Exact Linearization Method Research Articles

Chaos control in Shimizu Morioka system by Lie algebraic exact linearization

Chaos in Shimizu–Morioka system is controlled by applying a Lie algebraic exact linearization technique. In this state space exact linearization method, a non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original non-linear chaotic system into a linear controllable one. The controller is designed for an arbitrary output and the paper discusses the case of both linear and non-linear outputs. Necessary and sufficient conditions are derived for stabilization of the system to a point and onto a limit cycle. Numerical simulation has been conducted for all these aspects of the problem that conclusively establishes our analytical findings.

Recursive methods in control of flexible joint manipulators

This paper considers recursive solving methods in the control of modular and reconfigurable robot systems. The focus lies on the end-point accuracy and recursive methods for its improvement. The modeling of the robot systems under consideration is done by the Projection Equation in Subsystem representation. Due to gear elasticities and the lack of position sensors at the gearbox output shaft, deflections of the end-point cannot be compensated by standard PD motor control. Therefore, a novel approach is presented in this contribution to correct the resulting position errors of the end-points of the robot systems. This proposed method enables to do a flat parameterization of such elastically modeled systems in a recursive manner, which is contrasted to the generally used non-recursive exact feed-forward linearization method in minimal form for such under-actuated systems. The ability to do the computation in such a recursive way offers the possibility to do the calculations systems for systems with many degrees-of-freedom (DOF) as well, where standard analytical methods reach their limits. And for modular systems, it is applicable as well. For validation, the proposed method is implemented for a robot arm with seven joints and simulation results are presented.

Research on Application of Buck Converter Based on Data-Driven Model-Free Adaptive Controller

State feedback exact linearization method in Buck converters have been widely recognized in the domestic, and it achieved a good control effect, but because the method is based on the accurate modeling, so when the model of controlled object is not accurate enough or circuit parameters in the application are changed, state feedback exact linearization method will be difficult to achieve the ideal control effect. In this paper we use the based on data-driven model-free adaptive controller (MFAC) on Buck Converter Applications for the first time. We analyzed the output characteristic of model-free adaptive control and the state feedback when load changes by simulation. Through the experimental platform of practical, we compared MFAC and the state feedback. Results show that, when the circuit parameter varies in a large range, MFAC has better robustness and resistance mismatch capability, high steady accuracy.

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

SUMMARYThis paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.

Anti-Detection Simulation Study in Thruster Motor System of Underwater Robot Based on Anti-Control of Chaos

Using chaotic anti-control technology to solve the unique noise generated by ocean reconnaissance robot was proposed in this paper in order to improve robot concealment. The mathematical model of ocean reconnaissance robot which thruster device is used as permanent magnet brushless DC motor was transformed in favor of chaotic anti-control study. On this basis, applied time-delay state variable feedback exact linearization method to chaotic thruster device. So the strange attractor of thruster device changed by changing the anti-control controller parameters according to actual situation. Finally, the anti-control controller was designed and verified by computer simulation. The simulation results show that the electromagnetic torque of thruster system can be chaotication under the condition of ocean reconnaissance robot normal running using time delayed state variable feedback exact linearization method. So the electromagnetic torque chaos lead to the shaft vibration changed, and the noise of propeller unique voiceprint characteristic is changed also. As a result, achieve the purpose of confusing the enemy.

波動歯車装置を含む位置決め機構の厳密な線形化手法による非線形補償

波動歯車装置を含む位置決め機構の厳密な線形化手法による非線形補償

Synthesis of Approximating State Feedback for Robotic Manipulator

This paper invents a methodology to synthesize proportional derivative controller for robotic manipulator. The proposed design methodology is based on exact feedback linearization method. A proportional derivative controller candidate which linearly approximates the nonlinear controller which is resulted from exact feedback linearization method is evaluated under Lyapunov stability condition. We show the effectiveness of the proposed method by applying it to robotic manipulator model, obtaining the proportional derivative controller, simulating the closed loop behavior of the system. A comparison of the proposed method with exact feedback linearization method shows that there is no significant performance degradation when approximating exact feedback linearization by the proposed method.

Simple chaotic oscillator’s chaos behavior and its feedback control circuit design

The aim of this paper is to study a chaotic oscillators stability and chaos behavior and to determine the conditions for the stability and chaotic behavior of the chaotic oscillator by theoretical analysis. Furthermore,this study also aims to control the chaotic oscillator by an exact feedback linearization method. Finally,both numerical simulations and circuit experiments verify the validity of the theoretical analysis.

