Wodek Gawronski

Model reduction in limited time and frequency intervals

The controllability and observability gramians in limited time and frequency intervals are studied, and used for model reduction. In balanced and modal coordinates, a near – optimal reduction procedure is used, vielding the reduction error (norm of the different between the output of the orginal system and the reduced model) almost minimal. Several examples are given to illustrate the concept of model reduction in limited time or/and frequency intervals, for continuous- and discrete-time systems, as well as stable and unstable systems. In modal coordinates, the reduced model obtained from a stable system is always stable. In balanced coordinates it is not necessarily true, and stability conditions for the balanced reduced model are presented. Finally, model reduction is applied to advanced supersonic transport and a flexible truss structure.

Model reduction for flexible structures

Several conditions for a near-optimal reduction of general dynamic systems are presented focusing on the reduction in balanced and modal coordinates. It is shown that model and balanced reductions give very different results for the flexible structure with closely-spaced natural frequencies. In general, balanced reduction is found to give better results. A robust model reduction technique was developed to study the sensitivity of modeling error to variations in the damping of a structure. New concepts of grammians defined over a finite time and/or a frequency interval are proposed including computational procedures for evaluating them. Application of the model reduction technique to these grammians is considered to lead to a near-optimal reduced model which closely reproduces the full system output in the time and/or frequency interval.

Model reduction for flexible space structures

This paper presents the conditions under which modal truncation yields a near-optimal reduced-order model for a flexible structure. Next, a robust model reduction technique to cope with the damping uncertainties typical of flexible space structure is developed. Finally, a flexible truss and the COFS-1 structure are used to give realistic applications for the model reduction techniques studied in the paper.

Control and Pointing Challenges of Large Antennas and Telescopes

Extremely large telescopes will be constructed in the near future, and new radiotelescopes will operate at considerably higher radio frequencies; both features create significantly increased pointing accuracy requirements that have to be addressed by control system engineers. This paper presents control and pointing problems encountered during design, testing, and the operation of antennas, radiotelescopes, and optical telescopes. This collection of challenges informs of their current status, helps to evaluate their importance, and is a basis for discussion on the ways of improvement of antenna pointing accuracy

Torque-bias profile for improved tracking of the Deep Space Network antennas

Measurements at the drives of the NASA Deep Space Network (DSN) antennas indicated that the small gap between gear teeth was causing backlash at the gearboxes and elevation bullgear. Left uncorrected, backlash will deteriorate the antennas pointing precision. At DSN, the backlash was eliminated by implementing two identical drives that impose two nonidentical torques (a.k.a. torque bias, or counter-torque). The difference between these two torques depends on the antenna load, and is shaped by the drives electronic circuits. The paper explains the shaping principles of the circuit, and shows how the circuits can be modified to improve the antenna dynamics under external disturbances.

Application of the LQG and feedforward controllers to the deep space network antennas

The controller development and the tracking per- formance evaluation for NASAs Deep Space Network antennas are presented. A command preprocessor, LQG (linear quadratic Gaussian) controller, feedforward controller, and their combi- nation are designed, built, analyzed, and tested. The antenna exhibits nonlinear behavior when the input to the antenna andlor the derivative of this input exceeds the imposed limits; for slewing and acquisition commands, these limits are typically violated. A command preprocessor was designed to insure that the antenna behaves linearly, just to prevent nonlinear limit cycling. The estimator model for the LQG controller was identified from the data obtained from the field test. Based on an LQG balanced representation, a reduced-order LQG controller was obtained. The feedforward controller and the combination of the LQG and feedforward controller were also investigated. The performance of the controllers was evaluated with the tracking errors (due to following a command) and the disturbance errors (due to the disturbances acting on the antenna). The LQG controller has good disturbance rejection properties and satisfactory tracking errors. The feedforward controller has small tracking error but poor disturbance rejection properties. The combined LQG and feedforward controller exhibits small tracking errors, as well as good disturbance rejection properties. The cost of this perfor- mance, however, is found in the complexity of the controller. I. INTRODUCTION HE NASA Deep Space Network (DSN) antennas, oper- T ated by the Jet Propulsion Laboratory, consist of several antenna types and are located at Goldstone, CA; Canberra, Australia; and Madrid, Spain. The DSN serves as a commu- nication tool for space exploration. The DSS-13 antenna, a new-generation 34-m beam-waveguide antenna, is shown in Fig. 1. Future NASA missions will include low-Earth-orbiting satellites, which require significantly higher tracking rates (up to 0.4 deg/sec), when compared to the deep space missions (0.004-0.01 deg/sec). Thus the servos for the antennas require upgrading to follow commands with the required precision. Some upgrade options are presented in this paper, and are illustrated with simulation results and with field measurements. The existing PI controllers satisfy the requirements for deep- space X- band (8.4-GHz) tracking. For a higher tracking rate, a simple and reliable choice is the addition of a feedforward controller, described in (5) and (6). The model-based, linear quadratic Gaussian (LQG) controllers are an alternative to feedforward controllers. The LQG design approach for the DSN antennas is presented in (2)-(4) and (6). This paper

