Showing papers on "Feedback linearization published in 2004"

Integrated Guidance and Control of Moving-Mass Actuated Kinetic Warheads

Abstract: : Modeling, simulation, and integrated guidance-control of a kinetic warhead utilizing moving- mass actuators are discussed. Moving masses can be used in any speed range both in the atmosphere as well as outside it, as long as there is a force, either aerodynamic or propulsive, acting on the vehicle. Since they are contained entirely within the airframe geometric envelope, and because no mass expulsion is involved, moving-mass actuation technique offers significant advantages over conventional aerodynamic control surfaces and reaction control systems. The present research developed a high fidelity, nine degree-of-freedom simulation model of a kinetic warhead with three moving-mass actuators. This simulation model is used for actuator sizing and in the development of flight control systems. A software package for performing numerical feedback linearization technique is employed for the design of nonlinear flight control systems. Interception of non-maneuvering and weaving targets in both atmospheric and exo-atmospheric conditions are demonstrated.

Control of a Nonlinear Wing Section Using Leading- and Trailing-Edge Surfaces

Abstract: The control of nonlinear aeroelastic response of a wing section with a continuous stiffening-type structural nonlinearity is examined through analytical and experimental studies. Motivated by the limited effectiveness of using a single, trailing-edge control surface for the suppression of limit-cycle oscillations of a typical wing section, improvements in the control of limit-cycle oscillations are investigated through the use of multiple control surfaces, namely, an additional leading-edge control surface. The control methodology consists of a feedback linearization approach that transforms the system equations of motion via Lie algebraic methods and a model reference adaptive control strategy that augments the closed-loop system to account for inexact cancellation of nonlinear terms due to modeling uncertainty. Specifically, uncertainty in the nonlinear pitch stiffness is examined. It is shown through simulations and experiments that globally stabilizing control may be achieved by using two control surfaces.

Analysis and Control of Nonlinear Process Systems

Abstract: Basic Notions of Systems and Signals.- State-space Models.- Dynamic Process Models.- Input-output Models and Realization Theory.- Controllability and Observability.- Stability and The Lyapunov Method.- Passivity and the Hamiltonian View.- State Feedback Controllers.- Feedback and Input-output Linearization of Nonlinear Systems.- Passivation by Feedback.- Stabilization and Loop-shaping.

Feedback linearizability and explicit integrator forwarding controllers for classes of feedforward systems

Abstract: We identify a class of feedforward nonlinear systems that are linearizable by a coordinate change. Then we develop explicit expressions for the Lyapunov-based integrator forwarding recursive procedure of Sepulchre, Jankovic, and Kokotovic, which has its roots in a coordinate transformation proposed by Mazenc and Praly. The explicit expressions that we develop allow us to also find closed-form control laws for several classes of systems that are not feedback linearizable, including some that are in the feedforward form and others that are in what we refer to as the "block-feedforward" form. Performance advantages of Lyapunov-based forwarding controllers over nested saturation controllers have been well illustrated in the literature on examples. The analytical expressions for the Lyapunov functions and the control laws allow us to give quantitative performance bounds.

Input-output feedback linearization of time-delay systems

Abstract: In this note, the input-output linearization problem (IOLP) for a class of single-input-single-output nonlinear systems with multiple delays in the input, the output, and the state is studied. The problem is solved by means of various static or dynamic compensators, including state and output feedback. The mathematical setting is based on some noncommutative algebraic tools and the introduction of a nonlinear version of the so-called Roesser models for this class of systems. These are claimed to be the cornerstones for studying nonlinear time-delay systems. Necessary and sufficient conditions are given for the existence of a static or pure shift output feedback which solves the IOLP. Sufficient conditions for the existence of a dynamic state feedback solution are included as well.

High-performance induction motor speed control using exact feedback linearization with state and state derivative feedback

Abstract: This paper presents a novel nonlinear speed/position control strategy for the induction motor utilizing exact feedback linearization with state and state derivative feedback. The speed/position and flux control loops utilize nonlinear feedback which eliminates the need for tuning, while ordinary proportional-integral controllers are used to control the stator currents. The control scheme is derived in rotor field coordinates and employs an appropriate estimator for the estimation of the rotor flux angle, flux magnitude, and their derivatives. The overall control scheme can be easily implemented with a microprocessor-based control platform. An error sensitivity analysis is included which proves the system to be robust to parameter variation and even more, immune to rotor resistance variation. Simulation and experimental results validate the theoretical part of the paper and reveal the high performance and advantages of the novel control scheme.

