Showing papers on "Feedback linearization published in 1992"
TL;DR: In this article, the emergence of robust designs for nonlinear 'interval' plants is pointed out, and some of these tools can be made adaptive and applied to nonlinear systems with unknown parameters.
Abstract: It is argued that, for a cautious design, a nonlinear analysis is needed to reveal when and why linear tools fail. Emerging nonlinear tools that can be used to overcome the limitations of nonlinear designs are discussed. It is shown that some of these tools can be made adaptive and applied to nonlinear systems with unknown parameters. The emergence of robust designs for nonlinear 'interval' plants is pointed out. >
852 citations
TL;DR: In this paper, an approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree is studied, and a method for constructing approximate systems that are input output linearizable is provided.
Abstract: Approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree is studied. For such systems, a method for constructing approximate systems that are input-output linearizable is provided. The analysis presented is motivated through its application to a common undergraduate control laboratory experiment-the ball and beam-where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization. >
669 citations
16 Dec 1992
TL;DR: In this paper, a sliding-mode observer for a nonlinear system is proposed, which is based on the equivalent control method and does not require nonlinear state transformation, unlike the output global linearization approach.
Abstract: The sliding-mode observer for a nonlinear system is proposed. The observer is based on the equivalent control method. Compared with the known output global linearization approach it is given in terms of the system variables and does not require nonlinear state transformation. Several examples are presented which illustrate the proposed method. >
236 citations
TL;DR: In this paper, a differential field characterization of a class of dynamic feedback linearizable systems is given via the notion of differentially flat systems, where the linearizing dynamic feedback is obtained as an endogeneous dynamic feedback.
235 citations
TL;DR: In this paper, a control procedure that uses time delay control to achieve input/output linearization of a class of nonlinear systems is presented, which is characterized by a simple algorithm and enhanced robustness properties in comparison with current control algorithms.
Abstract: A control procedure that uses Time Delay Control to achieve input/output linearization of a class of nonlinear systems is presented. The control system is characterized by a simple algorithm and enhanced robustness properties in comparison with current control algorithms. The paper first reviews the fundamentals of input/output linearization. The use of Time Delay Control is then shown to result in an exact linear system for sufficiently small delay time. Modified controllers for systems with a low-pass filter are also investigated. Simulation results show that the algorithm works well with measurement noise. The controller is also tested on a single-link flexible arm to show the effectiveness of the simple algorithm in the control of complicated systems.
192 citations
TL;DR: In this paper, a set of extended quadratic controller normal forms of linearly controllable nonlinear systems is given, which is the generalization of the Brunovsky form of linear systems.
Abstract: In this paper, a set of extended quadratic controller normal forms of linearly controllable nonlinear systems is given, which is the generalization of the Brunovsky form of linear systems. A set of invariants under the quadratic changes of coordinates and feedbacks is found. It is then proved that any linearly controllable nonlinear system is linearizable to second degree by a dynamic state feedback.
183 citations
TL;DR: By using a simple exact linearization design method for scalar nonlinear control systems, a nonlinear excitation control of synchronous generator is proposed, which is new and effective for engineering.
163 citations
TL;DR: It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes.
Abstract: A neural-network-based direct control architecture is presented that achieves output tracking for a class of continuous-time nonlinear plants, for which the nonlinearities are unknown. The controller employs neural networks to perform approximate input/output plant linearization. The network parameters are adapted according to a stability principle. The architecture is based on a modification of a method previously proposed by the authors, where the modification comprises adding a sliding control term to the controller. This modification serves two purposes: first, as suggested by Sanner and Slotine,1 sliding control compensates for plant uncertainties outside the state region where the networks are used, thus providing global stability; second, the sliding control compensates for inherent network approximation errors, hence improving tracking performance.
A complete stability and tracking error convergence proof is given and the setting of the controller parameters is discussed. It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes. Two simulations are provided to demonstrate the features of the control method.
158 citations
12 May 1992
TL;DR: It is shown that by means of dynamic state feedback, it is possible for three-wheeled mobile robots to track arbitrary fast trajectories not reduced to equilibrium points by smooth time-varying laws.