Antenna control systems: from PI to H/sub /spl infin//

This paper discusses the compensation of antenna-pointing errors following the analysis and retrofit of the NASA Deep Space Network antenna control systems. The desired high-frequency communications with spacecraft (at Ka-band) require improved pointing precision over lower-frequency communications (at X-band). The quality of the antenna drives (hardware), the control algorithm (software), and the physical structure of the antenna (in terms of thermal deformations, gravity distortions, encoder mounting, and wind gusts) all influence pointing precision, and create the challenging task of remaining within the required pointing-error budget. Three control algorithms-PI (proportional-and-integral), LQG (linear-quadratic-Gaussian), and H/sub /spl infin//-are discussed, and their basic properties, tracking precision, and limitations as applied to antenna tracking are addressed. The paper shows that the PI algorithm is simple and reliable, but its performance is limited. It also explains how significant improvements in tracking precision are achieved when implementing the LQG control algorithm or the H/sub /spl infin// control algorithm. Still, pointing precision attributable to software modification is limited. It is pointed out that an additional increase of tracking precision requires concurrent improvements in the antenna drives.

LQG Controller Design Using GUI: Application to Antennas and Radio-Telescopes

The Linear Quadratic Gaussian (LQG) algorithm has been used to control the JPLs beam wave-guide, and 70-m antennas. This algorithm significantly improves tracking precision in a wind disturbed environment. Based on this algorithm and the implementation experience a Matlab based Graphical User Interface (GUI) was developed to design the LQG controllers applicable to antennas and radiotelescopes. The GUI is described in this paper. It consists of two parts the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display.

Design and performance of the monopulse control system

Ka-band (32 GHz) monopulse tracking has been chosen for the upcoming NASA missions. This decision requires an increased pointing accuracy for the Deep Space Network antenna servo systems that can be maintained in a noisy environment. The noise sources include wind gusts, encoder imperfections, and receiver noise. This article describes the selection of the position and monopulse controllers for the improved tracking accuracy, and presents the results of linear and non-linear simulations to confirm that servo performance will meet the requirements.

A balanced LQG compensator for flexible structures

The analysis of open-loop balanced flexible structures has been extended for closed-loop structures. LQG compensator gains (i.e., the gains of a controller and of an estimator) are obtained from the solutions of the controller Riccati equation (CARE) and the estimator Riccati equation (FARE). For the balanced compensator the solutions of CARE and FARE are equal and diagonal. Thus, a balanced LQG compensator puts the same effort into control and estimation of the system. An approximate balanced LQG compensator for flexible structures is determined in this paper. Its properties allow one to obtain a reduced-order compensator, which preserves the stability and performance of the full-order compensator. The performance of an LQG compensator depends on the weights of the quadratic performance index and on the variance of the estimator noise. The relationships between weights/variances and characteristic values of the system as well as between weights/variances and plant/estimator pole location are derived in this paper. Thus the weights can be determined in advance to meet the requirements of a closed-loop system.