Exact Linearization Technique Research Articles

Chaos Control in Three Dimensional Cancer Model by State Space Exact Linearization Based on Lie Algebra

This study deals with the control of chaotic dynamics of tumor cells, healthy host cells, and effector immune cells in a chaotic Three Dimensional Cancer Model (TDCM) by State Space Exact Linearization (SSEL) technique based on Lie algebra. A non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original chaotic TDCM system into a controlled one linear system. Numerical simulation has been carried using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.

Control of Quadrotor Unmanned Aerial Vehicles Using Exact Linearization Technique with the Static State Feedback

Control of Quadrotor Unmanned Aerial Vehicles Using Exact Linearization Technique with the Static State Feedback

Stability and Scalability of Homogeneous Vehicular Platoon: Study on the Influence of Information Flow Topologies

In addition to decentralized controllers, the information flow among vehicles can significantly affect the dynamics of a platoon. This paper studies the influence of information flow topology on the internal stability and scalability of homogeneous vehicular platoons moving in a rigid formation. A linearized vehicle longitudinal dynamic model is derived using the exact feedback linearization technique, which accommodates the inertial delay of powertrain dynamics. Directed graphs are adopted to describe different types of allowable information flow interconnecting vehicles, including both radar-based sensors and vehicle-to-vehicle (V2V) communications. Under linear feedback controllers, a unified internal stability theorem is proved by using the algebraic graph theory and Routh–Hurwitz stability criterion. The theorem explicitly establishes the stabilizing thresholds of linear controller gains for platoons, under a large class of different information flow topologies. Using matrix eigenvalue analysis, the scalability is investigated for platoons under two typical information flow topologies, i.e., 1) the stability margin of platoon decays to zero as $0(\mbox{1}/N^{2})$ for bidirectional topology; and 2) the stability margin is always bounded and independent of the platoon size for bidirectional-leader topology. Numerical simulations are used to illustrate the results.

Fuzzy Modeling and Synchronization of a New Hyperchaotic Complex System with Uncertainties

In this paper, the synchronization of a new hyperchaotic complex system based on T-S fuzzy model is proposed. First, the considered hyperchaotic system is represented by T-S fuzzy model equivalently. Then, by using the parallel distributed compensation (PDC) method and by applying linear system theory and exact linearization (EL) technique, a fuzzy controller is designed to realize the synchronization. Finally, simulation results are carried out to demonstrate the performance of our proposed control scheme, and also the robustness of the designed fuzzy controller to uncertainties.

Sensorless Exact Input-Output Linearization Control of the Induction Machine, Based on Parallel Stator Resistance and Speed MRAS Observer, with a Flux Sliding Mode Observer

Abstract: This paper presents an exact input-output linearization control scheme for rotor speed and rotor flux control of induction motor drive. In this scheme the motor model, is described in the fixed stator frame, and it is linearized, using exact inputoutput linearization technique, allowing a decoupled control of rotor flux and torque. To avoid the use of mechanical sensor, the rotor speed estimation is made by an observer using a specific MRAS (Model reference adaptive system) technique; this observer is designed to perform simultaneous estimation of stator resistance and rotor speed. In order to estimate rotor flux, a sliding mode observer is proposed in this paper. Simulation results are realized and presented to validate and to prove the effectiveness of the proposed Sensorless control.

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.

Digital Control of a Shunt Hybrid Power Filter Adopting a Nonlinear Control Approach

This paper proposes a nonlinear derivative-less control approach for controlling a three-phase shunt hybrid power filter (SHPF). The dynamic model of the SHPF system is first elaborated in the stationary frame and then transformed into a “dq” reference frame. The control system is divided into two separate loops, namely the two current dynamics inner loop and the dc voltage dynamic outer loop. The exact feedback linearization technique is used to decouple the inner loop variables. Proportional-integral controllers are utilized to control the SHPF input currents and dc-bus voltage. The proposed nonlinear control is first simulated and then validated on a 2.5-kVA laboratory prototype supported by the DS 1104 digital real-time controller board of dSPACE. Satisfactory results, such as low-ac-current total harmonic distortion, fast step response, and high robustness under load variation, are obtained. Significantly high correlation between the experimental results and the theoretical model, implemented with SIMULINK/Matlab, is obtained.

