Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
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Item Dynamics and Stability of Spacecraft with Fluid-Filled Containers(1994) Ozkazanc, Y.; Krishnaprasad, P.S.; ISRIn this dissertation, we study the dynamics, stability and control of spacecraft with fluid-filled containers. The spacecraft with fluid-filled containers is modeled as a rigid body containing perfect fluid. A general model for the system is obtained by using a Lagrangian approach where the configuration manifold is the cartesian product of the rotation group and the group of volume preserving diffeomorphisms. The dynamical equations are interpreted as a non-canonical Hamiltonian system on an infinite dimensional Poisson space. The geometry of the model is explicitly given by identifying its Lie-Poisson and Euler-Poincare structure. The equilibria of the system are investigated. Based on the developed model, three control problems are studied for spacecraft with fluid-filled containers. These problems are the stability of rigid rotations equilibria, the stabilization of rigid rotations by means of torque control and the attitude control problem. All stability and control problems are studied in an infinite dimensional nonlinear setting without resorting to approximations. A key feature of this dissertation is the exploitation of the mechanical and geometric structure of the system to address the stability and control problems.Item Active Vibration Damping by Parametric Control(1994) Shahidi, R.; Shayman, M.; ISRIn recent years, smart composites have been introduced in the market that open up new possibilities for controlling or sensing flexible structures. Internal properties of these composite materials which are either embedded into the structure or bonded to the surface of the structure can be manipulated, through application of magnetic field (in magneto-strictive material), voltage (in piezoelectric material), or heat (in Shape Memory Alloys).This dissertation is primarily concerned with those composites with variable stiffness or modulus of elasticity. The objective is to control the stiffness of the structure to achieve stability. A lumped parameter model of a non-shearable and inextensible beam is derived as an approximation to the continuum model with attached composites. Due to the ability to manipulate the modulus of elasticity of the composite, the spring constants of the finite dimensional model of the beam are identified as the control variables. We design nonlinear feedback control laws to damp vibrations in the resultant simple Hamiltonian control system while satisfying the input constraints. Then, the analysis is specialized to a class of bilinear system which is the state linearized version of the original system. Optimality of the proposed controller is studied and under special conditions a discontinuous control law is proposed which achieves a faster dissipation of the energy than the continuous one for some simulated cases.
Item An Improved Algorithm for Solving Constrained Optimal Control Problems(1994) Ma, Baoming; Levine, W.S.; ISRMotivated by the need to have an algorithm which (1) can solve generally constrained optimal control problems, (2) is globally convergent, (3) has a fast local convergence rate, a new algorithm, which solves fixed end-time optimal control problems with hard control constraints, end-point inequality constraints, and a variable initial state, is developed. This algorithm is based on a second-order approximation to the change of the cost functional due to a change in the control and a change in the initial state. Further approximation produces a simple convex functional. An exact penalty function is employed to penalize any violated end-point inequality constraints. We then show that the solution of the minimization of the convex functional, subject to linearized system dynamics, the original hard control constraints, the original hard initial state constraints, and linearized end-point constraints, generates a descent direction for that exact penalty function.We then show that the algorithm developed in this dissertation can also solve the following types of optimal control problems: (1) problems with a free end-time; (2) problems with path constraints; (3) problems with some design parameters that are also to be optimized.
Global convergence properties of a version of the algorithm are analyzed. In particular, it is shown that the algorithm is globally convergent under some conditions. The local convergence rate of the algorithm can be better than that of the first-order algorithms when some matrices are properly updated.
A version of the algorithm is implemented in a package which is easy to use. A variety of benchmark problems are solved. Finally, the algorithm is employed in solving two challenging biomechanics problems: (1) a human moving his arm from an initial resting position so as to touch an stop at a target with the tip of the index finger while the muscular stress, the joint constraint forces, and the neural excitations are minimized; (2) a human pedaling s stationary bicycle as fast as possible from rest. Those results demonstrate that the algorithm developed in this dissertation is effective in dealing with generally constrained optimal control problems.