Nonlinear control strategies for cascaded multilevel STATCOMs

Abstract: Two internal nonlinear control strategies based on the feedback linearization technique for cascaded multilevel static compensators (STATCOMs) are presented. The strategies depend on the control capability of the converter output voltage and are suitable for line frequency-switched converters. The first strategy considers a STATCOM where the voltage is set independently of the dc link voltage. Fast reactive power control within subcycle time response is achieved. The second strategy is constrained to a voltage whose amplitude remains proportional to the dc link voltage. Despite this limitation, the proposed strategy allows full stabilization of the STATCOM dynamics and relatively fast control of the reactive current (within one cycle). This may be adequate for most STATCOM applications. Simulation results, using power system computer-aided design/electromagnetic transient program (PSCAD/EMTP), presented for both strategies confirm the effectiveness of the control schemes to impose linear STATCOM dynamics. Preliminary experimental results from a five-level prototype are presented for a converter using fixed control angles.

Identification and control of a nonlinear discrete-time system based on its linearization: a unified framework

Abstract: This paper presents a unified theoretical framework for the identification and control of a nonlinear discrete-time dynamical system, in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a "higher order function." This representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system, and reveals the role played by the linearized system in a more transparent form. Under the assumption that the linearized system is controllable and observable, it is shown that: 1) the nonlinear system is also controllable and observable in a local domain; 2) a feedback law exists to stabilize the nonlinear system locally; and 3) the nonlinear system can exactly track a constant or a periodic sequence locally, if its linearized system can do so. With some additional assumptions, the nonlinear system is shown to have a well-defined relative degree (delay) and zero-dynamics. If the zero-dynamics of the linearized system is asymptotically stable, so is that of the nonlinear one, and in such a case, a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly, in a neighborhood of the equilibrium state. The tracking can be achieved by using the state vector for feedback, or by using only the input and the output, in which case the nonlinear autoregressive moving-average (NARMA) model is established and utilized. These results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete-time dynamical systems.

Linear Feedback Control

Abstract: The principle of feedback is introduced together with the popular proportional-integral-derivative controller in a general way and under different forms. Its influence on dynamics of simple linear processes is emphasized.

Synergetic control for DC-DC buck converters with constant power load

Abstract: An algorithm for design of synergetic control is derived, using as an example a system containing buck choppers with constant power load J.G. Ciezki et al. (1998). The closed loop system behavior is compared to that of the same system controlled by feedback linearization control. As a result, it is shown that synergetic control has better dynamics and a faster response. This system nullifies steady state error not only of output voltage but also in current sharing among parallel converters.

Motion Planning and Control of a Swimming Machine

Abstract: We propose a practical maneuvering control strategy for an aquatic vehicle (AV) that uses an oscillating foil as a propulsor. The challenge of this problem lies in the need to consider the hydrodynamic interaction as well as the underactuated and non-minimum phase natures of the AV system. The control task is decomposed into the off-line step of motion planning and the on-line step of feedback tracking. Optimal control techniques are used to compute a repertoire of time-scalable and concatenable motion primitives. The complete motion plan is obtained by concatenating time-scaled copies of the primitives. The computed optimal motion plans are regulated by a controller that consists of a cascade of linear quadratic regulator, input–output feedback linearization and sliding mode control. Time-varying linear quadratic controllers can also be time-scaled and concatenated. Therefore, they can be computed beforehand. The proposed strategy has been experimentally validated for both constrained longitudinal only m...

Active direct tilt control for stability enhancement of a narrow commuter vehicle

Abstract: Narrow commuter vehicles can address many congestion, parking and pollution issues associated with urban transportation. In making narrow vehicles safe, comfortable and acceptable to the public, active tilt control systems are likely to play a crucial role. This paper focuses on the development of an active direct tilt control system for a narrow vehicle that utilizes an actuator in the vehicle suspension. A simple PD controller can stabilize the tilt dynamics of the vehicle to any desired tilt angle. However, the challenges in the tilt control system design arise in determining the desired lean angle in real-time and in minimizing tilt actuator torque requirements. Minimizing torque requirements requires the tilting and turning of the vehicle to be synchronized as closely as possible. This paper explores two different control design approaches to meet these challenges. A Receding Horizon Controller (RHC) is first developed so as to systematically incorporate preview on road curvature and synchronize tilling with driver initiated turning. Second, a nonlinear control system that utilizes feedback linearization is developed and found to be effective in reducing torque. A close analysis of the complex feedback linearization controller provides insight into which terms are important for reducing actuator effort. This is used to reduce controller complexity and obtain a simple nonlinear controller that provides good performance.

