Showing papers on "Feedback linearization published in 1993"
TL;DR: In this article, a quasi-LPV (quasilinear parameter varying) state transformation is used to bring a longitudinal autopilot to a quasilevel form via a state transformation.
Abstract: This paper presents a gain-scheduled design for a missile longitudinal autopilot. The gain-scheduled design is novel in that it does not involve linearizations about trim conditions of the missile dynamics. Rather, the missile dynamics are brought to a quasilinear parameter varying (LPV) form via a state transformation. An LPV system is defined as a linear system whose dynamics depend on an exogenous variable whose values are unknown a priori but can be measured upon system operation. In this case, the variable is the angle of attack. This is actually an endogenous variable, hence the expression "quasi-LPV." Once in a quasi-LPV form, a robust controller using H synthesis is designed to achieve angle-of-attack control via fin deflections. The final design is an inner/outerloop structure, with angle-of-attack control being the inner loop and normal acceleration control being the outer loop.
386 citations
02 Jun 1993
TL;DR: In this article, a closed-loop system with positive, delayed feedback was shown to be stable for a range of delays using the Nyquist criterion, which is similar to the method proposed in this paper.
Abstract: This paper expands on a method proposed in [1] for stabilizing oscillatory system with positive, delayed feedback. The closed-loop system obtained is shown (using the Nyquist criterion) to be stable for a range of delays.
284 citations
TL;DR: Any linear system in controller canonical form perturbed by unknown global Lipschitz nonlinearities satisfying triangularity conditions is shown to be globally stabilizable by a fixed dynamic state feedback compensator whose order equals the state space dimensions.
243 citations
TL;DR: It is shown that the sixth-order nonlinear dynamical model of the induction motor consisting of rotor speed, two stator currents, two rotor fluxes and an integrator in the feedback controller can be made equivalent to two third-order decoupled linear systems by nonlinear state feedback through the stator input voltages.
Abstract: Dynamic state feedback is used to achieve feedback linearization of the induction motor. It is shown that the sixth-order nonlinear dynamical model of the induction motor consisting of rotor speed, two stator currents, two rotor fluxes and an integrator in the feedback controller can be made equivalent to two third-order decoupled linear systems by nonlinear state feedback through the stator input voltages. It is further shown that a nonsingular dynamic feedback linearizing transformation exists as long as the (electromagnetic) torque put out by the motor is nonzero. >
151 citations
TL;DR: In this paper, the authors present a preliminary study of a systematic methodology to account robustly for parametric uncertainties in the original system model, which is based on combining sliding control ideas with the recursive construction of a closed-loop Lyapunov function.
Abstract: To make input-output feedback linearization a practical and systematic design methodology for single-input nonlinear systems, two problems need to be addressed One is to handle systematically the difficulties associated with the internal dynamics or zero-dynamics when the relative degree is less than the system order The other is to account for the effect of model uncertainties in the successive differentiations of the output of interest While the first problem has recently received considerable attention, the second has been largely unexplored This paper represents a preliminary study of a systematic methodology to account robustly for parametric uncertainties in the original system model The approach is based on combining sliding control ideas with the recursive construction of a closed-loop Lyapunov function, and is illustrated with a simple example
134 citations
26 Jul 1993
TL;DR: It is shown that theinternal motion of the mobile robot is asymptotically stable when the reference point is commanded to move forward, whereas the internal motion is unstable when thereference point moves backward.
Abstract: Since the dynamics of a wheeled mobile robot is nonlinear, the feedback linearization technique is commonly used to linearize the input-output map. The input-output linearized system has a nonlinear internal dynamics. In this paper, the internal dynamics of the mobile robot under the look-ahead control is first characterized. The look-ahead control takes the coordinates of a reference point in front of the mobile robot as the output equation. Using a novel Lyapunov function, the stability of the internal dynamics is then analyzed. In particular, it is shown that the internal motion of the mobile robot is asymptotically stable when the reference point is commanded to move forward, whereas the internal motion is unstable when the reference point moves backward. Simulation and experimental results are provided to verify the analysis.
