John W. Sunkel

Design of Lifted Dual-Rate Digital Controllers for X-38 Vehicle

A new state-matching digital redesign method to x8e nd the lifted dual-rate pulse-amplitude-modulated (PAM) and pulse-width-modulated (PWM) digital controllers from a predesigned, state-feedback, continuous-time controller is presented. The proposed method provides close matching of the states of the continuous-time controlled analog system with those of the digitally redesigned system (including intersample behavior). The redesigned lifted dual-rate controller enables the digitally controlled X-38 vehicle to track the desired trajectory while remaining insensitive to modeling parameters, initial conditions, and exogenous disturbances for larger sample times than existing methods. The X-38 will require a PAM controller for commanding the electromechanical actuators that operate its aerodynamic surfaces for x8f ight in the atmosphere. PWM control will be used to command the reaction control jets during orbital operations. The proposed method provides a new alternative for indirect digital design of state-feedback multivariable continuous-time systems.

Digital redesign of an optimal momentum management controller for the Space Station

A new digital redesign technique is developed for determining the digital version of an optimal momentum management controller previously designed by the authors for the Space Station Freedom. The technique matches all the states at all sampling instants to find a pseudo-continuous time quadratic regulator. It is shown that the redesigned digital states closely match the continuous time optimal states. It is also shown how the redesign technique can be applied to a state estimator.

Robust optimal pole-placement in a vertical strip and disturbance rejection

Abstract This paper presents a linear quadratic regulator (LQR) for robust closed-loop pole-placement within a vertical strip, and disturbance rejection with an H ∞-norm constraint for the uncertain linear systems. The concerned systems cover both matched and mismatched uncertain linear systems with unstructured or structured uncertainties existing in both the system and input matrices. A set of tuning parameters is incorporated for some flexibility in finding a solution to the algebraic Riccati equation, and a controller gain parameter is selected for robust pole clustering. Also, a constraint is established to verify whether the proposed robust LQRs preserve H 2 optimality with respect to a specific quadratic cost function.

Digitally Redesigned Pulse-Width Modulation Spacecraft Control

This paper presents a new method for the design of control laws for systems with on-off nonlinear actuators. The new methodology improves the design of control laws for pulse-modulated systems by allowing the use of continuous-time multi-inputlmultioutput design procedures. Discrete-time state feedback control gains are developed from the digital redesign of continuous-time feedback gains, based on a geometric series approximation, to closely match the states of the closed-loop hybrid system to those of the original designed closed-loop continuous-time system at each sampling instant. A delay is then incorporated into a pulse-width modulator design to closely match the states of the modulated system to those of the discrete-time pulse-amplitude modulated system. The delay time is improved from previous work to provide a close match between the states for pulse durations of all sizes, in effect matching the states of the pulse-width modulated system to those of the closed-loop continuous-time system. The new control law design is applied to the problem of attitude control of the Space Shuttle Orbiter with the Hubble Space Telescope deployed on its remote manipulator. * Senior Member Technical Staff. Member A I M . t Professor, Electrical Engineering. Member AIAA. tt Aerospace Engineer. Member AIAA. Copyright O 1995 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Many paradigms are available for the synthesis of control laws for continuous-time systems, and though many methods also exist for developing discrete-time or digital controllers, it is often desirable to design a control law for the continuous-time plant. It is often more direct to determine the control specifications in the continuous-time or frequency domain. Also, direct digital control law design has difficulty in predetermining the hybrid control specifications and ignores inter sampling effects. Yet, these continuoustime control laws are generally implemented via discrete-time computer control, requiring that a discrete-time control, equivalent to the continuous-time control, be developed. The process of developing discrete-time control laws that provide closed-loop performance of the hybrid system equivalent to the performance of the designed closed-loop continuoustime system is known as digital redesign. Several techniques have been developed to digitally redesign continuous-time feedback controllers[l] ,[2] ,[3]. Unfortunately, the principal applied for the design of discrete-time control laws, i.e., that the amplitude of the control signal can take any finite value, which is why discrete-time control is often referred to as pulse-amplitude control (PAM), is not valid for all computer controlled systems. Systems that utilize onoff control devices, such as the reaction jet or electronic relay, can only provide a single finite value of control. To provide control with these types of actuator, either complex non-linear algorithms[4] must be developed or the control must be applied by modulating the pulse width, the pulse frequency or both the pulse width and frequency. These modulation techniques, in particular pulse-width modulation (PWM), allow the design of linear control laws to control non-linear systems. Although methods exist for the design of linear control laws for pulse width modulation systems[5], they still

