Dynamics and Controls Seminars

Abstracts 2000 -2001

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Monday, August 27, 2001
2:00 p.m.
479 EBU-II

Johan Åkesson
Department of Automatic Control
Lund Institute of Technology

This thesis deals with manual control of unstable systems, subject to control signal constraints. Allocation of control authority is critical in this situation. The manual control, or reference following, must not be performed at the risk of loosing stability. The conflicting objective is to achieve acceptable reference following performance. Design of control systems under such circumstances is critical, and has several important applications. One example is modern flight control systems for unstable fighter aircrafts. Experiments have been an important part of this work. An inverted pendulum of the Furuta type, has been used for experimental verification of the controller designs. This plant is unstable, but reasonably easy to analyze and perform experiments with. Theoretical as well as practical results are presented in this report. Controllers for the linearized pendulum model have been designed and simulated. Some of the designs were also implemented and evaluated on the real Furuta pendulum. The translation of the controllers from a simulation environment to the real plant proved quite difficult. Some modifications of the controllers had to be made, in order to achieve the desired results on the real Furuta pendulum. Compensation for friction also had to be done.

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Using linear algebra, necessary and sufficient conditions are developed for the force and geometric equilibrium of a tensegrity structure consisting of n_b bars and n_s strings in both a prestressed state and under the influence of an external load.An advantage of this approach is that both the magnitude and direction cosines of the forces are contained in vectors which can be solved using linear algebra.

One class of sufficient conditions is expressed in the form of the diagonalizability of a square matrix of dimension n_b through the choice of n_s parameters. An explicit algebraic expression is also developed for the stiffness matrix of the structure in terms of both the force coefficients and the unit vectors of the strings and bars which among other applications can be used to examine structural stability of the tensegrity equilibrium.

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Wednesday, July 18, 2001
Room 479, EBU-II
1:00 – 2:00 p.m.

Andrei V. Dmitruk
Leading Researcher
Central Economics & Mathematics Institute
Of the Russian Academy of Sciences
Moscow

"Quadratic Order Conditions of Some Types of Local Minima for Singular Extremals"

For the control system linear in the control, a general optimal control problem is considered, involving terminal equality and inequality constraints, a terminal functional to be minimized, and the pointwise constraint on the control. The admissible control set U is convex, closed and solid. We examine a totally singular trajectory, assuming that the control lies in the relative interior of one and the same face of U. (The case when the face is U itself is not forbidden).

We consider three types of minimum-the classical weak, strong, and an intermediate so-called Pontryagin minimum, which is an L1-minimum with respect to the control on any uniformly bounded control set.

We choose a special quadratic functional - the order of estimation - and give necessary and close to them sufficient conditions (adjoint pairs of conditions) of this order for a weak minimum, and separately for a Pontryagin minimum,. The latter pair differs from the former pair only by an additional pointwise condition including coefficients of the third variation of Lagrange function and taking into account the admissible control set U (a new condition of Legendre type).

In particular case when U is strictly convex, and the reference control lies on its boundary, the quadratic-order sufficient condition for a week minimum guarantees actually a strong minimum at the examined extremal. This theorem proved to be helpful in the problem of minimality of abnormal sub-Riemannian geodesics.

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Tuesday, July 10, 2001
2:00 p.m.
479 EBU-II

Professor Murat Arcak
Electrical, Computer & Systems Engineering
Rensselear Polytechnic Institute

"Construction And Output Feedback Applications Of A New Nonlinear Observer"

This talk addresses output feedback designs employing a recently developed observer for systems with slop-restricted nonlinearities. A new treatment of the observer construction shows that a certainty-equivalence design is possible for a class of systems with nonlinearities growing faster than linear.

Feasibility conditions are now available for the previously developed LMI observer. For a wider class of nonlinearities, a nonlinear gain assignment design is needed instead of a certainty-equivalence design.

The designs are illustrated with several physically motivated examples, including an active magnetic bearing system, jet engine surge and stall, and control of marine vessels.

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Tuesday, May 22, 2001
11:00 a.m.
479 EBU-II

Professor Ioan Landau
Laboratoire d'Automatique de Grenoble, France

"Direct Controller Order Reduction by Identification in Closed Loop Application
to Active Suspension Control"

The paper addresses the problem of directly estimating the parameters of a reduced order digital controller using a closed loop type identification algorithm.  The algorithm minimizes the closed loop plant input error between the nominal closed loop system and the closed loop system using the reduced order controller.  It is assumed that a plant model (if necessary validated in closed loop with the nominal controller) is available.  One of the original features of this approach is that it can use either simulated or real data.  The frequency bias distribution of the parameter estimates shows that the reduced order controller maintains the critical performance of the nominal closed loop system.  A theoretical analysis is provided.  Validation tests are proposed.  Experimental results, obtained on an active suspension, illustrate the performance of the proposed algorithms.

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Thursday, March 7, 2001
3:30 p.m.
479 EBU-II

Professor Masao Ikeda
Department of Computer-Controlled Mechanical Systems
Osaka University

"Robustness of Symmetric Controller for Symmetric Plants"

There are a large number of systems in diverse fields, the transfer function matrices of which are symmetric. An important symmetric system to be controlled is a large space structure with collocated sensors and actuators. This paper first show that for symmetric plants, symmetric controllers are more robust than non-symmetric ones in stabilization. That is, if there exists a robustly stabilizing non-symmetric controller for a symmetric plant with a norm-bounded uncertainty, then a symmetric controller also exists which robustly stabilizes the plant.

