The Application and Design of the Economical Nonlinear Controller

This anticle gives a design method of the economical nonlinear controller. The controller is composed of an expert intelligent coordination controller, a fuzzy prediction controller, a fuzzy feedforward controller, a nonlinear controller and so on. The consistence of a distributed control system based on this controller is also shown briefly.

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively.In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized.Finally, the effectiveness of the proposed method is confirmed by numerical simulations.

Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance

A nonlinear controller for disturbances rejection and collision avoidance is proposed for spacecraft formation flying.The formation flying is described by a nonlinear model with the J2 perturbation and atmospheric drag. Based on the theory of the state-dependent Riccati equation（SDRE）, a finite time nonlinear control law is developed for the nonlinear dynamics involved in formation flying. Then, a compensative internal mode（IM） control law is added to eliminate disturbances.These two control laws compose a finite time nonlinear tracking controller with disturbances rejection. Moreover, taking safety requirements into account, the repulsive control law is incorporated in the composite controller to perform collision avoidance manoeuvres. A numerical simulation is presented to demonstrate the effectiveness of the proposed method.Compared to the conventional control method, the proposed method provides better performance in the presence of the obstacles and external disturbances.

Nonlinear Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System

Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine,and national defense.Some general engineering methods for chaos control have been developed in recent years,but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints.Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator.In this paper,some efficient nonlinear control methods,including wavelet function feedback control as a special nonlinear control method,are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e.,Kapchinsky-Vladimirsky,full Gauss,3-sigma Gauss,water-bag,and parabola distributions) respectively.Particles-in-cell simulations show that after control of beam halo-chaos,the beam halo strength factor is reduced to zero,and other statistical physical quantities of beam halo-chaos are doubly reduced.The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator.Some potential application of the beam halo-chaos control in experiments is finally pointed out.

Review:Recent advances in nonlinear control technologies for shape memory alloy actuators

This paper reviews recent developments in nonlinear control technologies for shape memory alloy (SMA) actuators in robotics and their related applications. SMA possesses large hysteresis, low bandwidth, slow response, and non-linear behavior, which make them difficult to control. The fast response of the SMA actuator mostly depends upon, (1) type of controller, (2) rate of addition and removal of heat, and (3) shape or form of the actuator. Though linear controllers are more desirable than nonlinear ones, the review of literature shows that the results obtained using nonlinear controllers were far better than the former one. Therefore, more emphasis is made on the nonlinear control technologies taking into account the intelligent controllers. Various forms of SMA actuator along with different heating and cooling methods are presented in this review, followed by the nonlinear control methods and the control problems encountered by the researchers.

ABSOLUTE STABILITY OF TIME-VARYING NONLINEAR CONTROL SYSTEM

In this paper the authors study two classes of time-varying nonlinear control systems. A few sufficient conditions of absolute stability of these systems were obtained by means of classical analysis and the analogue of the variation of constants formula of nonlinear systems. Moreover, they gave some sufficient conditions of absolute stability in Hurwitz angle for these systems.

CONTROLLABILITY CANONICAL FORM FOR NONLINEAR CONTROL SYSTEMS

General nonlinear control systems are studied in this paper with the goal to transform them into the so-called controllability canonteal form via state transformation only. The conditions of transformability are given for both single input and multiple input cases. Besides, by an algebraic approach the procedure for constructing the state transformation is established. This paper is formulated in the framework of calculus rather than differential geometry approach.

A new adaptive backstepping method for nonlinear control of turbine main steam valve

A new approach for nonlinear adaptive control of turbine main steam valve is developed. In comparison with the existing controller based on ＂classical＂ adaptive backstepping, this method does not follow the classical certaintyequivalence principle in the design of adaptive control law. We introduce this approach, for the first time, to power systems and present a novel parameter estimator and dynamic feedback controller for a single machine infinite bus （SMIB） system with steam valve control. This system contains unknown parameters such as reactance of transmission lines. Besides preserving useful nonlinearities and the real-time estimation of uncertain parameters, the proposed approach possesses better performances with respect to the response of the system and the speed of adaptation. The simulation results demonstrate that the proposed approach is better than the design based on ＂classical＂ adaptive backstepping in terms of properties of stability and parameter estimation, and recovers the performance of the ＂full-information＂ controller. Hence, the proposed method provides an alternative for engineers in applications.

