Showing papers on "Feedback linearization published in 1994"

Nonlinear flight control using neural networks

Abstract: The theoretical developmentofa direct adaptivetracking controlarchitectureusingneuralnetworks ispresented. Emphasis is placed on utilization of neural networks in a  ight control architecture based on feedback linearization of the aircraft dynamics. Neural networks are used to represent the nonlinear inverse transformation needed for feedback linearization. Neural networks may be Ž rst trained off line using a nominalmathematicalmodel, which provides an approximate inversion that can accommodate the total  ight envelope. Neural networks capable of on-line learning are required to compensate for inversion error, which may arise from imperfect modeling, approximate inversion, or sudden changes in aircraft dynamics. A stable weights adjustment rule for the on-line neural network is derived. Under mild assumptions on the nonlinearities representing the inversion error, the adaptation algorithm ensures that all of the signals in the loop are uniformly bounded and that the weights of the on-line neural network tend to constant values. Simulation results for an F-18 aircraft model are presented to illustrate the performance of the on-line neural network based adaptation algorithm.

Partial feedback linearization of underactuated mechanical systems

Abstract: In this paper we discuss the partial feedback linearization control of underactuated mechanical systems. We consider an n degree of freedom system having m actuated, or active, degrees of freedom and l=n-m unactuated, or passive, degrees of freedom. It is known that the portion of the dynamics corresponding to the active degrees of freedom may be linearized by nonlinear feedback. In this paper we show, alternatively, that the portion of the dynamics corresponding to the passive degrees of freedom may be linearized by nonlinear feedback under a condition that we call strong inertial coupling. We derive and analyze the resulting zero dynamics which are crucial to an understanding of the response of the overall system. Simulation results are presented showing the performance of two link underactuated robots under partial feedback linearization control. >

H∞ control via measurement feedback for affine nonlinear systems

Abstract: This paper summarizes some recent results on the problem of disturbance attenuation via measurement feedback, with internal stability, for an affine nonlinear system. The solution of the problem is shown to be related to the existence of solutions of a pair of Hamilton-Jacobi inequalities in n independent variables, associated with state feedback and, respectively, output-injection design.

Nonlinear predictive controllers for continuous systems

Abstract: In this paper a new technique for the design of nonlinear feedback controllers to track desired response histories is presented. The controller is developed based on continuous minimization of predicted tracking errors. Some properties on the tracking performance and robustness of the controller are established. Both stateand output-tracking problems are considered in a unified framework. The effectiveness of this approach is demonstrated by an application in missile autopilot design.

Swing up control of the Acrobot

Abstract: Investigates the problem of swing up control of the Acrobot, a two-link, underactuated robot that is a useful vehicle to study problems in nonlinear control The author develops a swing up strategy based on partial feedback linearization The algorithm works by creating "unstable zero dynamics" which drives the first link of the Acrobot away from its open loop stable equilibrium toward the inverted position Control is switched to a linear controller, designed to balance the arm about the inverted configuration, whenever the swing up controller moves the Acrobot into the near vertical position Simulation results are presented showing the performance of the system >

Feedback linearization using neural networks

Abstract: For a class of single-input, single-output (SISO), continuous-time nonlinear systems, a neural network-based controller is presented that feedback linearizes the system. Control action is used to achieve tracking performance for a state-feedback linearizable, but unknown nonlinear system. A global stability proof is given in the sense of Lyapunov. It is shown that all the signals in the closed-loop system and the control action are GUUB. No learning phase requirement is needed and initialisation of the network is straightforward. >

Flexible-link robot arm control by a feedback linearization/singular perturbation approach

Abstract: A nonlinear tracking controller for the link-tip positions and velocities of a multi-link flexible robot arm is designed that gives guaranteed performance. The controller has three parts: a model-based trajectory generator, an inner loop based on input-output feedback linearization, and an outer loop that stabilizes the internal dynamics (e.g., the flexible modes) using a singular perturbation design. We show how to stabilize the internal dynamics by selecting a physically meaningful modified performance output for tracking; this output is the slow portion of the link-tip motions. That is, the tracking requirement is relaxed so that the internal dynamics are stabilizable through a boundary layer correction that attenuates the flexible mode vibrations. © 1994 John Wiley & Sons, Inc.