State-space exact linearization and stabilization with feedback control in SODE economic models

The paper presents a non-conventional control engineering strategy proposed by experimental physicists, employed for controlling Dynamical Systems and basically designed for the control of nonlinear systems (Liqun and Yan Zhu in Appl. Math. Mech. 19:67–73, 1998; Liqun and Yan Zhu in Phys. Lett. A 262:350–354, 1999). After a brief presentation of the strategy—called state space exact linearization method, this is applied to design a nonlinear feedback control law as well as a modified version of this law, to control the Kaldor (Chang and Smyth in Rev. Econ. Stud. 38:37–44, 1971) and the Bonhoeffer-Van Der Pohl (Grassman in Environment, Economics and their Mathematical Models, 1994) nonlinear systems used in macro-economic business cycles.

Observational linearization and tracking objective excitation control strategy based on phasor measurement unit

To improve the transient stability of multimachine power systems, observational linearization and tracking objective excitation control laws were derived from the phasor measurement unit (PMU), observational linearization, and tracking objective control theory based on synchronized coordinates and reference generator coordinates. The control strategies utilized real-time state variables obtained by PMU to linearize the state equations of the system, and then the linear optimal control strategy was used to design excitation controllers. The inaccuracy of the local linearization method and the complexity of the system models designed in the exact linearization method for nonlinear systems were avoided. Therefore, the control strategies were applied in real time. Simulation results show that the proposed method can improve the transient stability of power systems more efficiently than nonlinear optimal excitation control.

10506 多入力多出力非線形システムに対するロバスト制御系の一設計法とその応用(Visual Presentation Contest)

The feedback linearization problem is one of the most important control problems for nonlinear systems. Yamada and Nitta propose a design method of approximate linearization method that can apply almost all multivariable nonlinear systems. However their approximate linearization method does not guarantee the stability of the closed control system even if the uncertainty of the plant does not exist. Furthermore the method by Yamada and Nitta does not consider the stability of the closed control system when the uncertainty of the plant exists. In this paper, we examine a design method for robustly stabilizing controllers for multivariable nonlinear systems to which the exact linearization method is not applicable.

Minimum Energy Control of Exact-Linearized Relative Position/Attitude of Spacecraft

The present paper proposes a control scheme for position and attitude tracking of a spacecraft in order to inspect a malfunctioning satellite by maneuvering around the satellite. The proposed method is a nonlinear controller based on the exact-linearization techniques. The exact-linearization method is powerful for controlling nonlinear systems such as the position and attitude control control problem treated in the present paper, because each state variable of the linearized system can be controlled independently. After nonlinear systems are exactly linearized, any kind of control method can be applied to control the systems. The Linear Quadratic Regulator (LQR) is one example of such methods that can be used for controlling the exact-linearized systems. However from the real energy point of view, the exact-linearization method combined with LQR is not optimal, because the performance index is not a function of real energy, and is optimized with respect to the exact-linearized state variables, which are not equal to the real state variables. In the present study, considering the rotational motion of a target satellite, position of the chaser satellite relative to the target and the period of rotational motion of the target satellite, the energy consumption until achieving fly-around motion based on the exact-linearization is minimized. The effectiveness of the proposed method is verified, in comparison with the LQR control or an adaptive sliding-mode control on the exact-linearized system, through numerical simulations.

Minimum Acceleration Guidance Law for Spaceplane in Ascent Phase via Exact Linearization

A new guidance and control system for a spaceplane is presented. The dynamics of the spaceplane has strong nonlinearity, due to which it is difficult to determine the optimal trajectory analytically and to design a stable trajectory tracking system. Therefore, in this study, we attempt to design a guidance and control system using a state-space exact linearization method without any approximation. Then, a minimum acceleration guidance law is derived analytically by solving a two-point boundary-value problem. Lastly, a trajectory control system is designed to track the vehicle with respect to the reference trajectory generated by the guidance system. The numerical simulation results confirm the validity of the linearized model, the optimality of the guidance system and the good tracking property of the developed system.

Nonlinear controller construction based on a model with state-dependent representation for a nonlinear system

This paper addresses a method of nonlinear controller construction based on a model with a state-dependent representation for a nonlinear system. In this method, the controller construction and generation of manipulated values are separated. A nonlinear system and its controller are firstly expressed by the coefficients of the state-dependent representation without any approximation. At the stage of controller implementation for the nonlinear system, the manipulated values are calculated by means of an algorithm of the numerical analysis. The properties of the proposed method are analysed. With the analytical considerations and simulation studies, the proposed method is compared with several nonlinear control methods, such as exact linearization method and the linear approximation method, and its merits are verified.