Abstract: Smooth time-varying laws can solve the stabilization problem of nonholonomic mechanical systems. The authors show that by means of dynamic state feedback, it is possible for three-wheeled mobile robots to track arbitrary fast trajectories not reduced to equilibrium points. Dynamical modeling of nonholonomic mechanical systems for the case of three-wheeled mobile robots is considered. Dynamic feedback allows solution of the tracking problem for an omnidirectional mobile robot with less motors than degrees of freedom. This is possible by choosing output functions depending on the mass repartition of the robot. >
151 citations
TL;DR: In this paper, an algorithm utilizing the minimal number of integrations for the exact linearization of nonlinear systems to Brunovsky normal form under nonlinear feedback is presented, where the tools which are involved are based on classical constructions appearing in the theory of exterior differential systems.
Abstract: An algorithm utilizing the minimal number of integrations for the exact linearization of nonlinear systems to Brunovsky normal form under nonlinear feedback is presented. The tools which are involved are based on classical constructions appearing in the theory of exterior differential systems. >
123 citations
16 Dec 1992
TL;DR: In this paper, the stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using output feedback is considered, and emphasis is placed on the class of systems that can be transformed into a global normal form with no zero dynamics.
Abstract: The stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using output feedback is considered. Emphasis is placed on a class of systems that can be transformed into a global normal form with no zero dynamics. Semiglobal stabilization means that for every compact set of initial conditions, it is possible to design an output feedback controller that stabilizes the origin and includes the given compact set in the region of attraction. The system equations are allowed to depend on constant unknown parameters that do not change the vector relative degree of the system. The controller is robust with respect to these parameters. Global Lipschitz conditions are not required. >
TL;DR: In this article, an application of the feedback linearization technique to the design of a new command to line-of-sight (CLOS) guidance law for short-range surface-to-air (S2A) missiles is described.
Abstract: An application of the feedback linearization technique to the design of a new command to line-of-sight (CLOS) guidance law for short-range surface-to-air missiles is described. The key idea lies in converting the three-dimensional CLOS guidance problem to the tracking problem of a time-varying nonlinear system. The result may shed new light on the role of the feedforward acceleration terms used in the conventional CLOS guidance laws. Through computer simulation, the effect of the dynamics of the ground tracker and the autopilot on the guidance performance of the new CLOS guidance law is investigated. >
TL;DR: In this article, the problem of designing an output feedback control law for the stabilization of a class of non-minimum phase linear and nonlinear systems is considered, and a useful solution is given for the class of systems linearizable via state feedback.
12 May 1992
TL;DR: The authors propose an indirect adaptive scheme for incompletely controlled mechanical systems such as overhead cranes or, more generally, classical rigid manipulators ended by a simple pendulum, taking advantage of the particular structure of the equations.
Abstract: The authors propose an indirect adaptive scheme for incompletely controlled mechanical systems such as overhead cranes or, more generally, classical rigid manipulators ended by a simple pendulum. In the case of known parameters a dynamic state feedback produces full linearization. An adaptive version is obtained by a simple estimation method together with a certainty equivalence law, taking advantage of the particular structure of the equations. Global stability is discussed, and simulation results for the overhead crane are reported. >
13 Sep 1992
TL;DR: The feasibility of autopilot design for highly maneuverable bank-to-turn (BTT) missiles using feedback-linearization-based approaches is investigated and a sizable coupling between the longitudinal motion and lateral motion for large maneuvers is observed.
Abstract: The feasibility of autopilot design for highly maneuverable bank-to-turn (BTT) missiles using feedback-linearization-based approaches is investigated. Two schemes, namely, feedback linearization and robust feedback linearization, are designed and compared based on a full-scale six-degree-of-freedom HAVE DASH II terminal homing missile model. Although the feedback linearization controller is quite satisfactory in general, a sizable coupling between the longitudinal motion and lateral motion for large maneuvers is observed. This is attributed to the uncertainties arising from the approximation of the aerocoefficients and model simplification. The second scheme, which adds a robust outer-loop design based on Lyapunov's second method to the first scheme in order to account for this uncertainty, shows a significant improvement over the first scheme. >
24 Jun 1992
TL;DR: In this paper, the problem of synthesizing nonlinear state feedback controllers for nonlinear, non-minimum-phase processes in three different ways is addressed: partial linearization, inner-outer factorization, and single-output control.
