composite nonlinear feedback (TDCNF) control law, which is the combination of a tracking differentiator (TD) and a reduced order composite nonlinear feedback (CNF) control law. The TD, used here, mainly helps to provide a smooth reference signal and largely avoid actuator saturation. The reduced order CNF control law, on the one hand, estimates those unmeasurable state variables for measurement feedback control and, on the other hand, ensures satisfactory system performance. The stability of the newly developed TDCNF is proved in detail. Finally, to verify the effectiveness of the newly developed TDCNF control law, two illustrative examples are demonstrated and therein a novel design of the proposed control law is given. Simulation results show that the proposed control law can achieve good tracking performance and effectively avoid the actuator saturation.

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.

Composite Nonlinear Feedback Control for Output Regulation Problem of Linear Systems with Input Saturation

AbstractThis paper addresses output regulation problem for general linear systems subject to input saturation by composite nonlinear feedback (CNF) control. The CNF control law is constructed based on a switch control law which solves the output regulation problem by introducing a nonlinear feedback part. The purpose of the nonlinear feedback part is to improve the transient performance of the output response of the closed-loop system. It is shown that the nonlinear part of CNF control law does not change the solvability conditions of the output regulation problem. The effectiveness of the CNF control law is illustrated with an example by comparing the CNF control law and the original switch control law.

Structural design of composite nonlinear feedback control for linear systems with actuator constraint

AbstractThe performance of the composite nonlinear feedback (CNF) control law relies on the selection of the linear feedback gain and the nonlinear function. However, it is a tough task to select an appropriate linear feedback gain and appropriate parameters of the nonlinear function because the general design procedure of CNF control just gives some simple guidelines for the selections. This paper proposes an operational design procedure based on the structural decomposition of the linear systems with input saturation. The linear feedback gain is constructed by two linear gains which are designed independently to stabilize the unstable zero dynamics part and the pure integration part of the system respectively. By investigating the influence of these two linear gains on transient performance, it is flexible and efficient to design a satisfactory linear feedback gain for the CNF control law. Moreover, the parameters of the nonlinear function are tuned automatically by solving a minimization problem. The proposed design procedure is illustrated by applying it to design a tracking control law for the inverted pendulum on a cart system.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society