Application of nonlinear adaptive control techniques to an electrohydraulic velocity servomechanism

Abstract: Adaptive and nonadaptive versions of the feedback linearization control technique are used here for the control of a nonlinear electrohydraulic velocity Servomechanism, the nonlinear behavior arising from load friction as well as the valve flow-pressure drop relationship. An adaptive fuzzy controller is used here for the same application as well. The three controllers are compared based on simulation and experimental results of tracking performance as well as their ability to adjust to disturbances caused by variation in the system parameters.

Wheel force distribution for improved handling in a hybrid electric vehicle using nonlinear control

Abstract: In this paper a vehicle motion controller is presented. The idea is to use generalized forces acting on the center of gravity of the vehicle and then use a control allocation-like method to distribute the generalized forces to wheel forces. The controller is designed based on feedback linearization of a simple vehicle model. The performance of the controller is evaluated by simulations on a more complex vehicle model. The proposed controller can handle the new flexibility introduced by new powertrain configurations, this is shown by using the same controller on two different vehicle configurations.

Control of a Rotating Variable-Length Tethered System

Abstract: Techniques are developed and illustrated to control the motion of a tethered satellite system (TSS) comprising n point masses and interconnected arbitrarily by m idealized tethers. In particular, the control problem of a triangular and symmetrical TSS with n =3 point masses and m =3 tethers is discussed. The equations of motion are derived by the use of Lagrange’s equations. Several mission scenarios for a proposed NASA mission that consider the operation of an infrared telescope are introduced and asymptotic tracking laws based on input-state feedback linearization are developed. The effects of smoothness and nonsmoothness of desired mission trajectories on control performance are discussed. It is shown that required thrust levels can be significantly decreased by the use of additional tether length control to keep the TSS in a state corresponding to an instantaneous relative equilibrium at any point in time during the mission. In the final section, a mathematical model is proposed for the total required control impulse to facilitate a trade study that discusses the effects of the individual system parameters on the control input.

Stabilization of nonlinear nonminimum phase systems: adaptive parallel approach using recurrent fuzzy neural network

Abstract: In this paper, an adaptive parallel control architecture to stabilize a class of nonlinear systems which are nonminimum phase is proposed. For obtaining an on-line performance and self-tuning controller, the proposed control scheme contains recurrent fuzzy neural network (RFNN) identifier, nonfuzzy controller, and RFNN compensator. The nonfuzzy controller is designed for nominal system using the techniques of backstepping and feedback linearization, is the main part for stabilization. The RFNN compensator is used to compensate adaptively for the nonfuzzy controller, i.e., it acts like a fine tuner; and the RFNN identifier provides the system's sensitivity for tuning the controller parameters. Based on the Lyapunov approach, rigorous proofs are also presented to show the closed-loop stability of the proposed control architecture. With the aid of the RFNN compensators, the parallel controller can indeed improve system performance, reject disturbance, and enlarge the domain of attraction. Furthermore, computer simulations of several examples are given to illustrate the applicability and effectiveness of this proposed controller.

Velocity control of a wheeled inverted pendulum by partial feedback linearization

Abstract: In this paper, the dynamic model of a wheeled inverted pendulum (e.g. Segway (2003), Quasimoro (Salerno and Angeles, 2003), Joe (Grasser et al., 2002)) is analyzed from a controllability and feedback linearizability point of view. First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while taking the nonholonomic no-slip constraints into considerations. This model is compared with the previous models derived for similar systems. The strong accessibility condition is checked and the maximum relative degree of the system is found. Based on this result, a partial feedback linearization of the system is obtained and the internal dynamics equations are isolated. The resulting equations are then used to design a two-level controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch within a specified range. Simulation results are provided to show the efficacy of the controller.