Multivariable feedback linearizing control of Chlamydomonas reinhardtii photoautotrophic growth process in a torus photobioreactor

The objective of this paper is to design and to validate a nonlinear multivariable controller, based on the exact feedback linearization technique, which has the capacity to stabilize the photoautotrophic microalgae growth in photobioreactor regardless of the operation point or the transient trajectory. Two measurable outputs were selected, namely the biomass concentration and the pH, whose simultaneous control can be realized by manipulating the dilution rate and the injected carbon dioxide gas flowrate. A mechanistic dynamical model describing the interactions between physicochemical and biological phenomena inside the photobioreactor was used as a starting point for the controller design. Given its complexity, the model was reduced by differentiating the states with slow dynamics from the ones with fast dynamics that were converted into algebraic expressions. In addition, a dynamic time-varying expression was derived for the concentration of hydrogen ions (negative antilogarithm of pH) thus obtaining an appropriate I/O model for control purposes. The degree of interaction between I/O channels was determined through a relative gain array analysis, in order to establish if the system allows the implementation of decentralized SISO controllers or requires a centralized MIMO controller. The feedback linearization method was associated with a model based technique to furnish the immeasurable variables required by the nonlinear control algorithm. The nonlinear controller was implemented on a laboratory torus photobioreactor piloted at constant incident light flux intensity throughout the photoautotrophic growth of a Chlamydomonas reinhardtii culture, its efficiency being proved under several operating points.

Advances and selected recent developments in state and parameter estimation

This paper deals with two topics from state and parameter estimation. The first contribution of this work provides an overview of techniques used for determining which parameters of a model should be estimated. This is a question that commonly arises when fundamental models are used as these models often contain more parameters than can be reliably estimated from data. The decision of which parameters to estimate is independent of the observer/estimator design, however, it is directly affected by the structure of the model as well as the available data. The second contribution is an overview of recent developments regarding the design of nonlinear Luenberger observers, with special emphasis on exact error linearization techniques, but also discussing more general issues, including observer discretization, sampled data observers and the use of delayed measurements.

An Efficient Multiperiod MINLP Model for Optimal Planning of Offshore Oil and Gas Field Infrastructure

In this paper, we present an efficient strategic/tactical planning model for offshore oilfield development problem that is fairly generic and can be extended to include other complexities. The proposed multiperiod nonconvex MINLP (mixed integer nonlinear programming) model for multifield site includes three components (oil, water, and gas) explicitly in the formulation using higher order polynomials, avoiding bilinear and other nonlinear terms. With the objective of maximizing total NPV for long-term planning horizon, the model involves decisions related to FPSO (floating production, storage, and offloading) installation and expansions, field–FPSO connections, well drilling, and production rates in each time period. The model can be solved effectively with DICOPT for realistic instances and gives good quality solutions. Furthermore, it can be reformulated into an MILP after piecewise linearization and exact linearization techniques that can be solved globally in an efficient way. Solutions of realistic in...

Analysis of Exact Linearization and Aproximate FeedbackLinearization Techniques

This paper presents a study of linear control systems based on exact feedback linearization and approximate feedback linearization. As exact feedback linearization is applied, a linear controller can perform the control objectives. The approximate feedback linearization is required when a nonlinear system presents a noninvolutive property. It uses a Taylor series expansion in order to compute a nonlinear transformation of coordinates to satisfy the involutivity conditions.

Observer Design for a Class of Discrete-time Nonlinear Systems

Necessary and sufficient conditions are presented under which a discrete-time autonomous system with outputs is locally diffeomorphic to an output-scaled linear observable system or an output-scaled nonlinear system in the observer form. As a consequence of such characterizations, the nonlinear observer design problem is studied for a broader class of discrete-time nonlinear systems by using the exact linearization technique that is based on the differential geometric approach.

