Nonlinear Control Input Research Articles

Stabilization of gyrostat system with dead-zone nonlinearity in control input

This paper proposes a robust adaptive finite-time controller for stabilization of a non-autonomous electromechanical gyrostat system in the presence of model uncertainties and external disturbances. The effect of the dead-zone nonlinearity in the control input is also taken into account. Moreover, all parameters of the system are assumed to be fully unknown in advance. To deal with the system's unknown parameters, some adaptation laws are introduced. Subsequently, based on the finite-time control theory, an adaptive robust controller is proposed to stabilize the non-autonomous gyrostat system in a given finite time. Then, Lyapunov's stability theory is applied to prove the finite-time stability of the designed control scheme. Finally, a numerical simulation is given to demonstrate the efficacy and robustness of the proposed finite-time control approach.

Robust synchronization of a chaotic mechanical system with nonlinearities in control inputs

Centrifugal flywheel governors are known as chaotic non-autonomous mechanical devices used for automatic control of the speed of engines. The main characteristic of them is avoiding the damage caused by sudden change of the load torques. In this paper, the problem of robust finite-time synchronization of centrifugal flywheel governor systems is studied. The effects of unknown parameters, model uncertainties, external noises, and input nonlinearities are fully taken into account. We propose some adaptive laws to overcome the side effects of the unknown parameters of the system on the synchronization performance. Then, a robust adaptive switching controller is introduced to synchronize centrifugal flywheel governors with nonlinear control inputs in a given finite time. The finite-time fast convergence property of the proposed scheme is analytically proved and numerically illustrated.

Finite-time stabilization of non-autonomous uncertain chaotic centrifugal flywheel governor systems with input nonlinearities

The centrifugal flywheel governor is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by an abrupt change of load torque. Recent research has discovered that this system exhibits very rich and complex dynamics such as chaos. In this paper, the problem of finite-time stabilization of non-autonomous chaotic centrifugal flywheel governor systems in the presence of model uncertainties, external disturbances, fully unknown parameters and input nonlinearities is studied. Appropriate adaptation laws are designed to undertake the system’s unknown parameters. Using the adaptation laws and finite-time control theory, a robust adaptive controller is derived to stabilize the non-autonomous uncertain centrifugal flywheel governor system with nonlinear control inputs in a given finite time. The finite-time stability and convergence of the closed-loop system are analytically proved. A numerical simulation is given to show the robustness and effectiveness of the proposed finite-time controller and to verify the theoretical results of the paper.

Finite-time stabilization of a non-autonomous chaotic rotating mechanical system

This paper presents robust adaptive controllers for finite-time stabilization of non-autonomous chaotic horizontal platform systems (HPSs). The effects of uncertainties, unknown parameters and input nonlinearities are fully taken into account. Appropriate adaptation laws are designed to undertake the unknown parameters. Using the adaptation laws and finite-time control theory, first a robust adaptive controller is derived to stabilize the non-autonomous uncertain HPS in finite time. Then, considering the effects of input nonlinearities, another finite-time controller is introduced to stabilize the uncertain HPS with nonlinear control inputs. The finite-time stability and convergence of the proposed schemes are analytically proved. Two illustrative examples are given to show the robustness and feasibility of the proposed finite-time controllers.

Fuzzy adaptive tracking control of uncertain chaotic system with input perturbance and nonlinearity

In this paper, we investigate the signal tracking problem of the uncertain time-varying delay chaotic system with control input nonlinearity and the fuzzy adaptive variable structure control method is proposed. The fuzzy logic system approximates the nonlinearity of the system. The unknown time-varying delay uncertainties are compensated using an appropriate Lyapunov-Krasovskii functional. The proposed controller can make the tracking errors converge to an adjustable region and all signals of the closed system is bounded. The designed control method can have a certain robustness against the disturbance of the system. Finally, taking the simulations on a multi-scroll chaotic system for example, the effectiveness of the proposed method is illustrated.

Synchronization of modified Colpitts oscillators with structural perturbations

This paper deals with the problem of the synchronization of uncertain modified Colpitts oscillators. Considering the effect of external disturbances on the system parameters and nonlinear control inputs, a robust controller based on Lyapunov theory is designed for the output synchronization between a slave system and a master system in order to ensure the synchronization of uncertain modified Colpitts oscillator systems. This approach was chosen not only to guarantee a stable synchronization but also to reduce the effect of external perturbation. Nonadaptive feedback synchronization with only one controller for the system is investigated. Numerical simulations are performed to confirm the efficiency of the proposed control scheme.

