Optimal scanning control of flexible structures in two-dimensional space

A class of optimal control problems for hyperbolic systems in two-dimensional space is considered. An approach is proposed to damp the undesirable vibrations in the structures by pointwise moving force actuators extending over the spatial region occupied by the structure. A class of performance indices is introduced that includes functions of the state variable, its first and second-order space derivatives and first-order time derivative evaluated at a preassigned terminal time, and a suitable penalty term involving the control forces. A maximum principle is given for such general scanning control problem that facilitates the determination of the unique optimal control. A solution method is developed for the active vibration control of plates of general shape. The implementation of the method is presented and the effectiveness of a single moving force actuator is investigated and compared to a single fixed force actuator by a specific numerical example.     

Robust inverse optimal control for flexible structures

An inverse optimal control problem is formulated to develop robust control laws for purely oscillatory systems. The optimal control solution requires output feedback with specified constraints, leading to robustness with respect to unmodeled modes and a large class of parameter variations. The robustness properties are proved directly from known properties of control laws resulting from quadratic performance indices. The control laws are useful for poorly damped flexible structures.This research was supported by the Office of Naval Research, Contract No. N00014-77-C-0247.     

Shape control of piezolaminated thin-walled structures using nonlinear piezoelectric actuators

In the present paper a 2D-shell finite element model is proposed to carry out static analysis of piezolaminated composite shells by incorporating nonlinear constitutive relations in order to describe the electromechanical coupling under strong electric fields. The present shell element has 5 mechanical DOFs and 3 electrical DOFs per node. The developed composite piezolaminated shell element is employed to study the static behavior and shaping of spherical antenna reflector laminated with piezo-patches under both weak and strong electric fields. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Galerkin approximations of infinite-dimensional compensators for flexible structures with unbounded control action

Galerkin (finite elements) approximations of compensators/estimators for partially observed infinite-dimensional systems with unbounded control operators are considered. It is shown that these approximations enjoy two features: (i) they provide a near-optimal performance, and (ii) they retain uniform asymptotic stability properties (uniform with respect to the parameter of discretization) of the entire closed loop system. Examples of hyperbolic equations with boundary controls and boundary observations are provided.     

Hybrid optimization procedure applied to optimal location finding for piezoelectric actuators and sensors for active vibration control

This paper presents an efficient hybrid optimization approach using a new coupling technique for solving the constrained optimization problems. This methodology is based on genetic algorithm, sequential quadratic programming and particle swarm optimization combined with a projected gradient techniques in order to correct the solutions out of domain and send them to the domain’s border. The established procedures have been successfully tested with some well known mathematical and engineering optimization problems, also the obtained results are compared with the existing approaches. It is clearly demonstrated that the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature. The main application of this procedure is the location optimization of piezoelectric sensors and actuators for active control, the vibration of plates with some piezoelectric patches is considered. Optimization criteria ensuring good observability and controllability based on some main eigenmodes and residual ones are considered. Various rectangular piezoelectric actuators and sensors are used and two optimization variables are considered for each piezoelectric device: the location of its center and shape orientation. The applicability and effectiveness of the present methodological approach are demonstrated and the location optimization of multiple sensors and actuators are successfully obtained with some main modes and residual ones. The shape orientation optimization of sensors observing various modes as well as the local optimization of multiple sensors and actuators are numerically investigated. The effect of residual modes and the spillover reduction can be easily analyzed for a large number of modes and multiple actuators and sensors.     

Optimal vibration control of flexible spacecraft during a minimum-time maneuver

This paper is concerned with the simultaneous maneuver and vibration control of a flexible spacecraft. The problem is solved by means of a perturbation approach whereby the slewing of the spacecraft regarded as rigid represents the zero-order problem and the control of vibration, as well as of perturbations from the rigid-body maneuver, represents the first-order problem. The zero-order control is to be carried out in minimum time, which implies bang-bang control. On the other hand, the first-order control is a time-dependent linear quadratic regulator including integral feedback and prescribed convergence rate.This research was sponsored by USAF/ASD and AFOSR Research Grant F33615-86-C-3233 monitored by Drs. A. K. Amos and V. B. Venkayya, whose support is greatly appreciated.     