Abstract: The design of controllers for nonlinear, nonminimum-phase systems is very challenging and is currently considered to be one of the most difficult theoretical control problems Most control algorithms for nonlinear processes perform a linearization making use of an inverse of the system In the linear case, the system can be factored into the minimum-phase and the nonminimum-phase parts and only the first one is inverted for purpose of control design A similar scheme for nonlinear systems is still under investigation The present work adresses the problem of synthesizing nonlinear state feedback controllers for nonlinear, nonminimum-phase processes in three different ways The first approach consists of a partial linearization which preserves stability by using an approximate stable/anti-stable factorization The second technique can be viewed as an inner-outer factorization based approach And, finally, in the single-output case, it is shown (through an example) that stabilization of the internal dynamics of a nonmininum-phase system can be achieved by using an additional input if this is feasible in practice In this case, the manipulated variables have different roles, ie, one is chosen such as to input/output feedback linearize the system and the second is used to locally stabilize the resulting nonminimum-phase internal dynamics
TL;DR: In this paper, a pulse-width modulated control for a class of electromechanical system models is designed, where approximate feedback linearization based on the integral manifold approach is achieved in an average sense.
Abstract: A pulse-width modulated control for a class of electromechanical system models is designed. It is shown how approximate feedback linearization, based on the integral manifold approach, can be achieved in an average sense. A correction term to the duty ratio is included which, in an application to electromechanical actuators, compensates for the electrical transients that cause torque ripple. Although designed on the basis of a model obtained through averaging, simulations show that the correction term improves the trajectory tracking performance of the actual system. >
01 Oct 1992
TL;DR: A general method is presented that assures an exact feedback linearization for both rigid and flexible-joint robots, as the joint flexibility can cause instability of robot control.
Abstract: Nonlinear feedback control for force-controlled robots with constrained end-effector motion is considered. A general method is presented that assures an exact feedback linearization for both rigid and flexible-joint robots, as the joint flexibility can cause instability of robot control. The feedback control linearizes and decouples the original nonlinear system into a number of decoupled linear subsystems. The effect of stiction on the end-effector contact with the environment is inherently incorporated in the formulation, using the same constrained system formalism. A version of the controller with improved robustness characteristics, based on the robust servomechanism theory, is proposed. The derivation of the control algorithm for a two-link planar robot interacting with a rough plane surface is presented as an example. Numerical simulation results confirm the effectiveness of the method. The issues associated with real-time robot control, such as the choice of sampling frequency and the influence of modeling errors, are discussed. >
13 Sep 1992
TL;DR: In this article, 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. >
TL;DR: In this article, a nonlinear control strategy to improve the steady-state stability of a weak AC/DC power system is presented, which is based on the extension of feedback linearization techniques to nonlinear descriptor system models.
Abstract: A nonlinear control strategy to improve the steady-state stability of a weak AC/DC power system is presented. The approach is based on the extension of feedback linearization techniques to nonlinear descriptor system models. This method produces a nonlinear control strategy which is capable of enhancing system performance for various system operating conditions. The control law is determined and simulation results are given. >
TL;DR: In this article, the authors developed a feedback guidance logic for steering and accelerating a single-stage vehicle along the superand hypersonic segments of a near-minimum-fuel ascent trajectory.
Abstract: Single-stage vehicles using air-breathing propulsion hold promise for more economical delivery of payloads to orbit. Feedback guidance logic is developed for steering and accelerating such a vehicle along the superand hypersonic segments of a near-minimum-fuel ascent trajectory. Accurate solutions of the minimum-fuel ascent problem show the effects of dynamic pressure, acceleration, and heating constraints and establish a basis for the development and assessment of guidance logic. The two-time-scale behavior in the optimal solution allows the state space to be decomposed into a control-dependent slow manifold and a family of fast manifolds. Near-optimal guidance is obtained by constructing a composite control law from the control for flying the minimum-fuel reduced-order trajectory on the slow manifold and a control for tracking the optimal reduced-order trajectory. The tracking problem is solved as a family of regulation problems corresponding to the family of fast manifolds, using the feedback linearization methodology from nonlinear geometric control theory. A complete characterization is given of all state transformation-static feedback pairs that lead to exact linearization of the fast dynamics. Simulation shows that the composite control law produces a near-minimum-fuel ascent.
01 Jan 1992
TL;DR: In this article, a feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs), which consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model.
Abstract: The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
12 May 1992
TL;DR: An existing nonlinear design methodology developed by Krener, approximate feedback linearization, is applied to the control of underactuated single-input-single-output nonlinear systems and a method to simplify the dynamics using partial precompensation which uses the constraint equations of motion is presented.
Abstract: An existing nonlinear design methodology developed by Krener (1984, 1987), approximate feedback linearization, is applied to the control of underactuated single-input-single-output nonlinear systems A computational approach to test for the order of linearization as well as a method to compute the approximate output function is derived A method to simplify the dynamics using partial precompensation which uses the constraint equations of motion is presented This approach is applied to a simple example Simulation results showed a substantial improvement in the operating range of the linear controller by using this approach >
16 Dec 1992
TL;DR: In this paper, a procedure is given to describe any nonlinear control system in a so-called nonexact Brunovsky form, which is sufficient to be linearizable by dynamic feedback if, and only if, the basis of this Brunovskyform can be represented as an equivalent system of exact one-forms.