Shuttle entry guidance revisited using nonlinear geometric methods

Abstract: The entry guidance law for the Space Shuttle Orbiter is revisited using nonlinear geometric methods. The Shuttle guidance concept is to track a reference drag trajectory that has been designed to lead to a specified range and velocity. The current guidance law provides exponential tracking locally. We show that the approach taken in the original derivation of the Shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, we are led to an alternative, potentially superior, guidance law. To compare the two guidance laws, stability and performance domains in state space are defined, taking into account the nonlinear dynamics, a state constraint, and a control constraint. The stability and performance domains for the Shuttle law and the alternative law are constructed numerically. The effects of increasing the control capability and changing a parameter in the guidance laws are illustrated. The alternative guidance law achieves the desired performance over a larger domain of the state space; the stability domains for the two laws are similar. For the current operating domain of the Shuttle, the performance improvement offered by the alternative guidance law is probably not significant. With a larger operating domain for the Shuttle or some other entry vehicle, the alternative guidance law should be considered. A more comprehensive comparison taking into account important factors not considered here, such as robustness, would be necessary to decide whether or not the alternative guidance law is superior.

Rule-based control for a flexible-link robot

Abstract: This paper presents a design and implementation case study that focuses on endpoint position control of a two degree-of-freedom robot with very flexible links. Linear and nonlinear conventional control techniques have been shown to be somewhat successful in achieving various control objectives for the laboratory test beds of this and many other studies; however, their reliance on an accurate mathematical model of the process often limits their chances of achieving good endpoint position control. Here the authors investigate an alternative to conventional approaches where they employ rule-based controllers to represent and implement two general forms of knowledge that they have about how to best control the mechanism: i) experience gained from the use of a mathematical model and conventional control; and ii) an intuitive understanding of the dynamics of the two-link flexible robot. The authors begin the case study by assuming that the controls for the two links of the robotic mechanism can be designed and implemented independently and investigate the performance of rule-based fuzzy controllers which only use simple intuitive knowledge about how to control two independent links. Next, the authors show that if the rule-base is augmented with knowledge about the coupling effects between the two links, the controller can achieve improved performance over the uncoupled case. The final portion of the case study, which represents the authors' primary contribution, investigates the use of a two-level hierarchical rule-based controller with a simple upper-level "expert controller" that captures knowledge about how to supervise the application of low-level fuzzy controllers during movements in the robot workspace. Overall, the rule-based supervisory control results have proven to be extremely effective for vibration suppression in the laboratory test bed of this study, comparing favorably (in terms of performance, design complexity, and implementation issues) to a variety of conventional techniques attempted to date (including linear robust designs, feedback linearization, input command shaping, and adaptive approaches). >

Feedback linearization and driftless systems

Abstract: The problem of dynamic feedback linearization is recast using the notion of dynamic immersion. We investigate here a “generic” property which holds at every point of a dense open subset, but may fail at some points of interest, such as equilibrium points. Linearizable systems are then systems that can be immersed into linear controllable ones. This setting is used to study the linearization of driftless systems: a geometric sufficient condition in terms of Lie brackets is given; this condition is also shown to be necessary when the number of inputs equals two. Though noninvertible feedbacks are nota priori excluded, it turns out that linearizable driftless systems with two inputs can be linearized using only invertible feedbacks, and can also be put into a chained form by (invertible) static feedback. Most of the developments are done within the framework of differential forms and Pfaffian systems.

Differential flatness and absolute equivalence

Abstract: In this paper we give a formulation of differential flatness-a concept originally introduced by Fliess, Levine, Martin, and Rouchon (1992)-in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differential algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we show that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are not equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions are also discussed. >

Nonlinear differential-geometric techniques for control of a series DC motor

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. Two nonlinear feedback laws are considered based on feedback linearization and input-output linearization, respectively. Both of these control laws require knowledge of the speed and load-torque. The speed/torque estimation scheme and the control schemes are valid in the presence of magnetic saturation in the field circuit and when high-speed field-weakening is employed. By neglecting the armature inductance, the estimation is accomplished 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 nontrivial state-space transformation allowing control of the full state trajectory. An input-output linearization controller with stable internal dynamics is also explicitly constructed. Finally, simulations are given to demonstrate the algorithms. >

Nonlinear regulation of a Lorenz system by feedback linearization techniques

Abstract: In this paper we analyze some dynamical properties of a chaotic Lorenz system driven by a control input. These properties are the input-state and the input-output feedback linearizability, the stability of the zero dynamics, and the phase minimality of the system. We show that the controlled Lorenz system is feedback equivalent to a controllable linear system. We also show that the zero dynamics are asymptotically stable when the output is an arbitrary state. These facts allow designing control laws such that the closed-loop system has asymptotically stable equilibrium points with dynamic behavior free from chaotic transients. The controllers are robust in the sense that the closed-loop system is stable and non chaotic around a nominal set of parameter values. The results also show that the proposed controllers give better responses compared to linear algorithms obtained from standard linearization techniques, and exhibit a good performance even when the control input is bounded.