A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

In this paper, a Takagi–Sugeno (T–S) fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T–S fuzzy models with a small number of fuzzy IF–THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T–S fuzzy models lies in mathematical simplicity of analysis. Based on the T–S fuzzy hyperchaotic models, two fuzzy controllers are designed via parallel distributed compensation (PDC) and exact linearization (EL) techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.

Cross-Layer Fair Bandwidth Sharing for Multi-Channel Wireless Mesh Networks

In a wireless mesh network (WMN) with a number of stationary wireless routers, the aggregate capacity can be increased when each router is equipped with multiple network interface cards (NICs) and each NIC is assigned to a distinct orthogonal frequency channel. In this paper, given the logical topology of the network, we mathematically formulate a crosslayer fair bandwidth sharing problem as a non-linear mixedinteger network utility maximization problem. An optimal joint design, based on exact binary linearization techniques, is proposed which leads to a global maximum. A near-optimal joint design, based on approximate dual decomposition techniques, is also proposed which is practical for deployment. Performance is assessed through several numerical examples in terms of network utility, aggregate network throughput, and fairness index. Results show that our proposed designs can lead to multi-channelWMNs which are more efficient and fair compared to their singlechannel counterparts. The performance gain on both efficiency and fairness increase as the number of available NICs per router or the number of available frequency channels increases.

Dynamic modeling and nonlinear control strategy for an underactuated quad rotor rotorcraft

In this paper, a nonlinear dynamic MIMO model of a 6-DOF underactuated quad rotor rotorcraft is derived based on Newton-Euler formalism. The derivation comprises determining equations of motion of the quad rotor in three dimensions and seeking to approximate the actuation forces through modeling of the aerodynamic coefficients and electric motor dynamics. The derived model is dynamically unstable, so a sequential nonlinear control strategy is implemented for the quad rotor. The control strategy includes exact feedback linearization technique, using the geometric methods of nonlinear control. The performance of the nonlinear control algorithm is evaluated using simulation and the results show the effectiveness of the proposed control strategy for the quad rotor rotorcraft near quasi-stationary flight.

車輪に横滑りを有する車両の厳密な線形化によるロバスト軌道追従制御

In this paper, a new robust tracking controller for vehicles with active front steering and with side skidding is proposed. Conventional controllers, designed for vehicles without side skidding, assure exponential convergence to the desired trajectory. When applied to vehicles with side skidding, however, these controllers cause a large deviation from the trajectory. We have revised a conventional controller by representing it into time-state control form and by applying an exact linearization technique. Our controller cancels the dynamics of side skidding and successfully achieves exponential convergence to the desired trajectory. The controller assures robustness with respect to uncertainties on cornering forces and external disturbances by a natural extension using sliding mode. The advantages of the proposed controller are shown through simulations.

Fuzzy modeling and synchronization of hyperchaotic systems

Abstract This paper presents fuzzy model-based designs for synchronization of hyperchaotic systems. The T–S fuzzy models for hyperchaotic systems are exactly derived. Based on the T–S fuzzy hyperchaotic models, the fuzzy controllers for hyperchaotic synchronization are designed via the exact linearization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed method.

A19 車輪が横滑りする車両の厳密な線形化による四輪独立操舵角制御(OS8-1 メカニカルシステムのアドバンスト制御)

For cars without side skidding in their wheels, steering control based on time-state control form and exact linearization technique can achieve globally asymptotically stable tracking. But real cars always experience side skidding; their behavior depends on their velocity, roadbed and property of wheels. For this challenge, we have proposed a modified steering controller by inverse dynamics of vehicle with side skidding. Our controller assures exponential asymptotic tracking to the desired trajectory. In this paper, our steering controller is extended to the 4WS vehicle to achieve both the tracking control and the attitude control of the vehicle. Base on this extended controller, we realize an automatic deceleration method using active toe-in angle control.

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.

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.