Dr. Gary J. Balas

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Remembering Gary: A tribute by his graduate students and research staff
(Department of Aerospace Engineering and Mechanics, 2014-12-03)
Distinguished McKnight University Professor Gary J. Balas died November 12, 2014.
Video of the Dr. Gary J. Balas Memorial
(Department of Aerospace Engineering and Mechanics, 2014-12-03)
Distinguished McKnight University Professor Gary J. Balas died November 12, 2014. The memorial for Distinguished McKnight University Professor Gary J. Balas was held on December 3, 2014 at the Campus Club in Coffman Union at the University of Minnesota. Gary's family and his friends and colleagues in Aerospace Engineering and Mechanics thank everyone for your kind words and thoughts. Many thanks also for those who came and celebrated Gary's life by reflecting on his contributions to our lives.
Slideshow Presented at the Dr. Gary J. Balas Memorial
(Department of Aerospace Engineering and Mechanics, 2014-12-03)
Distinguished McKnight University Professor Gary J. Balas died November 12, 2014.
Gary J. Balas Memorial Memory Book
(Department of Aerospace Engineering and Mechanics, 2016-03)
The memorial for Distinguished McKnight University Professor Gary J. Balas was held on December 3, 2014 at the Campus Club in Coffman Union at the University of Minnesota. Gary's family and his friends and colleagues in Aerospace Engineering and Mechanics thank everyone for your kind words and thoughts. Many thanks also for those who came and celebrated Gary's life by reflecting on his contributions to our lives. The AEM Department has put together a memory book.
Identification of Flexible Structures for Robust Control
(Institute of Electrical and Electronic Engineers, 1989-06) Balas, Gary J.; Doyle, John C.
This article documents our experience with modeling and identification of an experimental flexible structure for the purpose of control design, with the primary aim being to motivate some important research directions in this area. Initially, a multi-input/multi-output model of the structure is generated using the finite element method. This model is inadequate for control design, due to its large variation from the experimental data. Next, Chebyshev polynomials are employed to fit the data with single-input/multli-output (SIMO) transfer function models. Combining these SIMO models leads to a multi-input/multi-output (MIMO) model with more modes than the original finite element model. To find a physically motivated model, an ad hoc model reduction technique which uses a priori knowledge of the structure is developed. The ad hoc approach is compared with balanced realization model reduction to determine its benefits. Descriptions of the errors between the model and experimental data are formulated for robust control design. Plots of select transfer function models and experimental data are included.
Robustness and Performance Trade-Offs in Control Design for Flexible Structures
(Institute of Electrical and Electronic Engineers, 1994-12) Balas, Gary J.; Doyle, John C.
Linear control design models for flexible structures are only an approximation to the “real” structural system. There are always modeling errors or uncertainty present. Descriptions of these uncertainties determine the trade-off between achievable performance and robustness of the control design. In this paper it is shown that a controller synthesized for a plant model which is not described accurately by the nominal and uncertainty models may be unstable or exhibit poor performance when implemented on the actual system. In contrast, accurate structured uncertainty descriptions lead to controllers which achieve high performance when implemented on the experimental facility. It is also shown that similar performance, theoretically and experimentally, is obtained for a surprisingly wide range of uncertain levels in the design model. This suggests that while it is important to have reasonable structured uncertainty models, it may not always be necessary to pin down precise levels (i.e., weights) of uncertainty. Experimental results are presented which substantiate these conclusions.
Optical Flow: A Curve Evolution Approach
(Institute of Electrical and Electronic Engineers, 1996-04) Kumar, Arun; Tannenbaum, Allen; Balas, Gary J.
A novel approach for the computation of optical flow based on an L1 type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flow-velocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving curves is proposed for computing the optical flow field. Computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach.
A Comparison between Hankel Norms and Induced System Norms
(Institute of Electrical and Electronic Engineers, 1998-11) Lu, Wayne W.; Balas, Gary J.
A general definition is formulated for the Hankel norms as the induced norms of a strictly proper stable linear time-invariant (LTIV) system mapping vector-valued Lp-past inputs to vector-valued Lq-future outputs. Some Hankel norms are derived by the maximum principle and duality. A property termed the system integral invariance is introduced by the derivation of those Hankel norms. Furthermore, the norm-induced initial conditions and the comparison between the Hankel norms and the induced system norms are also presented.
A Variational Approach to H∞ Control with Transients
(Institute of Electrical and Electronic Engineers, 1999-10) Lu, Wayne W.; Balas, Gary J.; Lee, E.B.