Abstract: A procedure is given to describe any nonlinear control system in a so-called nonexact Brunovsky form. A system is shown to be differentially flat, a property which is sufficient to be linearizable by dynamic feedback, if, and only if, the basis of this Brunovsky form can be represented as an equivalent system of exact one-forms. Sufficient conditions for equivalence between a basis of the Brunovsky form and a system of exact one-forms are given in the case of two-input systems. These sufficient conditions lead to a constructive procedure. >
TL;DR: In this article, the stochastic linearization approach is examined for non-linear systems subjected to parametric type excitations. And the Gaussian closure approach is shown to be an equivalent approach to the linear approach.
Abstract: The stochastic linearization approach is examined for non-linear systems subjected to parametric type excitations. It is shown that, for these systems too, stochastic linearization and Gaussian closure are two equivalent approaches if the former is applied to the coefficients of the Ito differential rule. A critical review of other stochastic linearization approaches is also presented and discussed by means of simple examples.
TL;DR: Optimal pursuit-evasion problem between two aircraft including nonlinear point-mass vehicle models and a realistic weapon envelope is analyzed and closed form solution is obtained in nonlinear feedback form, useful for on-board real-time implementation.
Abstract: Optimal pursuit-evasion problem between two aircraft including nonlinear point-mass vehicle models and a realistic weapon envelope is analyzed. Using a linear combination of flight time and the square of the vehicle acceleration as the performance index, closed form solution is obtained in nonlinear feedback form. Due to its modest computational requirements, this guidance law useful for on-board real-time implementation.
16 Dec 1992
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.
Abstract: The authors define and study a pair of nonlinear parallel projection operators associated with a nonlinear feedback system. The input-output L/sub 2/-stability of a feedback system is shown to be equivalent to a coordinating of the input and output spaces, which is also equivalent to the existence of a pair of nonlinear parallel projection operators onto the graph of the plant and the inverse graph of the controller. These projections have equal norms whenever one of the feedback elements is linear. A bound on this norm is given in the case of passive systems with unity negative feedback. >
09 Nov 1992
TL;DR: An adaptive feedback linearizing scheme for position control of a switched reluctance motor that compensates for all the nonlinearities 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.
Abstract: The authors present an adaptive feedback linearizing scheme for position control of a switched reluctance motor (SRM). This nonlinear adaptive control structure compensates for all the nonlinearities 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. First, a detailed nonlinear model of the SRM is developed, and the parameterization of the model and the electronic commutation strategy are established. The gradient algorithm is used for the adaptation law. The linearizing adaptive control is applied to a single link direct-drive manipulator. Simulation results are given to demonstrate the effectiveness of the control method. >
01 Jan 1992
TL;DR: The internal motion of the mobile robot when the reference point moves forward is asymptotically stable whereas the internal motion when thereference point moves backward is unstable.
Abstract: A wheeled mobile robot is subject to both holonomic and nonholonomic constraints. Representing the motion and constraint equations in the state space, this paper studies the feedback linearization of the dynamic system of a wheeled mobile robot. The main results of the paper are: (1) It is shown that the system is not input-state linearizable. (2) If the coordinates of a point on the wheel axis are taken as the output equation, the system is not input-output linearizable by using a static state feedback; (3) but is input-output linearizable by using a dynamic state feedback. (4) If the coordinates of a reference point in front of the mobile robot are chosen as the output equation, the system is input-output linearizable by using a static state feedback. (5) The internal motion of the mobile robot when the reference point moves forward is asymptotically stable whereas the internal motion when the reference point moves backward is unstable. A nonlinear feedback is derived for each case where the feedback linearization is possible. Disciplines Robotics Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-92-45. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/503 On Feedback Linearization of Mobile Robots MS-CIS-92-45 GRASP LAB 321 Xiaoping Yun Yosl~io Yamamot o University of Pennsylvania School of Engineering and Applied Science Computer and Information Science Department Philadelphia, PA 19104-6389
TL;DR: In this paper, the authors consider the problem of approximately feedback linearizing a single input nonlinear system around the equilibrium manifold e while making the error terms be of highest order on e. A constructive procedure is presented and illustrated with a simple example.