Item Techniques for Designing Rotorcraft Control Systems, Final Report(1994) Yudilevitch, G.; Levine, William S.; ISROver the last two and a half years we have been demonstrating a new methodology for the design of rotorcraft flight control systems (FCS) to meet handling qualities requirements. This method is based on multicriterion optimization as implemented in the optimization package CONSOL-OPTCAD (C-O). This package has been developed at the Institute for Systems Research (ISR) at the University of Maryland at College Park. This design methodology has been applied to the design of a FCS for the UH-60A helicopter in hover having the ADOCS control structure. The controller parameters have been optimized to meet the ADS-33C specifications. Furthermore, using this approach, an optimal (minimum control energy) controller has been obtained and trade- off studies have been performed.Item Design Choices and Usage of the Portable CONSOL Environment(1994) Krikor, Gebran; ISRThis document deals with the design choices and goals of the Portable CONSOL, project. The original version of CONSOL-OPTCAD, a software package for the optimization-based design of engineering systems developed at the University of Maryland, was designed for use under SunOS on UNIX workstations. The idea behind the Portable CONSOL project is to create a portable engine which implements the functionality of CONSOL-OPTCAD but which will make versions of CONSOL for other computer platforms possible.Given the technological advancements since the original implementation of CONSOL-OPTCAD, it is now feasible to have a version of CONSOL which can be run on many different computer platforms. With personal computers now available which are as powerful (or more powerful) than the UNIX workstations for which CONSOL-OPTCAD was originally designed, a version of CONSOL capable of running on desktop personal computers is now desirable. One of the results of this project has been the development of a version of CONSOL which can be run on multiple architectures, including Sun OS, Linux, MS-DOS, MS-Windows, and OS/2.
Other results from this project include new user interfaces for CONSOL, which allow for easier user manipulation and control of the optimization process. Support for more external simulators is being developed, as well as new graphical tools to enhance the usefulness of CONSOL as an optimization tool.
Item Coherent Signal Processing Using Arrays of Arbitrary Geometry(1994) Wang, H.; Liu, K.J. Ray; ISRThe existing spatial smoothing (SS) technique, although it is effective in decorrelating coherent signals, can only be applied to uniformly spaced linear arrays which are very sensitive to the directions-of-arrival (DOA's) and can be used to estimate arimuth angles only. To significantly improve the robustness of DOA estimation and of beamforming and to estimate both arimuth and elevation angles, we developed techniques for applying SS to arrays of arbitrary geometry. We found that an array must have an orientational invariance structure with an ambiguity free center array for applying SS. We also study the cause of ambiguities in a multiple signal environment and find the necessary and sufficient conditions for an array manifold to be ambiguity free. If an array is also central symmetric, the forward/backward spatial smoothing can be used to improve the resolution. Finally, we expand the application of our technique not only to MUSIC and adaptive beamforming algorithms but also to ESPRIT algorithm. All the predicted results are verified by simulations.Item G-Snakes: Nonholonomic Kinematic Chains on Lie Groups(1994) Krishnaprasad, Perinkulam S.; Tsakiris, D.P.; ISRWe consider kinematic chains evolving on a finite-dimensional Lie group G under nonholonomic constraints, where snake-like global motion is induced by shape variations of the system. In particular, we consider the case when the evolution of the system is restricted to a subspace h of the corresponding Lie algebra g, where h is not a subalgebra of g and it can generate the whole algebra under Lie bracketing. Such systems are referred to as G- snakes. Away from certain singular configurations of the system, the constraints specify a (partial) connection on a principal fiber bundle, which in turn gives rise to a geometric phase under periodic shape variations. This geometric structure can be exploited in order to solve the nonholonomic motion planning problem for such systems.G-snakes generalize the concept of nonholonomic Variable Geometry Truss assemblies, which are kinematic chains evolving on the Special Euclidean group SE (2) under nonholonomic constraints imposed by idler wheels. We examine in detail the cases of 3-dimensional groups with real non-abelian Lie algebras such as the Heisenberg group H(3), the Special Orthogonal group SO (3) and the Special Linear group SL(2).