Robust Adaptive Neural Network Control for a Class of Uncertain MIMO Nonlinear Systems With Input Nonlinearities

In this paper, robust adaptive neural network (NN) control is investigated for a general class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems with unknown control coefficient matrices and input nonlinearities. For nonsymmetric input nonlinearities of saturation and deadzone, variable structure control (VSC) in combination with backstepping and Lyapunov synthesis is proposed for adaptive NN control design with guaranteed stability. In the proposed adaptive NN control, the usual assumption on nonsingularity of NN approximation for unknown control coefficient matrices and boundary assumption between NN approximation error and control input have been eliminated. Command filters are presented to implement physical constraints on the virtual control laws, then the tedious analytic computations of time derivatives of virtual control laws are canceled. It is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed-loop system. Finally, simulation results are presented to illustrate the effectiveness of the proposed adaptive NN control.

Robust performance for an energy sensitive wireless body area network – an anti-windup approach

This paper applies a robust anti-windup (AW) based control scheme to optimise throughput rate for an 802.15.4 wireless body area network (WBAN) that is subject to naturally occurring input saturation constraints. The technique uses an intuitively appealing two step design procedure. Firstly, a robust H∞ loop-shaping linear controller is designed providing nominal (un-saturated) robust performance. Then Weston–Postlethwaite AW compensation techniques are used to minimise the adverse effects of any control input non-linearities on closed loop performance. The methodology provides guaranteed quality of service (in this context taken to mean that sufficient data is always available to reassemble the required biometric waveforms, e.g. ECG) while concurrently minimising power consumption over an extended usage period. This joint robust performance question is validated on an experimental mote based 802.15.4 wireless sensor network.

Adaptive Dynamic Inversion via Time-Scale Separation

This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.

Adaptive Variable Structure and Active Vibration Reduction for Flexible Spacecraft under Input Nonlinearity

This paper is concerned with vibration control of a flexible spacecraft in the presence of parametric uncertainty/external disturbances as well as control input nonlinearity through distributed piezoelectric sensor/actuator technology. To satisfy pointing requirements and simultaneously suppress vibrations, two separate control loops are adopted. The first uses piezoceramics as sensors and actuators to actively suppress certain flexible modes by designing suboptimal positive position feedback (SOPPF) compensators which add damping to the flexible structures in certain critical modes. The problem of determining the SOPPF gain is formulated as static output feedback problem. The second feedback loop is designed based on an output feedback sliding mode control (OFSMC) design where control input nonlinearity is taken into consideration. The controller has the ability to reject the disturbance, deal with uncertainty and to ensure that the system trajectories globally converge to the sliding mode. Furthermore, an adaptive version of the proposed controller is achieved through releasing the limitation of knowing the bounds of the uncertainties and perturbations in advance. Simulation studies for the proposed control strategy on a flexible spacecraft have been carried out which demonstrate the effectiveness of the proposed approach.

Synchronization and anti-synchronization coexist in two-degree-of-freedom dissipative gyroscope with nonlinear inputs

This study demonstrates that synchronization and anti-synchronization can coexist in two-degree-of-freedom dissipative gyroscope system with input nonlinearity. Because of the nonlinear terms of the gyroscope system, the system exhibits complex motions containing regular and chaotic motions. Using the variable structure control technique, a novel control law is established which guarantees the hybrid projective synchronization including synchronization, anti-synchronization and projective synchronization even when the control input nonlinearity is present. By Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode, and two variable structure controllers (VSC) are designed to guarantee the hitting of the sliding surfaces. Numerical simulations are presented to verify the proposed synchronization approach.

Robust synchronization of drive–response chaotic systems via adaptive sliding mode control

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.

3315 記述関数法に基づくアクティブサスペンションのインテグラルスライディングモード制御(非線形制御理論とその応用(1))

This paper presents an integral sliding mode controller with describing function method for active suspension systems. The proposed controller can occur a desirable limit cycle in the vicinity of switching surface, since the controller despairs perfect sliding modes. As a result, deterioration of the control effect due to the chattering in the high frequency range, such as increase in acceleration of the sprung mass related to the ride comfort, can be suppressed. The nonlinear switching control input in the proposed controller is based on the twisting algorithm. A necessity condition and a setting procedure for the parameters of the controller are demonstrated. A consideration of the robustness for the proposed method is presented. Finally, simulation results show the effectiveness of the proposed controller.

Decentralized control for synchronization of delayed neural networks subject to dead-zone nonlinearity

This article aims to present a decentralized synchronization scheme for a class of delayed neural networks subject to dead-zone nonlinearity in control input. On the basis of the drive–response concept and the Lyapunov stability theory, a decentralized control law is proposed for guaranteeing global synchronization even when input nonlinearity is present. The proposed controller is suitable for application in delayed cellular neural networks (DCNNs) and delayed Hopfield neural networks (DHNNs) with no restriction on the derivative of the time-varying delays. Finally, computer simulations are provided to demonstrate the effectiveness of the proposed synchronization scheme.

Chaos and adaptive control in two prey, one predator system with nonlinear feedback

We show that the continuous time three species prey–predator populations can be asymptotically stabilized using a nonlinear feedback control inputs. The necessary feedback control law for asymptotic stability of this system is obtained. The system appears to exhibit a chaotic behavior for a range of parametric values. The range of the system parameters for which the subsystems converge to limit cycles is determined. The results of some other models in the literature can be obtained as special cases of the present model. Numerical examples and analysis of the results are presented.