118 citations
TL;DR: In this article, a necessary condition for dynamic feedback linearizability of control systems x dot = f(x,u), in which the controls enter nonlinearly, is derived.
77 citations
TL;DR: Recent methods for nonlinear control are compared, including feedback linearization, generalized controller canonical forms, and input-output linearization for shunt DC motor control.
Abstract: The problem of controlling a shunt DC motor is considered. Recent methods for nonlinear control are compared, including feedback linearization, generalized controller canonical forms, and input-output linearization. Connections between the approaches, as well as their respective advantages are discussed in detail. >
71 citations
TL;DR: In this paper, the local linearization approach to nonlinear filtering of time series generated from continuous time stochastic dynamical systems is discussed and a simple and powerful method for the non-linear filtering is introduced.
Abstract: The local linearization approach to nonlinear filtering of time series generated from continuous time stochastic dynamical systems is discussed and a simple and powerful method for the nonlinear filtering is introduced Some numerical results of applications of the filter are shown
67 citations
02 Jun 1993
TL;DR: In this paper, the authors propose a control design for non-minimum phase nonlinear systems that result in stable output regulation or tracking with acceptable closed-loop performance, based on the decomposition of a system into an input-output subsystem and an internal dynamics.
Abstract: Control design for minimum phase nonlinear systems has been well developed in the literature via the input-output linearization method developed in [Isi89] and elsewhere. Since a minimum phase system has stable internal dynamics, one may only need to design a control for the linear subsystem after performing input-output linearization for such a system. This paper addresses the design of controls for non-minimum phase nonlinear systems that result in stable output regulation or tracking with acceptable closed-loop performance. The approach is based on the decomposition of a system into an input-output subsystem and an internal dynamics. The developed results are applied to the classical inverted pendulum on a cart example. Simulation and experimental results are reported.
62 citations
TL;DR: In this article, the authors define a pair of nonlinear parallel projection operators associated with a nonlinear feedback system and show that these projections have equal norms whenever one of the feedback elements is linear.
15 Dec 1993
TL;DR: In this article, the authors use the geometric approach to develop a sufficient condition for feedback linearizability of multi-input discrete time systems, and when this condition is satisfied the linearizing transformation and feedback are obtained by solving a set of partial differential equations.
Abstract: We use the geometric approach to develop a sufficient condition for feedback linearizability of multi-input discrete time systems. When this condition is satisfied the linearizing transformation and feedback are obtained by solving a set of partial differential equations. >
TL;DR: Based on feedback linearization theory, an approach to attitude control of a space station using control moment gyros (CMGs) is developed and a linearizing transformation is derived to obtain a simple linear representation of the nonlinear pitch axis dynamics.
Abstract: Based on feedback linearization theory, an approach to attitude control of a space station using control moment gyros (CMGs) is developed. A linearizing transformation is derived to obtain a simple linear representation of the nonlinear pitch axis dynamics. A feedback control law for trajectory tracking is derived. Extension of this approach to linearization of the coupled yaw and roll axis dynamics and control is presented. >
02 May 1993
TL;DR: A nonlinear tracking controller for the link-tip positions and velocities of a multi-link flexible robot arm that gives guaranteed performance is designed and it is found that the flexible mode trajectories have two parts.
Abstract: A nonlinear tracking controller for the link-tip positions and velocities of a multi-link flexible robot arm that gives guaranteed performance is designed. The controller has three loops: an outer tracking loop, an inner loop based on input-output feedback linearization, and an additional inner loop that stabilizes the internal dynamics, e.g., the flexible modes, using a singular perturbation design. It is found that the flexible mode trajectories have two parts. One part depends algebraically on the desired tip positions. A boundary layer correction part can be used to stabilize the flexible motion. >
TL;DR: In this article, a non-linear adaptive feedback-linearizing control is designed for a five-order model of a three-phase switched reluctance motor (SRM), which includes both electrical and mechanical dynamics.
