Showing papers on "Feedback linearization published in 1996"

Theory of Robot Control

Abstract: Part 1 Rigid manipulators: modelling and identification joint space control task space control motion and force control. Part 2 Flexible manipulators: elastic joints flexible links. Part 3 Mobile robots: modelling and structural properties feedback linearization nonlinear feedback control. Appendix: control background.

Nonlinear control design: geometric, adaptive and robust

Abstract: STATE FEEDBACK. Feedback Linearization. Adaptive Feedback Linearization. Output Tracking. OUTPUT FEEDBACK. Adaptive Observers. Stabilization and Exponential Tracking. Robust Regulation and Adaptive Tracking.

Nonlinear Process Control

Abstract: The need for nonlinear process control systems introduction to nonlinear systems topics in nonlinear system theory identification techniques for nonlinear systems feedback linearization techniques nonlinear model control strategies design of nonlinear state observers artificial neural networks.

Linearization of Discrete-Time Systems

Abstract: The algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete-time nonlinear systems. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools, whereas this is not the case for nonlinear continuous-time systems, in which case the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recasted through the language of differential forms. In the event that a system is not feedback linearizable, the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system. A discrete-time system may be linearizable by dynamic state feedback, though it is not linearizable by static state feedback. Necessary and sufficient conditions are given for the existence of a so-called linearizing output, which in turn is a sufficient condition for dynamic state feedback linearizability.

Linear and nonlinear state-space controllers for magnetic levitation

Abstract: The problem of precisely controlling (within sensor resolution) the height of a steel ball above the ground by levitating it against the force of gravity using an electromagnet is considered. The state variables used to model the system are the ball's position below the magnet, the ball's speed and the current in the electromagnet. Two state-space controllers are compared in terms of their performance in controlling the ball's position. The first controller is based on feedback linearization where a nonlinear state-space transformation along with nonlinear state feedback is used to linearize the system exactly. A linear controller is then used on the resulting system to control the ball's position. As a direct measurement of ball speed is not available, a nonlinear observer with linear error dynamics is used to estimate the speed. The second controller is a standard linear state feedback controller whose design is based on a linear model found by perturbing the nonlinear system model about an operating po...

Intelligent planning and control for multirobot coordination: An event-based approach

Abstract: A new planning and control scheme for multirobot coordination is presented. First, the event-based planning and control theory is introduced. The most important step is the design of an event-based motion reference for the multirobot system. It drives the system to achieve the best possible coordination. Hybrid position/force controllers which are able to perform a large class of tasks are designed based on the combination of general task space with the well-known nonlinear feedback linearization technique. To improve the force control performance, the dynamics of joint motors have been considered in the force control. For a given task, a task projection operator can be found for each robot with the consideration of redundancy management. It projects the feedback linearized model to the actual task space. A distributed computing architecture is proposed to implement this scheme in a parallel computation. The event-based coordination scheme was experimentally implemented and tested for the coordinated control of two 6 DOF PUMA 560 robots with very good results.

Control of Wing Rock Motion Using Adaptive Feedback Linearization

Abstract: The theory of adaptive control of feedback linearizable systems is applied to designing the control of wing rock motion with the extension of the technique to include tracking. The adaptation law is designed to adjust the aerodynamic parameters in the model. Precise tracking and maximum performance can be achieved if sufficient rolling moment derivative because of lateral control components are available. Case studies and simulation are carried out to illustrate the results.

Stability and flying qualities robustness of a dynamic inversion aircraft control law

Abstract: Dynamic inversion, or feedback linearization theory, represents a commonly used nonlinear control method for designing aircraft control laws. This method has the ability to control a highly nonlinear plant but suffers from the lack of guaranteed robustness. The stability and flying qualities robustness of a dynamic inversion based control law, designed for a prototype aircraft, to uncertain aerodynamic parameters is analyzed. The results indicate that the pitch plane stability and flying qualities are robust to parameter uncertainties, but the lateral directional flying qualities are sensitive to uncertain stability derivatives.

A normal form approach to approximate input-output linearization for maximum phase nonlinear SISO systems

Abstract: A control synthesis scheme is presented for nonlinear single-input-single-output systems which have completely unstable (antistable) zero dynamics. The approach is similar in spirit to linear approaches for nonminimum phase systems and involves the derivation of an input-output linearizing controller for a suitably-defined nonlinear minimum phase approximation to the original system. The linearizing controller achieves an approximately linear input-output response and internal stability.