Robust optimal pole-clustering in a vertical strip and disturbance rejection for uncertain Lagrange's systems

This paper presents an approach to design a state-feedback robust control law for uncertain Lagranges systems such that the designed closed-loop systems have the properties of robust pole-clustering within a vertical strip and disturbance rejection with anH∞-norm constraint. This approach is based on solving an algebraic Riccati equation with the adjustable scalars and prespecified parameters. The uncertainties considered include both unstructured and structured uncertainties in the system and the input matrices. Also, a constraint is established to verify that the proposed robust LQRs preserveH2 optimality with respect to a specific quadratic cost function.

Self-Tuning Control of Attitude and Momentum Management for the Space Station

This paper presents a hybrid state-space self-tuning design methodology using dual-rate sampling for suboptimal digital adaptive control of attitude and momentum management for the Space Station. This new hybrid adaptive control scheme combines an on-line recursive estimation algorithm for indirectly identifying the parameters of a continuous-time system from the available fast-rate sampled data of the inputs and states and a controller synthesis algorithm for indirectly finding the slow-rate suboptimal digital controller from the designed optimal analog controller. The proposed method enables the development of digitally implementable control algorithms for the robust control of Space Station Freedom with unknown environmental disturbances and slowly time-varying dynamics

Robust stabilization, robust performance, and disturbance attenuation for uncertain linear systems☆

Abstract : This paper presents a linear quadratic regulator approach to the robust stabilization, robust performance, and disturbance attenuation of uncertain linear systems. The state-feedback designed systems provide both robust stability with optimal performance and disturbance attenuation with H infinity-norm bounds. The proposed approach can be applied to matched and/or mismatched uncertain linear systems. For a matched uncertain linear system, it is shown that the disturbance-attenuation robust-stabilizing controllers with or without optimal performance always exist and can be easily determined without searching; whereas, for a mismatched uncertain linear system, the introduced tuning parameters greatly enhance the flexibility of finding the disturbance-attenuation robust-stabilizing controllers.

Observer-based controller for robust pole clustering in a vertical strip and disturbance rejection

This paper presents an observer-based robust feedback controller to achieve robust pole clustering within a vertical strip and disturbance rejection with an /spl Hscr//sub /spl infin//-norm constraint for uncertain linear systems. The systems of interest include both matched and mismatched uncertain linear systems with structured or unstructured uncertainties existing in both the system and input matrices. The controller is obtained by solving two Riccati equations (one for the controller and the other for the observer) and checking three conditions (two for robust pole clustering). A set of tuning parameters is incorporated to enhance flexibility in finding the controller.<<ETX>>

Optimal uniform-damping ratio controller for sequential design of multivariable systems

An optimal uniform-damping ratio controller is developed for the sequential design of a multivariable control system so that the designed closed-loop poles of the respective multivariable system and reduced-order observer are exactly placed on the negative real axis and/or the boundaries of desired sectors with constant-damping ratios. The functions in the quadratic performance index to be minimized are chosen as a combination of the weighted outputs, reduced states and inputs. Also, the optimal uniform-damping ratio controller is a combination of optimal output-feedback and optimal reduced-order state-feedback controllers. A numerical example is given to demonstrate the design procedure.

AUTONOMOUS CONTROL FOR SUBSONIC FLIGHT OF THE X-38

A multivariable autonomous control scheme is designed for the subsonic flight-test regime of the X-38 Space Station Crew Return Vehicle. To accomplish this task, a six degree of freedom model and medium fidelity simulation is created. About a calculated trim condition, a linearized model is calculated. Using this linear model and the guidance scheme dictated by mission design, a linear quadratic command tracking control law is synthesized. Simulation results from this control scheme are presented.