Abstract: In this paper a non-linear adaptive feedback-linearizing control is designed for a fifth-order model of a three-phase switched reluctance motor (SRM) which includes both electrical and mechanical dynamics. This non-linear adaptive control structure compensates for all the non-linearities between inputs and outputs, allows the use of a linear controller for motion tracking and improves the performance by reducing torque ripple of the SRM.
A validated non-linear model of the SRM is used for the system simulation, while the control algorithm contains an adaptive scheme based on the parametrized model. Simulation results are given to demonstrate the effectiveness of the control method.
TL;DR: A method for the approximate linearization of nonlinear control systems based on the ‘state-space exact linearization’ method is presented, which is straightforward to implement.
Abstract: A method for the approximate linearization of nonlinear control systems based on the ‘state-space exact linearization’ method is presented. An explicit procedure, both for the single-input and for the multiple-input case, is given, which is straightforward to implement.
02 Jun 1993
TL;DR: In this article, it is shown that both speed and load-torque can be estimated from the current measurements for use in two proposed nonlinear controllers, based on feedback linearization and input-output linearization.
Abstract: The problem of controlling a Series DC motor using only current measurements is considered. It is shown that both speed and load-torque may be estimated from the current measurements for use in two proposed nonlinear controllers. The two proposed feedback laws are based on feedback linearization and input-output linearization. Further, both the speed/torque estimation scheme and the control schemes are valid in the prescence of magnetic saturation in the field circuit and when high-speed field-weakening is employed. The estimation is accomplished by using nonlinear state-space and output-space transformations to construct an observer with linear error-dynamics whose rate of convergence may be arbitrarily specified. (Such an observer could provide reliability to existing systems in the event of a speed sensor failure.) The feedback-linearization controller involves a non-trivial state-space transformation allowing control of the full state trajectory. It is then shown that a simpler input-output linearization controller with stable internal dynamics exists and is explicitly constructed.
TL;DR: In this article, a discrete time servo controller is designed for the surface actuators and the engine, where the reference inputs are given by the continuous time control law, and the performance of the RFCS is demonstrated through computer simulation using the nonlinear model of an aircraft which has half o f the right wing broken off.
Abstract: The feedback I inearization method is appl ied to odation of aircraft failures occuring at the control effectors or the airframe. The failures are identified as parameter changes in the six-degree-offreedom nonlinear equations of motion by the recursive least square algorithm. The control parameters are updated using the latest estimated system parameters. In order to allow one to use digital computer in implementation, a discrete time servo controller is designed for the surface actuators and the engine, where the reference inputs are given by the continuous time control law. The performance of the RFCS is demonstrated through computer simulation using the nonlinear model of an aircraft which has half o f the right wing broken off.
TL;DR: In this article, a method for the solution of the asymptotic linearization of uncertain nonlinear systems by means of a continuous control law is presented, which is based on a continuous first-order estimator and control laws with piecewise continuous derivatives.
Abstract: In this paper a new method for the solution of the asymptotic linearization of uncertain nonlinear systems by means of a continuous control law is presented. The main feature of this approach consists of a continuous first-order estimator and control laws with piecewise continuous derivatives. As an important by-product of this theory we can deal easily with the case of some uncertain systems which do not satisfy the matching condition, and with systems presenting first order unmodelled dynamics.
15 Dec 1993
TL;DR: In this paper, the authors summarize and extend some recent results on the problem of when a discrete-time nonlinear system is feedback equivalent to a lossless system via smooth state feedback.
Abstract: In this paper we summarize and extend some recent results on the problem of when a discrete-time nonlinear system is feedback equivalent to a lossless system and the problem of global stabilization via smooth state feedback. In particular, we show how the criterion of zero-state detectability for discrete-time passive systems can be carried out in the absence of the KYP lemma, and how the feedback equivalence idea can be applied to stabilize a class of discrete-time nonlinear systems by means of smooth state feedback. >
TL;DR: A toolbox for nonlinear control system design is presented that contains modules to approximate systems by polynomial systems of arbitrary-order and then render them input-output linear or input-state linear with arbitrary- order error terms.