The Exact Velocity Linearization Method

The aim of this paper is to present a new method for the nonlinear controller design. The underlying theory evolves from the introduced transfer function of nonlinear systems, that can be used in similar way as transfer functions of classical linear systems. The presented algebra of transfer functions is the same as the linear one. Therefore, the controller design can follow the linear system synthesis. The paper shows, how to design a nonlinear PID controller using the direct method synthesis and also shows that the nonlinear state controller following the pole-placement method is equivalent to the exact linearization method. Since the presented method leads to results identical with the exact linearization method, it has been denoted as the exact velocity linearization method.

121 厳密線形化された宇宙機の相対位置・姿勢運動に対するエネルギー最小制御

The present paper proposes a control scheme for position and attitude tracking of a spacecraft in order to inspect a malfunctioning satellite by maneuvering around the satellite. The proposed method is a nonlinear controller based on the exact-linearization techniques. The exact-linearization method is powerful for controlling nonlinear systems such as the position and attitude control problem treated in the present paper, because each state variable of the linearized system can be controlled independently. After nonlinear systems are exactly linearized, any kind of control method can be applied to control the systems. The Linear Quadratic Regulator (LQR) is one example of such methods that can be used for controlling the exact-linearized systems. However, from the real energy point of view, the exact-linearization method combined with LQR is not optimal, because the performance index is not an energy function and is optimized with respect to the exact-linearized state variables, which are not equal to the real state variables. In the present study, considering the rotational motion of a target satellite, position of the chaser satellite relative to the target and the period of rotational motion of the target satellite, the energy consumption for the fly-around motion using the exact-linearization is optimize. The effectiveness of the proposed method is verified, in comparison with the exact-linearized method with LQR and the adaptive exact-linearized method with LQR, through numerical simulation.

Approximate Input-state Feedback Linearization for Non-linear Systems and Control for the Acrobot

In this paper, we consider a design method of approximate feedback linearization for non-linear systems to which the exact linearization method is not applicable. We adopt a two-step procedure to solve the approximate linearization. First, a state transformation matrix is settled, so that the non-linear system is transformed approximately into the controllable canonical form. Second, a standard non-linear linearization method is used to transform the controllable canonical form into a stable linear system. Finally, the application of the proposed method to the Acrobot, which is known as a system to which the exact linearization method cannot be applied, is shown to illustrate the effectiveness of the proposed method.

Velocity Control for a Mechanical System with Nonlinear Friction Using Friction Estimation

For precision control of mechanical systems moving at low velocity, stick-slip behavior should be considered. lt is known that the behavior is caused by negative viscosity of nonlinear friction. In this paper, we consider a control of a typical two mass-spring system with nonlinear friction. In the system, a driver and a load is connected by a spring, and the nonlinear friction acts the load. In order to compensate the nonlinear friction, the exact linearization method of nonlinear systems is applied to the two mass-spring system. Since the frictional properties are unknown, they are estimated by a disturbance observer and the recursive least squares method. Experimental results show the effectiveness of the proposed controller. ln the experiments, the friction is directly measured. The measurement results also show the validity of the proposed friction estimation method.

The integration of ordinary differential equations: factorization and transformations

This paper is based on a uniform theory of factorization and transformation of nth ( n≥2) order ordinary differential equations (ODEs) that are used to constructively solve problems of integrability. This method of factorization of differential operators is developed not only in a base differential field, but also in its algebraic and transcendental extensions. For the first time, the method is extended to nonlinear equations. A new method of exact linearization is proposed that includes transformations used earlier. This method allows us to constructively study nonlinear and nonstationary problems in mathematical simulations with the help of a computer algebra system called REDUCE (as well as other systems).

Nonlinear Phenomena on a Two-Link Planer Manipulator with a Free Joint

The dynamics of a manipulator with free joints is described by nonlinear ordinary differential equations with nonintegrable differential constraints. Such a dynamical system cannot be converted to a linear system using an exact linearization method such as the computed torque method. Control methods using nonlinear properties of such a system are studied in many fields of robotics. In this paper, we consider behavior of the free link on a two-link planer manipulator under commanding repetitive tasks to the actuated link. As previous reported, we numerically observed some periodic motions and chaotic states as a steady state on the manipulator. Computing bifurcation diagrams and basins of attraction for typical periodic motions, we investigate a relation between the viscous friction of the free joint and bifurcation phenomena on the manipulator. We also observe some periodic motions on an experimental manipulator system.