This paper presents a variational approach to H∞ control with transients in the state feedback case. The approach here provides a precise description with equality, instead of inequality, in the necessary and sufficient conditions for the existence of a linear controller. Furthermore, the solution existence and uniqueness are proved in terms of certain properties of the indefinite Riccati equations derived in this paper. The linear time-variant (LTV) plant on ﬁnite horizon is considered ﬁrst, and then the results are extended to the linear time-invariant (LTIV) plant on the inﬁnite horizon. By this approach, it can be directly concluded that only suboptimal H∞ state feedback control can be achieved in an input–output point of view and that the performance measure γ(μ1/2 used in this paper) is a strict upper bound.
Sensor Selection Via Closed-Loop Control Objectives
(Institute of Electrical and Electronic Engineers, 1999-11) Balas, Gary J.; Young, Peter Michael
The ability to stabilize a system and achieve performance objectives using active feedback control is highly dependent on the location, quality, type, and number of control actuators and sensors. One role of a control engineer is to interact with the system designer to locate, size, and determine the quality of actuators and sensors required for effective control. This paper addresses one of these issues: location of sensors based on closed-loop objectives. A systematic approach, based on H2 optimal control design techniques, is developed for sensor selection which achieves desired performance objectives and includes system constraints. This approach is applied to the selection of sensors for active vibration attenuation on the NASA Langley Mini-Mast experimental structure.
Road Adaptive Active Suspension Design using Linear Parameter-Varying Gain-Scheduling
(Institute of Electrical and Electronic Engineers, 2002-01) Fialho, Ian; Balas, Gary J.
This paper presents a novel approach to the design of road adaptive active suspensions via a combination of linear parameter-varying control and nonlinear backstepping techniques. Two levels of adaptation are considered: the lower level control design shapes the nonlinear characteristics of the vehicle suspension as a function of road conditions, while the higher level design involves adaptive switching between these different nonlinear characteristics, based on the road conditions. A quarter car suspension model with a nonlinear dynamic model of the hydraulic actuator is employed. Suspension deflection, car body acceleration, hydraulic pressure drop, and spool valve displacement are used as feedback signals. Nonlinear simulations show that these adaptive suspension controllers provide superior passenger comfort over the whole range of road conditions.
Invariant Subspaces for LPV Systems and their Applications
(Institute of Electrical and Electronic Engineers, 2003-11) Balas, Gary J.; Bokor, Jozsef; Szabo, Zoltan
The aim of this note is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter-varying (LPV) systems by introducing the concept of parameter-varying invariant subspaces. For LPV systems affine in their parameters, algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems.
Control with Disturbance Preview and Online Optimization
(Institute of Electrical and Electronic Engineers, 2004-02) Jarvis-Wloszek, Zachary; Philbrick, Douglas; Kaya, M. Alpay; Packard, Andrew; Balas, Gary J.
We present an intuitive and self-contained formulation of a stability preserving receding horizon control strategy for a system where limited preview information is available for the disturbances. The simplicity of the derivation is due to (and its benefits somewhat offset by) a set of stringent and highly structured assumptions. The formulation uses a suboptimal value function for terminal cost, and relies on optimization strategies that only require a trivial improvement property, allowing implementation as an “anytime” algorithm. The nature of this strategy’s performance is clarified with linear examples.
Decentralized Receding Horizon Control and Coordination of Autonomous Vehicle Formations
(Institute of Electrical and Electronics Engineers, Inc., 2008-01) Keviczky, Tamas; Borrelli, Francesco; Fregene, Kingsley; Godbole, Datta; Balas, Gary J.
This paper describes the application of a novel methodology for high-level control and coordination of autonomous vehicle teams and its demonstration on high-fidelity models of the organic air vehicle developed at Honeywell Laboratories. The scheme employs decentralized receding horizon controllers that reside on each vehicle to achieve coordination among team members. An appropriate graph structure describes the underlying communication topology between the vehicles. On each vehicle, information about neighbors is used to predict their behavior and plan conflict-free trajectories that maintain coordination and achieve team objectives. When feasibility of the decentralized control is lost, collision avoidance is ensured by invoking emergency maneuvers that are computed via invariant set theory.
Optimally Scaled H Infinity Full Information Control Synthesis with Real Uncertainty
(American Institute of Aeronautics and Astronautics, 1996) Balas, Gary J.; Lind, Rick; Packard, Andy
An algorithm to synthesize optimal controllers for the scaled H Infinity full information problem with real and complex uncertainty is presented. The control problem is reduced to a linear matrix inequality, which can be solved via a finite dimensional convex optimization. This technique is compared with the optimal scaled H Infinity full information with only complex uncertainty and D-K iteration control design to synthesize controllers for a missile autopilot. Directly including real parametric uncertainty into the control design results in improved robust performance of the missile autopilot. The controller synthesized via D-K iteration achieves results similar to the optimal designs.
Validation of an Experimentally Derived Uncertainty Model
(American Institute of Aeronautics and Astronautics, 1998) Lim, K.B.; Cox, D.E.; Balas, Gary J.; Juang, J.N.