Abstract: A toolbox for nonlinear control system design is presented. The package contains modules to approximate systems by polynomial systems of arbitrary-order and then render them input-output linear or input-state linear with arbitrary-order error terms. The package also includes interfaces to create LATEX for viewing results and automatic code generation for implementation of the results. The possibilities for real-time control are also discussed. >
15 Dec 1993
TL;DR: The Goursat normal form theorem gives conditions under which a Pfaffian exterior differential system is equivalent to a certain normal form as discussed by the authors, and it provides a unified framework for understanding feedback linearization, chained form, and differential flatness.
Abstract: The Goursat normal form theorem gives conditions under which a Pfaffian exterior differential system is equivalent to a certain normal form This paper details how the Goursat normal form and its extensions provide a unified framework for understanding feedback linearization, chained form, and differential flatness >
15 Dec 1993
TL;DR: The main result proved is that if the first k d-relative degrees are equal to each other, then the input-output response of a nonlinear control system can be linearized to degree k.
Abstract: The paper addressed the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback. The main result proved is that if the first k d-relative degrees are equal to each other, then the input-output response of a nonlinear control system can be linearized to degree k. Any system having linear d-relative degree can be linearized to any degree by dynamic feedbacks. One example of signal tracking using dynamic feedback linearization method to improve the performance is also given. >
Patent•
05 Oct 1993
TL;DR: A temperature compensation method for a microprocessor based electro-pneumatic converter device including an initial calibration sequence, a compensation sequence, and an operation sequence is presented in this article.
Abstract: A temperature compensation method for a microprocessor based electro-pneumatic converter device including an initial calibration sequence, a compensation sequence, and an operation sequence. Linearization of an electro-pneumatic positioner including the steps of adjusting the positioner feedback linkage until a predetermined reference position is attained, reading a position feedback value and determining the required feedback linearization value to achieve a linear relationship between the output/input. A calibration method and a configuration method independent of calibration for a microprocessor based electro-pneumatic converter device including an initial calibration sequence, a configuration sequence, and an operation sequence.
TL;DR: In this paper, the authors describe the application of feedback linearization to automatic steering of ships and present a direct adaptive version of both the course-keeping and turning controller for both course-changing and turning maneuvers.
Abstract: The application of feedback linearization to automatic steering of ships is described. The flexibility of the design procedure allows the autopilot to be optimized for both course-keeping and course-changing maneuvers. Direct adaptive versions of both the course-keeping and turning controller are derived. The advantages of the adaptive controllers are improved performance and reduced fuel consumption. The application of nonlinear control theory also allows the designer to compensate for nonlinearities in the control design in a systematic manner. >
25 May 1993
TL;DR: In this article, a sliding mode control is applied to design autopilot for HAVE DASH II bank-to-turn (BTT) missile systems, which is evaluated using six degree of freedom simulation and shows a significant improvement over the feedback linearization approach.
Abstract: Sliding mode control is applied to design autopilot for HAVE DASH II bank-to-turn-(BTT) missile systems. The design is evaluated using six degree of freedom simulation and shows a significant improvement over the feedback linearization approach.
20 Jun 1993
TL;DR: It is shown that demanding performance requirements such as rapid periodic speed variations can be realized with advanced methods.
Abstract: Field-oriented motor control fits in a wide class of induction motor control methods. Alternatives include feedback linearization and observer-based nonlinear control. Comparisons are made among various vector controls, and also some advanced scalar controls. It is shown that demanding performance requirements such as rapid periodic speed variations can be realized with advanced methods. New scalar methods offer possible alternatives for less demanding drives. >
TL;DR: In this paper, a controller design method consisting of H∞ control and exact linearization via nonlinear state feedback is proposed to yield the linear system which exactly equals to the linearization of the plant around an equilibrium point.
TL;DR: The present work addresses continuous-time systems for which the linearization has either a simple zero eigenvalue or a pair of simple pure imaginary eigenvalues and employs results on stability of bifurcations of parameterized systems.
TL;DR: In this paper, a parametric response study suggests situations with unacceptable levels of deflections and accelerations for certain proposed missions, as well as station libration and payload positioning errors.