Modified Projective Synchronization of a New Hyperchaotic System via Nonlinear Control

In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two identical hyperchaotic systems by directing the scaling factor onto the desired value. With symbolic computation system Maple and Lyapunov stability theory, numerical simulations are given to perform the process of the synchronization.

An improved nonlinear control strategy for deep space formation flying spacecraft

This paper aims to provide further study on the nonlinear modeling and controller design of formation flying spacecraft in deep space missions. First, in the Sun-Earth system, the nonlinear formation dynamics for the circular restricted three-body problem （CRTBP） and elliptic restricted three-body problem （ERTBP） are presented. Then, with the Floquet mode method, an impulsive controller is developed to keep the Chief on the desired Halo orbit. Finally, a nonlinear adaptive control scheme based on Nonzero set- point LQR and neural network is proposed to achieve high precision formation maneuver and keeping. The simulation results indicate that the proposed nonlinear control strategy is reasonable as it considers not only the orbit keeping of the Chief, but also the formation modeling inaccuracy. Moreover, the nonlinear adaptive control scheme is effective to improve the control accuracy of the formation keeping.

Improving the Performance of Motor Drive Servo Systems via Composite Nonlinear Control

This paper presents a discrete-time design of robust compositenonlinear controller to achieve fast and accurate set-pointtracking for motor servo systems subject to actuator saturationand disturbances.The basic idea here is to use a combination oflinear and nonlinear control,together with a disturbancerejection mechanism based on extended state observer.The linearcontrol part is designed to yield a fast response,and thenonlinear part serves to reduce the overshoot,while the extendedstate observer estimates simultaneously the state vector and theunknown disturbance for control and compensation.The closed-loopstability is analyzed using the Lyapunov theory.Practicalapplication in a permanent magnet synchronous motor position servosystem is given to demonstrate the effectiveness of the proposedcontrol scheme.

Robust Nonlinear Control of Continuous Stirred Tank Reactors

This paper deals with the temperature tracking control problem of continuous stirred tank reactors (CSTRs) widely used in chemical engineering. Design of robust tracking controller for a class of CSTRs plant with uncertainties is presented using input output feedback linearization techniques. The control scheme has been applied to a first order irreversible exothermic reaction process carried out in a CSTR, and simulation results show that it is effective.

Nonlinear control for global stabilization of multiple-integrator system by bounded controls

The global stabilization problem of the multiple-integrator system by bounded controls is considered. A nonlinear feedback law consisting of nested saturation functions is proposed. This type of nonlinear feedback law that is a modification and generalization of the result given in [1] needs only [（n ＋ 1）/2] （n is the dimensions of the system） saturation elements, which is fewer than that which the other nonlinear laws need. Furthermore, the poles of the closedloop system can be placed on any location on the left real axis when none of the saturation elements in the control laws is saturated. This type of nonlinear control law exhibits a simpler structure and can significantly improve the transient performances of the closed-loop system, and is very superior to the other existing methods. Simulation on a fourth-order system is used to validate the proposed method.

Synchronization of perturbed chaotic systems via nonlinear control

Chaos synchronization of systems with perturbations was investigated.A generic nonlinear control scheme to realize chaos synchronization of systems was proposed.This control scheme is flexible and practicable,and gives more freedom in designing controllers in order to achieve some desired performance.With the aid of Lyapunov stability theorem and partial stability theory,two cases were presented:1) Chaos synchronization of the system without perturbation or with vanishing perturbations;2) The boundness of the error state for the system with nonvanishing perturbations satisfying some conditions.Finally,several simulations for Lorenz system were provided to verify the effectiveness and feasibility of our method.Compared numerically with the existing results of linear feedback control scheme,the results are sharper than the existing ones.