However, this fact may not be true if there is a restriction on the order of controllers. Any symmetric robust controller may be of higher order than the lowest-order non-symmetric robust controller. Actually, an example of a symmetric plant is presented, which is stabilizable by non-symmetric static feedback. However, in addition, it is also shown that if there is a non-symmetric stabilizing controller whose order is not lower than that of the plant, a symmetric stabilizing controller of the same order exists. Therefore, we can say that in a class of controllers whose orders are sufficiently high, symmetric controllers are more suitable for robust stabilization of symmetric plants.

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This talk focuses on the application of optimal control to develop control strategies for wall-bounded turbulent flows. A novel aspect of our research is that we use a reduced order model, namely large-eddy simulation (LES), in order to both predict the state of the turbulent flow as well as the optimal control. By so doing, our LES based methods exploit the success of the dynamic subgrid-scale model to greatly improve the efficiency of optimal control formulations applied to turbulent flows. We begin by briefly presenting techniques for optimal control of turbulent flows based on the dynamic subgrid-scale LES model. The optimal control formulation is implemented using model-based predictive control where the flow sensitivity is computed from the adjoint LES equations. Our LES results for optimal control of terminal turbulent kinetic energy are compared to Direct Numerical Simulation (DNS) at turbulence Reynolds numbers of and 180. These comparisons indicate that, similar to DNS, optimal control based on LES can relaminarize low Reynolds number turbulent channel flow but with significantly lower computational expense. At the optimal control yields 40% drag reduction but relaminarization is not achieved. Results are also presented for a novel hybrid LES/DNS Scheme in which the optimization iterations are performed using LES while the flow is advanced in time using DNS. These hybrid simulations retain the computational efficiency of LES and the accuracy of DNS. Results from hybrid simulations clearly demonstrate that the controls computed based on LES optimization are also viable in the context of DNS. In all cases, the agreement between LES, DNS, and hybrid LES\DNS indicates that reliable turbulence control strategies can be efficiently developed based on LES. We have recently used our LES based methods to perform turbulence control simulations at which are the highest Reynolds number conrtolled flow simulations yet performed and preliminary results from these simulations will be presented.

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In their celebrated 1968 paper on nonlinear stability, Zames and Falb determined a class of multipliers that preserve positivity of monotone SISO nonlinearities. They conjectured that their results might also hold for incrementally positive, norm-bounded MIMO nonlinearities. In this talk, we demonstrate that their conjecture regarding MIMO nonlinearities holds true only if a further restriction is applied. Specifically, we show that it suffices either to restrict the nonlinearity to be the gradient of a convex real-valued function or to restrict the multiplier to be a real- valued function of frequency. We also describe new multiplier matrices for repeated SISO nonlinearities, giving the entire class of such multipliers. Our results extend the capability of IQC/conic-sector stability criteria, permitting less conservative robustness analysis for systems with MIMO nonlinearities such as may occur in nonlinear models of aircraft, spacecraft, robots, MEMS and other electromechanical systems.

Following his visit and seminar at UCSD, Prof. Safonov is scheduled to give a talk to the local AIAA chapter meeting at ORINCON on Thursday evening 1/18/01 at 6pm on the introduction to unfalsified adaptive control and its uses. ORINCON can be found at 9363 Towne Center Dr (contact: Mark Owen 619 553 2041)

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Thursday,  November 9, 2000
1:00 p.m.
Room 479, EBU-II

Gregory Hagen
Mechanical & Environmental Engineering
University of California, Santa Barbara

"Stall inception Modeling and Control in Axial Compressors"

Axil compressors are limited in performance by the flow instabilities of stall and surge.  Recently it has been shown that there are two types of stall inception: modal and spike types.  We present a model that describes the three dimensional nature of the flow during both types of stall inception, which matches closely with experimental data.  the Global behavior of spike stall inception presents the need to design globally stabilizing controllers.  We consider the problem of global stabilization of the system over one spatial dimension, which is a semilinear dissipative parabolic partial differential equation.  We present a finite dimensional controller with a finite number of measurements available for feedback.  For the compensator design, we consider Lyapunov functions based on the infinite dimensional dynamics of the state and error systems.  Linear quadratic regulator (LQR) designs are used to stabilized the systems with robustness to spillover destabilization.  the stability analysis easily extends to systems over two spatial dimensions.

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Friday, October 27, 2000
EBU-II   479
11:00 A.M.

Professor Theodore Tachim Medjo
Mathematics Department
Florida International University

  "Robust Control Problems in Fluid Mechanics"

In this work we study a class of robust control problems in fluid mechanics recently proposed in [1].  Using a method of [2], we provide another proof of the existence and the uniqueness of solutions to the robust control problems under weaker assumptions as compared to [1].  From the numerical point of view, the method used in this article is particularly important since it provides a constructive way to approximate the solutions to these nonlinear control problems.

For additional information, call Linda at (858) 822-1269