Constrained nonlinear optimal control: a converse HJB approach

Abstract: Extending the concept of solving the Hamilton-Jacobi-Bellman (HJB) optimization equation backwards [2], the so called converse constrained optimal control problem is introduced, and used to create various classes of nonlinear systems for which the optimal controller subject to constraints is known. In this way a systematic method for the testing, validation and comparison of different control techniques with the optimal is established. Because it naturally and explicitly handles constraints, particularly control input saturation, model predictive control (MPC) is a potentially powerful approach for nonlinear control design. However, nonconvexity of the nonlinear programs (NLP) involved in the MPC optimization makes the solution problematic. In order to explore properties of MPC-based constrained control schemes, and to point out the potential issues in implementing MPC, challenging benchmark examples are generated and analyzed. Properties of MPC-based constrained techniques are then evaluated and implementation issues are explored by applying both nonlinear MPC and MPC with feedback linearization.

Adaptive Control of Feedback Linearizable Nonlinear Systems With Application to Flight Control

Abstract: The question of output trajectory control of a class of input-output feedback linearizable nonlinear dynamical systems using state variable feedback in the presence of parameter uncertainty is considered. For the derivation of a control law, a hypersurface is chosen which is a linear function of the tracking error, its derivatives, and the integral of the tracking error. An adaptive control law is derived such that in the closed-loop system, the trajectory asymptotically converges to this hypersurface. For any trajectory evolving on this surface, the tracking error tends to zero. Based on these results, a new approach to the design of an adaptive flight control system is presented. In the closed-loop system, trajectory control of the sets of output variables roll angle, angle of attack, and sideslip angle ( ,#,/?) using aileron, rudder, and elevator control is presented. Simulation results are obtained to show that precise simultaneous longitudinal and lateral maneuvers can be performed in spite of large uncertainty in the aerodynamic parameters.

Feedback control of two-time-scale nonlinear systems

Abstract: This article concerns a class of two-time-scale single-input single-output nonlinear systems. For such systems, combination of singular perturbation and geometric methods is employed to synthesize well-conditioned static state feedback laws that induce a well-characterized input-output behaviour and guarantee stability of the closed-loop system. The developed control laws are applied to two nonlinear chemical processes with time-scale multiplicity and their performance is evaluated through simulations.

Control and flight performance of tethered satellite small expendable deployment system-II

Abstract: The second mission of the small expendable deployment system (SEDS-II) followed the successful mission of SEDS-I, which deployed freely a small instrumented probe on a 20-km tether. Unlike SEDS-I, the deployment of SEDS-II was controlled to provide a small libration amplitude and tether velocity at the end of deployment. The preflight goal for SEDS-II was a maximum libration of less than 10 deg and a final velocity of less than 1 m/s. The control problem was made difficult by the limited capabilities of the SEDS sensors and onboard computer and the large uncertainties inherent in the response of the actuator (brake) and the plant (deployer). The nonlinear, nonautonomous control problem is divided in two parts by using a numerically formulated feedback linearization, i.e., by devising 1) a nonlinear control (reference) trajectory and 2) a linear control about the reference trajectory. An ad hoc feedback law that forces the perturbed system to follow the reference trajectory is derived by using a linearized variational model. The controller is then tested, through computer simulations, for large deviations of the model parameters on the nonlinear model. The relevant flight data are also presented and compared to the reference values to demonstrate the validity and robustness of the control law, which provided a maximum libration amplitude of less than 4 deg and a final tether velocity of less than 0.02 m/s.

Robust adaptive NN feedback linearization control of nonlinear systems

Abstract: In this paper, a robust adaptive neural network feedback linearization control law is presented for a class of nonlinear dynamic systems. First, the ‘GL’ matrices and the corresponding operator are introduced, which brings a new methodology into the analysis of neural networks. Secondly, the basic ideas of Feedback Linearization Control (FLC) of nonlinear systems are discussed. Finally, a robust adaptive neural network FLC of nonlinear systems is presented. It is shown that uniformly stable adaptation is assured and asymptotic tracking is achieved if Bounded Basis Functions (BBF) are used, and output tracking errors also converge to zero

Design of Nonlinear Autopilots for High Angle of Attack Missiles

Abstract: Two nonlinear autopilot design approaches for a tail-controlled high angle of attack air-to-air missile are described. The research employs a highly nonlinear, time varying pitch plane rigid- body dynamical model of a short range missile. Feedback linearization technique together with linear control theory are then used for autopilot design. In order to manage the difficulties associated with "zerodynamics" that arise in tail controlled missiles, two distinct approaches for approximate feedback linearization are advanced. The first approach imposes a time-scale structure in the closed-loop dynamics, while the second technique redefines the output. Performance of these autopilots are illustrated in a nonlinear simulation.