The nonlinear control of simulator of hexapod parallel mechanism

In order to enhance the innervation fidelity of simulators,a nonlinear controller is developed,which guarantees parallel mechanisms closed loop system global asymptotical stability and the convergence of posture tracking error in Cartesian space. The problems of rapid tracking under the condition of the wide range,nonlinear and variable load are solved. After the nonlinear controller is actually applied to the hexapod parallel mechanisms of simulator,the dynamic-static capabilities of motion system are tested by amplitude-frequency response and posture precision. The experimental results show that the static precision improves ten times and system output amplitude increases and the phase lag reduces with respect to the same input signal in Cartesian space in comparison with the traditional proportional and derivative (i.e. PD) controlling method in joint space. Therefore the nonlinear controller can effectively improve the dynamic-static response performance of the hexapod parallel mechanisms of simulators in Cartesian space.

TIME PRECISE INTEGRATION METHOD FOR CONSTRAINED NONLINEAR CONTROL SYSTEM

For the constrained nonlinear optimal control problem, by taking the first term of Taylor series, the dynamic equation is linearized. Thus by, introducing into the dual variable (Lagrange multiplier vector), the dynamic equation can be transformed into Hamilton system from Lagrange system on the basis of the original variable. Under the whole state, the problem discussed can be described from a new view, and the equation can be precisely solved by, the time precise integration method established in linear dynamic system. A numerical example shows the effectiveness of the method.

THE INVARIANT MANIFOLD METHOD AND THE CONTROLLABILITY OF NONLINEAR CONTROL SYSTEM

The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application. A. M. Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics:of rigid body to nonlinear control system for the first time,and obtained a series of efficient results. Based on Kovalev's oriented manifold method, firstly, by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out. Then the realization of the necessary condition wars discussed. At last, the motion of a rigid body with two rotors,vas, investigated and the necessary condition which is satisfied by this system,vas proved.

A nonlinear control method for the electromagnetic suspension system of the maglev train

To deal with the inherent nonlinearity and open-loop instability of the electromagnetic suspension（EMS） system,a new nonlinear control method is proposed.The simulation results show that,for a PID controller,the over-shoot of the system response to an airgap step disturbance is about 3 mm,and the transient time is 6 s;however,for the proposed nonlinear controller,there is no overshoot and transient time within 2 s.The proposed method has a faster response and stronger robustness.With a designed bi-DSP suspension controller,this nonlinear control method was implemented on the Shanghai Urban Maglev Test Line（SUMTL） to validate its effectiveness and feasibility.

High-Accuracy Pneumatic Position Control by Applying Nonlinear Control and Arranging Transient Process

By applying a nonlinear control and arranging a transient process, the initiative error of the pneumatic servo positioning system is reduced largely, and a larger gain of the controller is used to improve the responding speed of the system at the same damping ratio. Therefore, a compromise is made among the responding speed, overshoot, robustness, adaptability and stability. In addition, a dynamic output feedback controller, including position velocity and acceleration （PVA） feedback, is designed to improve the performance of the system. And a nonlinear controller is reconstructed based on the linear output feedback controller to decrease noises and disturbances. The dynamic responses of the system are simulated and tested. Results show that the error is kept within 0.02 mm under different mass loads and the positioning transient process is smooth, without overshoot and speedy.

Nonlinear Control of Induction Motor： A Combination of Nonlinear Observer Design and Input-Output Linearization Technique

This paper deals with a nonlinear control strategy of induction motor that combines an input-output linearization control technique and a nonlinear observer design. It is well known that induction motors are the most widely used motors in electrical appliances, industrial control and automation. However, it is also known that induction motor control is a complex task that is due to its nonlinear characteristics. Two main features of the proposed approach are worth to be mentioned. Firstly, a nonlinear control is carried out using a nonlinear feedback linearization technique involving non available state variable measurements of the induction motor system. Secondly, a nonlinear observer is designed to estimate these pertinent but unmeasurable state variables of the machine. The circle-criterion approach is performed to compute the observer gain matrices as a solution of LMI （linear matrix inequalities） that ensure the stability conditions, in the sense of Lyapunov, of the estimated state error dynamics of the designed observer. Simulation results are presented to validate the effectiveness of the proposed approach.