Feedback linearization and equivalent-disturbance compensation control strategy for piezoelectric stage

Piezoelectric stages use piezoelectric actuators and flexure hinges as driving and amplifying mechanisms,respectively.These systems have high positioning accuracy and high-frequency responses,and they are widely used in various precision/ultra-precision positioning fields.However,the main challenge with these devices is the inherent hysteresis nonlinearity of piezoelectric actuators,which seriously affects the tracking accuracy of a piezoelectric stage.Inspired by this challenge,in this work,we developed a Hammerstein model to describe the hysteresis nonlinearity of a piezoelectric stage.In particular,in our proposed scheme,a feedback-linearization algorithm is used to eliminate the static hysteresis nonlinearity.In addition,a composite controller based on equivalent-disturbance compensation was designed to counteract model uncertainties and external disturbances.An analysis of the stability of a closed-loop system based on this feedback-linearization algorithm and composite controller was performed,and this was followed by extensive comparative experiments using a piezoelectric stage developed in the laboratory.The experimental results confirmed that the feedback-linearization algorithm and the composite controller offer improved linearization and trajectory-tracking performance.

Impact angle control over composite guidance law based on feedback linearization and finite time control

The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation of guidance systems into the feedbackable linearization model, in which the guidance law is obtained without considering the impact angle via FLC. For the purpose of the line of sight(LOS) angle and its rate converging to the desired values, the second-order LOS angle is considered as a double-integral system. Then, this paper utilizes FTC to design a controller which can guarantee the states of the double-integral system converging to the desired values. Numerical simulation illustrates the performance of the IACG, in contrast to the existing guidance law.

Feedback linearization of the nonlinear model of a small-scale helicopter

In order to design a nonlinear controller for small-scale autonomous helicopters, the dynamic characteristics of a model helicopter are investigated, and an integrated nonlinear model of a small-scale helicopter for hovering control is presented. It is proved that the nonlinear system of the small-scale helicopter can be transformed to a linear system using the dynamic feedback linearization technique. Finally, simulations are carried out to validate the nonlinear controller.

Investigation on full vehicle height control algorithm using feedback linearization method

Aiming to improve the control accuracy of the vehicle height for the air suspension system,deeply analyzing the processes of variable mass gas thermodynamics and vehicle dynamics,a nonlinear height control model of the air suspension vehicle was built. To deal with the nonlinear characteristic existing in the lifting and lowering processes,the nonlinear model of vehicle height control was linearized by using a feedback linearization method. Then,based on the linear full vehicle model,the sliding model controller was designed to achieve the control variables. Finally,the nonlinear control algorithm in the original coordinates can be achieved by the inverse transformation of coordinates. To validate the accuracy and effectiveness of the sliding mode controller,the height control processes were simulated in Matlab,i. e.,the lifting and lowering processes of the air suspension vehicle were taken when vehicle was in stationary and driving at a constant speed. The simulation results show that,compared to other controllers,the designed sliding model controller based on the feedback linearization can effectively solve the ＂overshoot＂problem,existing in the height control process,and force the vehicle height to reach the desired value,so as to greatly improve the speed and accuracy of the height control process. Besides,the sliding mode controller can well regulate the roll and pitch motions of the vehicle body,thereby improving the vehicle＇s ride comfort.

A Fully Differential Interface Circuit of Closed-loop Accelerometer with Force Feedback Linearization

In this paper,a fifth-order fully differential interface circuit( IC) is presented to improve the noise performance for micromechanical sigma-delta( Σ-Δ) accelerometer. A lead compensator is adopted to ensure the stability of the closed-loop high-order system. A low noise capacitance detection circuit is described with a correlated-double-sampling( CDS) technique to decrease 1 /f noise and offset of the operational amplifier. This paper also proposes a self-test technique for the interface circuit to test the harmonic distortion. An electrostatic force feedback linearization circuit is presented to reduce the harmonic distortion resulting in larger dynamic range( DR). The layout of the IC is implemented in a standard 0. 6 μm CMOS technology and operates at a sampling frequency of 250 kHz. The interface consumes 20 mW from a 5 V supply. The post-simulation results indicate that the noise floor of the digital accelerometer is about- 140 dBV /Hz1 /2at low frequency. The sensitivity is 2. 5 V /g and the nonlinearity is 0. 11%. The self-test function is achieved with 98. 2 dB thirdorder harmonic distortion detection based on the electrostatic force feedback linearization.