Adaptive nonlinear excitation control of power systems with unknown interconnections

Abstract: Adaptive nonlinear excitation control of large-scale power systems is considered in this paper. The approach used is an adaptive feedback linearizing control to enhance the robustness to unknown or varying interconnection parameters like equivalent reactances of the transmission lines. Control design based on external feedback linearization may not be robust to handle varying power-system configurations. Inexact cancellation of terms due to uncertainties may result in performance deterioration like inter-system oscillations. Adaptation in estimated parameters is utilized to achieve an asymptotically exact cancellation of terms. It is shown that the adaptive control results in bounded states and maintains the desired performance. The control scheme developed is applied to a power system with two generators and an infinite bus connected through a network of transformers and transmission lines. Simulation studies for unknown interconnections arising due to faults and subsequent line switchings in the transmission network are carried out. The performance using the nonadaptive feedback linearizing control is shown to degrade for network configuration variations arising due to transmission line faults. The response obtained using the proposed scheme is compared with that using a conventional IEEE Type I excitation control. The studies validate the fact that connective stability and robust performance is maintained for unknown interconnection topology using the adaptive feedback linearizing scheme. >

Control of balance for a nonlinear nonholonomic non-minimum phase model of a bicycle

Abstract: A feedback control law is derived that causes a nonlinear, nonholonomic, nonminimum phase model of a riderless powered two-wheeled bicycle to stably track arbitrary smooth trajectories of roll-angle and non-zero rear-wheel velocity.

Experiments on rigid body-based controllers with input preshaping for a two-link flexible manipulator

Abstract: Dynamics of multi-link flexible manipulators are highly nonlinear. Furthermore, the vibrational frequencies of these manipulators are configuration-dependent. Therefore, any feedforward or feedback algorithm has to deal with these frequency variations. In this paper, an inner-loop nonlinear controller based on feedback linearization of O(1) dynamics derived from an asymptotic expansion is utilized. It is shown that this control scheme significantly reduces the frequency variations due to the geometric configuration of the arm and cancels some of the nonlinearities due to Coriolis and centripetal effects. The advocated control law is compared and contrasted to an independent joint-based PD controller. However, since the aforementioned controllers are joint-based control schemes, significant vibrations are still induced at the end-effector. To this end, these control schemes are augmented with an input preshaper for vibration suppression. The objective is to preshape the reference input signals so that a vibration free output is achieved. The input preshaping scheme is shown to be effective when the plant dynamics are linear and time-invariant. These assumptions do not hold for the multi-link flexible manipulators as alluded to above. Application of an inner-loop nonlinear control to cancel some of the nonlinearities and to reduce configuration dependence of structural frequencies enhances the performance of the advocated input preshaping scheme or any other outer-loop linear control design. Experimental and simulation results for a two-link flexible manipulator are provided to validate the effectiveness of the advocated controllers. >

Gain scheduled control of magnetic suspension system

Abstract: A gain scheduling approach for the suspension control of a nonlinear MAGLEV system is presented. We show that this technique is very useful for improving not only performance to the operational disturbances originating aerodynamic force but also robustness to the uncertainty of payload. As a scheduling variable, even though the external disturbance need to be estimated in real time, but the additive measurement is not required. Some simulations show that the gain scheduling control system performs very well comparing with other methods using a nonlinear feedback linearization or a fixed gain linear feedback.

Input/output linearization control of an electro servo-hydraulic actuator

Abstract: This paper presents a nonlinear control concept for servo-hydraulic actuators based on exact i/o-linearization techniques. Servo-hydraulic actuators have dominant nonlinearities due to the valve orifice flow characteristics. In most applications, they cannot be globally approximated by linear models over an extended working range. In this paper an input-output linearization technique, which exactly compensates the global nonlinearities of the system, is applied to a servo-hydraulic actuator and compared with a standard linear multi-sensor controller. The controlled actuator provides excellent transient and robustness behaviour shown in the simulation results. >