Optimal placement of distributed actuators for a controlled smart elastic plate

The performance and the efficiency of smart structures controlled by piezoelectric wafers decisively depend on the locations of the actuators and sensors. For the evaluation and testing of time consuming numerical optimisation techniques, which are currently a part of our research, benchmark examples are required. As such a benchmark example a simply supported plate structure is inverstigated, where the active controlled behaviour can still be described analytically. In the paper the optimisation algorithm is briefly described and the results of a typical example are presented.     

Distributed parameter control of nonlinear flexible structures with linear finite-dimensional controllers

In many applications, mechanically flexible structures must be actively controlled to improve their performance. These structures are distributed parameter systems but they must be controlled by on-line computers and a few control actuators and sensors. A variety of controllers based on reduced-order linearized models of the structure may be designed to satisfy a given set of performance requirements. In actual operation, any such controller operates on the total structure and not the model. This paper determines bounds on the controller interaction with the unmodeled part of the structure; such bounds can be used to guarantee the successful operation of the linearly controlled structure even in the presence of nonlinear interactions.     

Pattern-forming systems for control of large arrays of actuators

Summary. We consider an approach for coordinating the activity of a large array of microactuators via diffusive (i.e., nearest-neighbor) coupling combined with reactive growth and decay, implemented via interconnection templates which have been artificially engineered into the system (for example, in collocated microelectronic circuitry, or through the formulation of active material layers). Such coupled systems can support interesting spatiotemporal patterns, which in turn determine the actuation patterns. Generating such spatiotemporal patterns typically involves stressing the interconnections by raising or lowering a parameter resulting in the crossing of stability thresholds. The possibility of making such parametric adjustments via feedback on a slower timescale offers a solution to the problem of communicating effectively within a large array: The communication is achieved through the interconnection template. The mathematics behind this idea leads us into the rich domain of nonlinear partial differential equations (PDEs) with spatiotemporal pattern solutions. We present a global nonlinear stability analysis that applies to certain model pattern-forming systems. The nonlinear stability analysis could serve as a starting point for control system design for systems containing large microactuator arrays. Received August 1, 2000; accepted August 16, 2001 Online publication November 5, 2001     

Optimal control problems in hybrid systems with active singularities

The optimal control problem for systems with controlled unilateral phase constraints is considered. The definition of the generalized solutions is introduced, the transformation method for the original optimal control problem within the class of generalized solution to a standard optimal control problem is proposed, and the necessary optimality conditions are found.     

A modal approach to flatness‐based control of flexible structures

Modal coordinates are used to construct a state and input parameterizing flat output for flexible structures and to design open‐loop controls. This is illustrated for the boundary control of a Timoshenko beam model. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal benchmarking for active portfolio managers

Within an agency theoretic framework adapted to the portfolio delegation issue, we show how to construct optimal benchmarks. In accordance with US regulations, the benchmark-adjusted compensation scheme is taken to be symmetric. The investor’s control consists in forcing the manager to adopt the appropriate benchmark so that his first-best optimum is attained. Solving simultaneously the manager’s and the investor’s dynamic optimization programs in a fairly general framework, we characterize the optimal benchmark. We then provide completely explicit solutions when the investor’s and the manager’s utility functions exhibit different CRRA parameters. We find that, even under optimal benchmarking, it is never optimal for the manager, and therefore for the investor, to follow exactly the benchmark, except in a very restrictive case. We finally assess by simulation the practical importance, in particular in terms of the investor’s welfare, of selecting a sub-optimal benchmark.     