FEEDBACK LINEARIZATION CONTROL FOR ELECTRONICALLY CONTROLLABLE CLUTCH OF VEHICLE

An investigation is made to the friction chutch engagement control of automotive AMT systems based on a nonlinear dynamic model with double inputs. According to friction torque transmission characteristics during clutch engagement, an equivalent, fully controllable and linearized model and the feedback linearization control are derived from the original system with nonlinearities via homomorphic transforms. By the resulting mathematical modeling, computer simulations are made both for the original nonlinear and feedback linearized systems with incorporation of ordinary PID controllers to follow ideal vehicle dynamic responses. It has been shown by comparison between the two sets of numerical results that the feedback linearization control designed for the nonlinear system is of fine accuracy and robustness in model tracking behaviors of clutch engagements.

Feedback linearization based control for weak grid connected PV system under normal and abnormal conditions

This paper proposes a control strategy for interface of distributed energy sources into the weak grid system with a focus on the energy and ancillary services.A novel controller has been designed and implemented to tackle the challenges of coupling terms in the LCL filter,the transient behavior under sudden changes,and the voltage support under fault condition using the feedback linearization technique.The controller proposed has been implemented on the PV system connected with the weak grid using the LCL filter and the performance of the controller has been verified using Matlab/Simulink through simulation under different conditions.The results of the controller proposed have been compared with the conventional PI dual loop controller.The simulation results obtained demonstrate the effectiveness and simplicity of the controller design strategy.

A sliding-mode variable-structure controller based on exact feedback linearization for automatic navigation system

In order to improve the path tracking accuracy and robustness of the agricultural machinery navigation system,a sliding-mode variable-structure controller based on exact feedback linearization was presented.Firstly,based on the differential geometry theory and the affine nonlinear kinematics model,the corresponding nonlinear coordinate change matrix and nonlinear state variable feedback equations were deduced,and an exact feedback linearization model was then established.Secondly,based on the exact feedback linearization model,a sliding-mode variable-structure controller was designed by selecting suitable linear switching function and exponential reaching law.Finally,the comparative experiments were carried out.And the experimental results indicated that the proposed method had a high tracking accuracy and robustness.The maximum lateral error of the straight line tracking was less than 0.06 m,and maximum lateral error of the curve path tracking was less than 0.09 m.Experimental results show that the transplanter based on this automatic navigation system can effectively track the predefined path.

Composite Control of Nonlinear Singularly Perturbed Systems via Approximate Feedback Linearization

This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.

A transverse local feedback linearization approach to human head movement control

In the mid-nineteenth century, Donders had proposed that for every human head rotating away from the primary pointing direction, the rotational vectors in the direction of the corresponding axes of rotation, is restricted to lie on a surface. Donders＇ intuition was that under such a restriction, the head orientation would be a function of its pointing direction. In this paper, we revisit Donders＇ Law and show that indeed the proposed intuition is true for a restricted class of head-orientations satisfying a class of quadratic Donders＇ surfaces, if the head points to a suitable neighborhood of the frontal pointing direction. Moreover, on a suitably chosen subspace of the 3D rotation group SO（3）, we describe a head movement dynamical system with input control signals that are the three external torques on the head provided by muscles. Three output signals are also suitably chosen as follows. Two of the output signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders＇ surface. We claim that the square system is locally feedback linearizable on the subspace chosen, and the linear dynamics is decomposed into parts, transverse and tangential to the Donders＇ surface. We demonstrate our approach by synthesizing a tracking and path-following controller. Additionally, for different choices of the Donders＇ surface parameters, head gaits are visualized by simulating different movement patterns of the head-top vector, as the head-pointing vector rotates around a circle.

CONTROLLING CHAOTIC OSCILLATIONS OF VISCO-ELASTIC PLATESBY THE LINEARIZATION VIA OUTPUTFEEDBACK

Controlling chaotic oscillations of viscoelastic plates are investigated in this paper. Based on the exact linearization method in nonlinear system control theory, a nonlinear feedback control law is presented for a class of non_affine control systems. The mathematical model describing motion of nonlinear viscoelastic plates is established, and it is simplified by the Galerkin method. The phase space portrait and the power spectrum are employed to demonstrate chaos in the system. The deflection is treated as an output, and is controlled to given periodic goals.