The discrepancies between measurement data and an analytical nominal model for a large gapmagnetic suspension testbed is accounted for by an uncertainty model. The results show that uncertainty bounds corresponding to a combination of additive and diagonal input multiplicative uncertainty can be obtained directly by calculating the smallest norm of the difference between the measured and nominal model response. Use of the identified uncertainty model allowed a strong correlation between design predictions and experimental results. In addition, robust controllers based on the experimentally derived uncertainty model show significant stability and performance improvements over controllers designed with assumed ad hoc uncertainty levels.
Control of the F-14 Aircraft Lateral-Directional Axis during Powered Approach
(American Institute of Aeronautics and Astronautics, 1998) Balas, Gary J.; Packard, Andrew K.; Renfrow, Joseph; Mullaney, Chris; M'Closkey, Robert T.
The design of linear controllers for the F-14 aircraft lateral-directional axis during powered approach using the structured singular-value (μ) framework is presented. Controllers are designed for an angle of attack of 10.5 deg and an airspeed of 137 kn, the on-speed flight condition. Each controller is implemented in a simplified nonlinear simulation and the full-order Fortran nonlinear simulation of the F-14. Pilot-in-the-loop simulations are used to verify their performance in the crewed flight simulator at the U.S. Naval Air Warfare Center, Patuxent River, Maryland. The μ controllers out perform the current analog and newly developed digital lateral-directional powered approach flight control system in pilot-in-the-loop simulations.
Application of Parameter-Dependent Robust Control Synthesis to Turbofan Engines
(American Institute of Aeronautics and Astronautics, 1999) Wolodkin, Gregory; Balas, Gary J.; Garrard, William L.
Recent results in multivariable robust control synthesis for linear parameter-varying (LPV) systems are applied to the control of a turbofan engine over a wide range of power codes. Seven linear, time-invariant models are used in the control design. The resulting LPV controller consists of seven linear controllers, gain scheduled via linear interpolation. This gain-scheduled controller is obtained directly as part of the described design process, as opposed to conventional processes, where the gain schedules are developed after the fact to connect point designs. A model matching approach is employed such that the resulting closed loop resembles a decoupled set of second-order systems with specified rise times and overshoots. The performance of linear H point designs are compared with the LPV controller at fixed operating points. A nonlinear simulation is performed with the turbofan engine and LPV controller schedules as a function of the power code. The LPV controller exhibits excellent tracking of reference commands as the power code varies in time.
Comparison of μ- and H2-Synthesis Controllers on an Experimental Typical Section
(American Institute of Aeronautics and Astronautics, 1999) Vipperman, Jeffrey S.; Barker, Jeffrey M.; Clark, Robert L.; Balas, Gary J.
An experimental comparison of H2 - and μ-synthesized flutter suppression control systems was performed. A simple parametric uncertainty can be used to track changes in system dynamics as a function of dynamic pressure. The control system was implemented experimentally on a NACA 0012 test model of a typical section mounted in a low-speed wind tunnel. The pitching angle, flap angle, and plunge deflection of the airfoil were measured with sensors and fed back through the control compensator to generate a single control signal commanding the trailing-edge flap of the airfoil. The model of the aeroelastic system, including the dynamics of the sensors and actuators in the bandwidth of interest, was obtained using system identification techniques. For comparison purposes, an H2 control system with standard linear quadratic Gaussian weightings also was designed and implemented. When compared to the H2 control system, the μ-synthesis controller provided better disturbance rejection in the bandwidth of the unsteady aeroelastic dynamics. In addition, the μ controller required less control energy than the H2 control system. The final advantage of μ-synthesis is the ability to design an aggressive μ control system that is stabilizing across the range of operating dynamic pressures.
Gain-Scheduled Linear Fractional Control for Active Flutter Suppression
(American Institute of Aeronautics and Astronautics, 1999) Barker, Jeffrey M.; Balas, Gary J.; Blue, Paul A.
A gain-scheduled controller for active flutter suppression of the NASA Langley Research Center’s Benchmark Active Controls Technology wing section is presented. The wing section changes significantly as a function of Mach and dynamic pressure and is modeled as a linear system whose parameters depend in a linear fractional manner on Mach and dynamic pressure. The resulting gain-scheduled controller also depends in a linear fractional manner on Mach and dynamic pressure. Stability of the closed-loop system over a wide range of Mach and dynamic pressure is demonstrated. Closed-loop stability is demonstrated via time simulations in which both Mach and dynamic pressure are allowed to vary in the presence of input disturbances. The linear fractional gain-scheduled controller and an optimized linear controller (designed for comparison) both achieve closed-loop stability, but the gain-scheduled controller outperforms the linear controller throughout the operating region.