Item User's Guide for CFSQP Version 2.0: A C Code for Solving (Large Scale) Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality Constraints(1994) Lawrence, Craig T.; Zhou, J.L.; Tits, A.L.; ISRCFSQP is a set of C functions for the minimization of the maximum of a set of smooth objective functions (possibly a single one) subject to general smooth constraints. If the initial guess provided by the user is infeasible for some inequality constraint or some linear equality constraint, CFSQP first generates a feasible point for these constraints; subsequently the successive iterates generated by CFSQP all satisfy these constraints. Nonlinear equality constraints are turned into inequality constraints (to be satisfied by all iterates) and the maximum of the objective functions is replaced by an exact penalty function which penalizes nonlinear equality constraint violations only. When solving problems with many sequentially related constraints (or objectives), such as discretized semi- infinite programming (SIP) problems, CFSQP gives the user the option to use an algorithm that efficiently solves these problems, greatly reducing computational effort. The user has the option of either requiring that the objective function (penalty function if nonlinear equality constraints are present) decrease at each iteration after feasibility for nonlinear inequality and linear constraints has been reached (monotone line search), or requiring a decrease within at most four iterations (nonmonotone line search). He/She must provide functions that define the objective functions and constraint functions and may either provide functions to compute the respective gradients or require that CFSQP estimate them by forward finite differences.CFSQP is an implementation of two algorithms based on Sequential Quadratic Programming (SQP), modified so as to generate feasible iterates. In the first one (monotone line search), a certain Armijo type arc search is used with the property that the step of one is eventually accepted, a requirement for superlinear convergence. In the second one the same effect is achieved by means of a "nonmonotone" search along a straight line. The merit function used in both searches is the maximum of the objective functions if there is no nonlinear equality constraints, or an exact penalty function if nonlinear equality constraints are present.
Item Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups, Part II: A General Constructive Control Algorithm(1994) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRIn this paper we present a general algorithm for constructing open-loop controls to solve the complete constructive controllability problem for drift-free invariant systems on Lie groups that satisfy the Lie algebra controllability rank condition with up to ( p - 1) iterations of Lie brackets, p = 1,2,3. Specifically, given only the structure constants of the given system, an initial condition Xi, a final condition Xf and a final time tf, the algorithm specifies open-loop, small (e) amplitude sinusoidal controls such that the system starting from Xi, reaches Xf at t = tf, with O (ep) accuracy. The algorithm is based on the formulas and geometric interpretation of the average approximations to the solution given in Part I to this paper. To illustrate the effectiveness of the algorithms, we apply it to three problems: the spacecraft attitude control problem with only two controls available, the unicycle motion planning problem and the autonomous underwater vehicle motion control problem with only three controls available.Item Motion Control of Drift-Free, Left-Invariant Systems on Lie Groups(1994) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRIn this paper we address the constructive controllability problem for drift free, left-invariant systems on finite-dimensional Lie groups with fewer controls than state dimension. We consider small (e) amplitude, low-frequency, periodically time-varying controls and derive average solutions for system behavior. We show how the pth-order average formula can be used to construct open-loop controls for point-to-point maneuvering of systems that require up to ( p - 1) iterations of Lie brackets to satisfy the Lie algebra controllability rank condition. In the cases p =2,3, we give algorithms for constructing these controls as a function of structure constants that define the control authority, i.e., the actuator capability, of the system. The algorithms are based on a geometric interpretation of the average formulas and produce sinusoidal controls that solve the constructive controllability problem with O (ep) accuracy in general (exactly if the Lie algebra is nipotent). The methodology is applicable to a variety of control problems and is illustrated for the motion control problem of an autonomous underwater vehicle with as few as three control inputs.