Sliding Mode Control of Hydraulic Pressure in Electro-Hydraulic Brake System Based on the Linearization of Higher-Order Model

The possibility to enhance the stability and robustness of electrohydraulic brake(EHB)systems is considered a subject of great importance in the automotive field.In such a context,the present study focuses on an actuator with a four-way sliding valve and a hydraulic cylinder.A 4-order nonlinear mathematical model is introduced accordingly.Through the linearization of the feedback law of the high order EHB model,a sliding mode control method is proposed for the hydraulic pressure.The hydraulic pressure tracking controls are simulated and analyzed by MATLAB/Simulink soft considering separately different conditions,i.e.,a sine wave,a square wave and a square wave with superimposed sine disturbance.The results show that the proposed strategy can track the target within 0.25 s,and the mean observed error is less than 1.2 bar.Moreover,with such a strategy,faster response and less overshoot are possible,which should be regarded as significant advantages.

Finite-time State Feedback Stabilization Method for a Class of Flexible Manipulators

Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators.

Controlling chaos in RCL-shunted Josephson junction by delayed linear feedback

The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.

A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.

POSITIVE PERIODIC SOLUTION FOR A NONAUTONOMOUS LOGISTIC MODEL WITH LINEAR FEEDBACK REGULATION

A nonautonomous delayed logistic model with linear feedback regulation is proposed in this paper. Sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solution of the model

Control and Stabilization of Chaotic System Based on Linear Feedback Control Method

In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.

Adaptive nonlinear model predictive control design of a flexible-link manipulator with uncertain parameters

This paper presents a novel adaptive nonlinear model predictive control design for trajectory tracking of flexible-link manipulators consisting of feedback linearization, linear model predictive control, and unscented Kalman filtering. Reducing the nonlinear system to a linear system by feedback linearization simplifies the optimization problem of the model predictive controller significantly, which, however, is no longer linear in the presence of parameter uncertainties and can potentially lead to an undesired dynamical behaviour. An unscented Kalman filter is used to approximate the dynamics of the prediction model by an online parameter estimation, which leads to an adaptation of the optimization problem in each time step and thus to a better prediction and an improved input action. Finally, a detailed fuzzy-arithmetic analysis is performed in order to quantify the effect of the uncertainties on the control structure and to derive robustness assessments. The control structure is applied to a serial manipulator with two flexible links containing uncertain model parameters and acting in three-dimensional space.

Nonlinear Adaptive Slewing Motion Control of Spacecraft Truss Driven by Synchronous V-gimbaled CMG Precession

The slewing motion control of a truss arm driven by a V-gimbaled control-moment-gyro （CMG） is a nonlinear control problem. The V-gimbaled CMG consists of a pair of gyros that must precess synchronously. The moment of inertia of the system, the angular momentum of the gyros and the external disturbances are not exactly known. With the help of feedback linearization and recursive Lyaptmov design method, an adaptive nonlinear controller is designed to deal with the unknown items. Performance of the proposed controller is verified by simulation.

Distributed tracking control of unmanned aerial vehicles under wind disturbance and model uncertainty

A distributed robust method is developed for cooperative tracking control of unmanned aerial vehicles under unknown wind disturbance and model uncertainty. The communication network among vehicles is a directed graph with switching topology. Each vehicle can only share its states with its neighbors. Dynamics of the vehicles are nonlinear and affected by the wind disturbance and model uncertainty. Feedback linearization is adopted to transform the dynamics of vehicles into linear systems. To account for the wind disturbance and model uncertainty, a robust controller is designed for each vehicle such that all vehicles ultimately synchronize to the virtual leader in the three-dimensional path. It is theoretically shown that the position states of the vehicles will converge to that of the virtual leader if the communication network has a directed spanning tree rooted at the virtual leader. Furthermore, the robust controller is extended to address the formation control problem. Simulation examples are also given to illustrate the effectiveness of the proposed method. © 2016 Beijing Institute of Aerospace Information.