Improving the performance of stabilizing controls for nonlinear systems

Abstract: There are a variety of tools for computing stabilizing feedback control laws for nonlinear systems. The difficulty is that these tools usually do not take into account the performance of the control, and therefore systematic improvement of an arbitrary stabilizing control law is extremely difficult and often impossible. The objective of this article is to present a design algorithm that addresses this problem. The algorithm that we present iteratively computes a sequence of control laws with increasingly improved performance. We also consider implementation issues and discuss some of the successes and difficulties that we have encountered. Finally, we present a number of illustrative examples and compare our algorithm with perturbation methods.

Approximate Feedback Linearization: A Homotopy Operator Approach

Abstract: In this paper, we present an approach for finding feedback linearizable systems that approximate a given single-input nonlinear system on a given compact region of the state space. First, we show that if the system is close to being involutive, then it is also close to being linearizable. Rather than working directly with the characteristic distribution of the system, we work with characteristic one-forms, i.e., with the one-forms annihilating the characteristic distribution. We show that homotopy operators can be used to decompose a given characteristic one-form into an exact and an antiexact part. The exact part is used to define a change of coordinates to a normal form that looks like a linearizable part plus nonlinear perturbation terms. The nonlinear terms in this normal form depend continuously on the antiexact part, and they vanish whenever the antiexact part does. Thus, the antiexact part of a given characteristic one-form is a measure of nonlinearizability of the system. If the nonlinear terms are small, by neglecting them we obtain a linearizable system approximating the original system. One can design control for the original system by designing it for the approximating linearizable system and applying it to the original one. We apply this approach for design of locally stabilizing feedback laws for nonlinear systems that are close to being linearizable.

Feedback linearization and solar pressure satellite attitude control

Abstract: The question of large angle pitch attitude maneuver of satellites using solar radiation pressure is considered. For pitch axis maneuver, two highly reflective control surfaces are used to generate radiation moment. Based on dynamic feedback linearization, a nonlinear control law is derived for large pitch attitude control. In the closed-loop system, the response characteristics of the pitch angle are governed by a fourth-order linear differential equation. Robustness of control system is obtained by the integral error feedback. Simulation results are presented to show that in the closed-loop system, attitude control of the satellite is accomplished in spite of the parameter uncertainty in the system.

Optimal feedback control of a nonlinear system - Wing rock example

Abstract: A procedure is presented for optimizing a state feedback control law for a nonlinear system with respect to a positive performance index. The Hamilton-Jacobi-Bellman equation is employed to derive the optimality equations wherein this performance index is minimized. The closed-loop Lyapunov function is assumed to have the same matrix form of state variables as the performance index. The constant interpolated terms of these matrix forms are easily determined so as to guarantee their positive definitenesses. The optimal nonlinear system is asymptotically stable in the large, as both the closed-loop Lyapunov function and performance index are positive definite. An unstable wing rock equation of motion is employed to illustrate this method. It is shown that the wing rock model using nonlinear state feedback is asymptotically stable in the large. Both optimal linear and nonlinear state feedback cases are evaluated.

Nonlinear games: examples and counterexamples

Abstract: Popular nonlinear control methodologies are compared using benchmark examples generated with a "converse Hamilton-Jacobi-Bellman" method (CoHJB). Starting with the cost and optimal value function V, CoHJB solves HJB PDEs "backwards" algebraically to produce nonlinear dynamics and optimal controllers and disturbances. Although useless for design, it is great for generating benchmark examples. It is easy to use, computationally tractable, and can generate essentially all possible nonlinear optimal control problems. The optimal control and disturbance are then known and can be used to study actual design methods, which must start with the cost and dynamics without knowledge of V. This paper gives a brief introduction to the CoHJB method and some of the ground rules for comparing various methods. Some very simple examples are given to illustrate the main ideas. Both Jacobian linearization and feedback linearization combined with linear optimal control are used as "strawmen" design methods.