Feedback linearization of transverse dynamics for periodic orbits

Abstract: In this paper we give necessary and sufficient conditions for feedback linearization of the transverse dynamics (TFL) of a nonlinear affine single-input system in a neighborhood of a periodic orbit. The TFL procedure provides a means of finding coordinates that are tuned to the structure of the control system with respect to the periodic orbit. An autonomous feedback control providing exponential stability of the periodic orbit is easily designed in the transverse coordinate system. >

Non linear control of PWM rectifier by state feedback linearization and exact PWM control

Abstract: This paper describes two nonlinear studies concerning a PWM rectifier. A nonlinear control scheme using state feedback linearization is presented, followed by an exact compensation method for the nonlinear switching effects of PWM. The two control laws developed in this paper show higher performance than traditional cascade control methods. >

Some properties and stability results for sector-bounded LTI systems

Abstract: This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector [a, b] in terms of linear matrix inequalities in its state-space realization matrices, which represent a generalization of similar conditions for bounded /spl Hscr//sub /spl infin//-norm systems. Further, a weaker definition of LTI systems strictly inside sector [a,b] is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems. >

Robust semi-global stabilization of minimum-phase input-output linearizable systems via partial state and output feedback

Abstract: In this paper we consider the problem of robust semi-global stabilization and/or semi-global practical stabilization of minimum-phase input-output linearizable systems. The results of this paper significantly extend the recent work of Teel-Praly on SISO minimum-phase systems in several directions. Among these directions are the development of MIMO theory and the relaxation of the restriction on the interaction between nonlinear zero dynamics and the state of the linearizable part of the system.

Nonlinear control and Lie-Backlund transformations: towards a new differential geometric standpoint

Abstract: Nonlinear control is related to Lie-Backlund transformation of some infinite-dimensional manifolds. State-variable representations, feedback and, especially, dynamic feedback linearization, i.e., flatness, are briefly examined, as well as the relationship with the differential algebraic approach. This setting provides a most natural framework for time scalings. We indicate via the carlike robot how to utilize this new time for stabilizing around a trajectory a driftless flat system. >

Nonlinear control of a bioreactor model using exact and I/O linearization

Abstract: A nonlinear multivariable bioreactor system has been the subject of two differential geometry feedback control design approaches. Exact linearization and input/output linearization are applied to the bioreactor model and verified by simulation experiments. Exact linearization via state feedback shows a high degree of coupling on the controlled variables and large changes on the manipulated variables. Input/output linearization, with the ability of implementing independent, decoupled control loops, gives more satisfactory results. The issues of invertabiity and parameter uncertainties are also discussed in this paper.

Adaptive passification of nonlinear systems

Abstract: In this paper we consider feedback passive systems, defined as nonlinear systems that can be rendered (strictly) passive by means of state feedback. For feedback passive systems in a parametric normal form, we present an adaptive controller that effectively "passifies" the system. The proposed control uses techniques of speed-gradient (S-G) methodology. Stability results can be given which do not require the plant to be linear in the parameters. Moreover, examples indicate that the S-G approach has several good features such as avoiding overparametrization, preserving physical structure and improving the speed of convergence. >

Adaptive nonlinear control of spacecraft

Abstract: The problem of spacecraft attitude control and momentum management is addressed using nonlinear controllers based on feedback linearization. A chief limitation of the feedback linearization technique is that it requires an exact cancellation of nonlinear terms in order to obtain linear input-output behavior. Adaptive nonlinear controllers for linearizable systems are investigated to overcome this restriction and to achieve asymptotic linear behavior. The adaptive nonlinear approach is shown to effectively control the Space Station attitude and effector momentum, while providing accurate estimates of inertias.

A neural network controller for flexible-link robots

Abstract: The object of this paper is to achieve tracking control of a partially known flexible-link robot arm. We show how to stabilize the internal dynamics by selecting a physically meaningful modified performance output for tracking. The controller is composed of a singular-perturbation-based fast control and an outer-loop slow control. The slow subsystem is controlled by a neural network (NN) for feedback linearization, plus a PD outer-loop for tracking, and a robustifying term to assure the closed-loop stability. No off-line training or learning is needed for the NN. Tracking and stability are proven using Lyapunov techniques that yield a novel modified NN weight tuning algorithm. >

Control of feedback linearizable systems with input unmodeled dynamics

Abstract: Considers nonlinear systems with stable linear unmodeled dynamics at the input. First the authors illustrate the main instability mechanisms on an example. Then the authors propose a dynamic feedback design which guarantees global boundedness in the presence of input unmodeled dynamics. The authors apply this design to feedback linearizable systems, for which global asymptotic stability is also achieved. >