Control of Three-axis Stabilized Flexible Spacecraft Using Variable Structure Strategies Subject to Input Nonlinearities

This paper proposes a robust control algorithm for stabilization of a three-axis stabilized flexible spacecraft in the presence of model uncertainty, external disturbances and control input nonlinearities. This control algorithm is based on a variable structure output feedback control design technique, and explicitly accounts for the control input nonlinearities in the stability analysis. The proposed variable structure output feedback controller ensures the global reaching condition of the sliding mode of the spacecraft dynamics system. Moreover, in the sliding mode, the investigated dynamic system still retains the robustness with respect to the uncertainties and disturbances it possesses for a system with linear input. An attractive additional feature of the control method is that the structure of the controller is independent of the elastic mode dynamics of the spacecraft, since in practice the measurement of flexible modes is typically difficult or impractical. It is also shown that an adaptive version of the proposed controller can be achieved by removing the need to know the bounds of the uncertainties and perturbations in advance. Numerical simulations show that the precise attitude control and vibration suppression can be accomplished using the derived controller for both cases with and without adaptive control.

Adaptive Variable Structure Maneuvering Control and Vibration Reduction of Three-axis Stabilized Flexible Spacecraft

This paper proposes a robust control algorithm for stabilization of a three-axis flexible spacecraft in the presence of model uncertainty, external disturbances and control input nonlinearities. This control algorithm is based on variable structure output feedback control design technique that explicitly accounts for the control input nonlinearities in the stability analysis. Asymptotically and exponentially stable design methods are investigated for constructing the controller to stabilized uncertain system with input nonlinearities. Two kinds of the controller are presented that both ensures the global reaching condition of the sliding mode of the spacecraft dynamics system. Moreover, in the sliding mode, the dynamics system under study still bears the insensitivity to the uncertainties and disturbances as the system with linear input. An additional attractive feature of the control method is that the structure of controller is independent of the elastic mode dynamics of the spacecraft, since in practice the measurement of flexible modes is not easy or feasible. It is also shown that an adaptive version of the proposed controller is achieved through removing requirements of knowing the bounds of the uncertainties and perturbations in advance. Furthermore, a modified adaptation control law is given to improve the adaptive performances such that a new controller is designed which can guarantee the boundedness of the closed-loop system. Numerical simulations show that the precise attitude and vibration suppression can be accomplished using the derived controller for both cases with and without adaptive control.

Effectiveness and limitation of circle criterion for LTI robust control systems with control input nonlinearities of sector type

AbstractThis paper considers linear time invariant systems with sector type nonlinearities and proposes regional ℒ︁2 performance analysis and synthesis methods based on the circle criterion. In particular, we consider the effect of non‐zero initial states and/or an ℒ︁2 disturbance inputs on the ℒ︁2 norm of a selected performance output. We show that both analysis and synthesis problems can be recast as linear matrix inequality (LMI) optimization problems, where, for synthesis, the outputs of the nonlinear elements are assumed available for control. Moreover, it is shown when the circle criterion does or does not help to improve the performance bound in robust control synthesis when compared with the existing linear analysis method. Copyright © 2005 John Wiley & Sons, Ltd.

Compensation of Actuator Dynamics in Nonlinear Missile Control

This brief presents an approach to the compensation of the actuator dynamics in nonlinear missile control. In general, actuator dynamics are not considered in nonlinear missile control systems. Here, we analyzed the influences of actuator dynamics on the nonlinear missile controller and found that the second-order actuator dynamics showed risks of potentially destabilizing the overall system. Thus, to accommodate for the influence of the actuator dynamics, a compensator is proposed where the information of the nonlinear control input and the actual fin deflection is incorporated. We also conducted performance and stability analysis for the proposed control system, including actuator dynamics. We were able to confirm the validity of the proposed approach based on simulation results for the first- and second-order actuator dynamics.

Output Feedback Sliding Mode Control for Bending and Torsional Vibration Control of 6-story Flexible Structure

We discuss bending and torsional vibration control of a 6-story flexible structure. In the case in which the vibration control of high-rise buildings is considered, it is necessary to design a controller which shows good control performances, and which is simply designed so that personnel expenses are reduced. To this end, we have applied a sliding mode control theory, which is one of nonlinear robust control theories. By adopting this theory, the control system may easily be designed in a very short time. However, since it is in few cases that each story is provided with a sensor, this controller is generally designed as a state feedback controller, and is difficult to realize a state feedback. Therefore, the sliding mode controller should be designed as an output feedback controller. Accordingly, we have designed two output feedback sliding mode controllers by using minimum error excitation method. The first controller is constructed with only nonlinear control inputs, and the second controller is constructed with both linear and nonlinear inputs. We have investigated their performances by numerical simulations and experiments. In this paper, design methods, control system design constraints, and characteristics in flexible structural control will be explained.