Succinct data structures for flexible text retrieval systems

We propose succinct data structures for text retrieval systems supporting document listing queries and ranking queries based on the tf*idf (term frequency times inverse document frequency) scores of documents. Traditional data structures for these problems support queries only for some predetermined keywords. Recently Muthukrishnan proposed a data structure for document listing queries for arbitrary patterns at the cost of data structure size. For computing the tf*idf scores there has been no efficient data structures for arbitrary patterns.Our new data structures support these queries using small space. The space is only 2/ times the size of compressed documents plus 10n bits for a document collection of length n, for any 0<1. This is much smaller than the previous O(nlogn) bit data structures. Query time is O(m+qlogn) for listing and computing tf*idf scores for all q documents containing a given pattern of length m. Our data structures are flexible in a sense that they support queries for arbitrary patterns.     

Optimal control for the dam problem

Consider the variational inequality for the rectangular dam problem and assume that fluid can be withdrawn from the bottom at a rate proportional tok(x). Denote byp(x, y) the pressure of the fluid in the dam corresponding to a particular choice ofk. Consideringk(x) as a control variable varying in a class {0k(x)N, k(x)dxM}, we introduce the functionalJ(k)=g(y)p(x, y) whereg(y) is a given positive and monotone nondecreasing function. We characterize the controlsk ₀ which minimizeJ(k). This work is partially supported by National Science Foundation MCS-8300293     

Optimal two-layer selection policy for a flexible manufacturing system

This paper deals with the selection problem in a manufacturing system. The manufacturing system consists of a flexible manufacturing cellC ₀ which feedsM flexible manufacturing cellsC _1i ,i=1, ...,M. In addition, each cellC _1i ,i=1, ...,M, is feeding several production lines. Sufficient conditions on optimal feedback selection policies for theM+1 flexible manufacturing cells are derived. These selection policies maximize the probability of the system output reaching some demand before any of the system buffers is being overflowed. A numerical study is conducted.     

Robust stabilizing compensators for flexible structures with collocated controls

For flexible structures with collocated rate and attitude sensors/actuators, we characterize compensator transfer functions which guarantee modal stability even when stiffness/inertia parameters are uncertain. While the compensators are finite-dimensional, the structure models are allowed to be infinite-dimensional (continuum models), with attendant complexity of the notion of stability; thus exponential stability is not possible and the best we can obtain is strong stability. Robustness is interpreted essentially as maintaining stability in the worst case. The conditions require that the compensator transfer functions be positive real and use is made of the Kalman-Yakubovic lemma to characterize them further. The concept of positive realness is shown to be equivalent to dissipativity in infinite dimensions. In particular we show that for a subclass of compensators it is possible to make the system strongly stable as well as dissipative in an appropriate energy norm.This research was supported in part under NASA Grant No. NCC 2-374.     

Optimal design of elastic structures for multipurpose loading

The optimal design of elastic beams subjected to two alternative loading systems is considered for compliance constraints and a minimum-cross-section constraint. Sufficient conditions for optimality are established, and a technique for determining the optimal design is presented. Two examples are given. Generalizations to more than two loading systems and more complex structures are straightforward.     

Optimal control for lithium-ion batteries

Modelling, simulation and optimal control for a lithium-ion battery cell is discussed. The model involves ionic concentrations, currents and potentials in the electrodes and the separator together with the battery temperature as state variables. The resulting system is a nonlinear PDAE system with 10 partial, 1 ordinary differential and 4 algebraic equations involving the Butler-Volmer kinetics for describing the interaction of ionic currents and potentials. Time-optimal charging of the battery subject to age-preventing leads to a state-constrained optimal control problem which is solved in two ways. A first-discretize-then-optimize approach leads to a high-dimensional nonlinear optimization problem which is solved by an efficient solver. As an alternative, a feedback control law along an active arc of the state constraint of order 1 is derived to formulate and solve the corresponding so-called induced optimization problem. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)