Experimental evaluation of nonlinear robust control for SMES to improve the transient stability of power systems

Abstract: This paper presents a new approach and corresponding experiments for the nonlinear robust control of a superconducting magnetic energy storage (SMES) unit to improve the transient stability of power systems. Based on the result of SMES prototype experience, a new dynamic model with disturbances of SMES is adopted, and transferred to the per unit system for simplifying the dynamic analysis and controller design. Then, feedback linearization scheme and linear H/sub /spl infin// control theory are applied to design a novel SMES nonlinear robust controller in a one-machine infinite bus (OMIB) power system. In order to confirm such positive effects of the proposed control strategy, experiments are carried on a laboratory setup of SMES comparing that with a conventional proportional-integral (PI) controller. The results of the experiments demonstrate that the proposed nonlinear robust controller has more excellent performance to improve the transient stability of power systems than that of conventional PI controllers.

Adaptive Backstepping Control Based Autopilot Design for Reentry Vehicle

Abstract: A robust controller design methodology for high speed reentry vehicles (HSRV) is presented in this paper. The design methodology is based on a nonlinear backstepping technique. High speed reentry vehicles often contain signiflcant nonlinearities in the dynamics equation of motion which are partially caused by the high velocities and ∞ight path trajectories. These two factors tend to produce signiflcant aerodynamic forces and moments on the vehicle. The nonlinear backstepping control technique provides an alternative to methods such as piecewise linearization-based gain scheduling and feedback linearization. Backstepping approaches utilize Lyapunov theory to guarantee stability of the closed system and the methods are inherently recursive. Nonlinear optimization is also used to guarantee the accuracy of the mapping between the actuators and applied moments and an adaptive term is included to compensate for the moment bias. The proposed design procedure turns out to be simpler than designs based on alternative methods and the design appears relatively easy to implement.

Modeling and Control Design for a Magnetic Levitation System

Abstract: We study the problem of controlling the position of a platen levitated using linear motors in threedimensional space. We develop a nonlinear six-state model of the system and provide two nonlinear controllers solving the set point stabilization problem. The first controller is derived by decomposing the model in two subsystems, applying feedback linearization to one of them, and using the invariance principle to prove attractiveness of the origin of the second subsystem. The second controller is found by dynamic feedback linearizing the entire system dynamics. In both cases we provide a rigorous procedure to determine the operating range of the device.

A new synthesis method for unit coordinated control system in thermal power plant - ADRC control scheme

Abstract: The new nonlinear control technology-active disturbance rejection control is introduced, and the novel unit ADRC coordinated control scheme for thermal power generation unit is proposed. The key element of ADRC is extended state observer (ESO). The real-time dynamic linearization is implemented by disturbance estimation via ESO and disturbance compensation via control law, instead of differential geometry based feedback linearization and direct feedback linearization theory which need accurate mathematical model of plant. The decoupling for MIMO coordinated system of boiler-turbine unit is also easily implemented by employing ADRC. The simulation results on STAR-90 show that the ADRC coordinated control scheme can effectively solve problems of strong nonlinearity, uncertainty, coupling, large time delay. And it can improve greatly the control performance of coordinated control system. The structure of ADRC coordinated control scheme is simple and clear. It is evident that the proposed scheme lends itself well in providing innovative solutions to practical unit coordinated system problems.

Control of a laboratory helicopter using switched 2-step feedback linearization

Abstract: A control structure based on feedback (input-output) linearization has been applied to the longitudinal subsystem of a laboratory double-rotor helicopter. This article focuses on the longitudinal subsystem which is underactuated in sense that the number of control variables is less than the number of degrees of freedom. A switching control law between exact and approximate input-output linearization is proposed. The feedback linearization has been applied in two steps, first to the nonlinear actuator, and then to the entire system. This law has been tested by simulated and experimental results.

Nonlinear attitude control for a rigid spacecraft by feedback linearization

Abstract: Attitude control laaw design for spacecraft large angle maneuvers is investigated in this paper. The feedback linearization technique is applied to the design of a nonlinear tracking control law. The output function to be tracked is the quaternion attitude parameter. The designed control law turns out to be a combination of attitude and attitude rate tracking commands. The attitude-only output function, therefore, leads to a stable closed-loop system following the given reference trajectory. The principal advantage of the proposed method is that it is relatively easy to produce reference trajectories and associated controller.