Performance Regulation and Tracking via Lookahead Simulation: Preliminary Results and Validation

This paper presents an approach to target tracking that is based on a variable-gain integrator and the Newton-Raphson method for finding zeros of a function. Its underscoring idea is the determination of the feedback law by measurements of the system's output and estimation of its future state via lookahead simulation. The resulting feedback law is generally nonlinear. We first apply the proposed approach to tracking a constant reference by the output of nonlinear memoryless plants. Then we extend it in a number of directions, including the tracking of time-varying reference signals by dynamic, possibly unstable systems. The approach is new hence its analysis is preliminary, and theoretical results are derived for nonlinear memoryless plants and linear dynamic plants. However, the setting for the controller does not require the plant-system to be either linear or stable, and this is verified by simulation of an inverted pendulum tracking a time-varying signal. We also demonstrate results of laboratory experiments of controlling a platoon of mobile robots.Comment: A modified version will appear in Proc. 56th IEEE Conf. on Decision and Control, 201

Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold

We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold. We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix. The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences

Magnetic Actuators and Suspension for Space Vibration Control

The research on microgravity vibration isolation performed at the University of Virginia is summarized. This research on microgravity vibration isolation was focused in three areas: (1) the development of new actuators for use in microgravity isolation; (2) the design of controllers for multiple-degree-of-freedom active isolation; and (3) the construction of a single-degree-of-freedom test rig with umbilicals. Described are the design and testing of a large stroke linear actuator; the conceptual design and analysis of a redundant coarse-fine six-degree-of-freedom actuator; an investigation of the control issues of active microgravity isolation; a methodology for the design of multiple-degree-of-freedom isolation control systems using modern control theory; and the design and testing of a single-degree-of-freedom test rig with umbilicals

Bond graph model based control of robotic manipulators

The performance of robotic manipulators is critical to their widespread use in industry. As manipulators become faster, their potential productivity can rise thus improving the return on the investment required to purchase them. Improving accuracy, on the other hand, increases the range of tasks for which the manipulator is suitable. The speed and accuracy of a manipulator is partly determined by the capability of the algorithm used to control it. Whilst being a highly non-linear multiple input, multiple output device, however, most industrial controllers are derived on the basis that the robot is a series of independent, linear actuator+ link subsystems. The resulting independent joint controller is simple to design and implement but is limited in its performance as link interactions and the non-linear effects of centrifugal and Coriolis forces degrade the accuracy at high manipulator velocities. Improvements in the control of manipulators may be made by incorporating a mathematical model of the manipulator in the control algorithm. Control schemes such as `computed torque' incorporate an inverse model of the manipulator to calculate the input torques required to force the end-effector to follow a desired trajectory. The equations of motion required to implement these controllers are large and complex even for relatively simple manipulators. This thesis explores how bond graph representations of robotic manipulators may be used to automate the implementation of model based controllers. To provide a practical basis for this research the bond graph derived controllers are tested on an experimental rigid, planar, direct drive two-link manipulator. It is shown how the bondgraph for this manipulator, including d.c. motor actuators, can be constructed and used to derive the equations of motion of the manipulator automatically. The bond graph model is then validated by comparing simulations obtained using these equations of motion with experimental data

Trade-offs on fault estimation via proportional multiple-integral and multiple-resonant observers for discrete-time systems

The authors develop a fault estimation strategy which is based on a novel proportional multiple-integral (PMI) and multiple-resonant observer. This observer is an extension of the well-known PMI observer and it is able to estimate from low to high-frequency fault signals. The proposed estimation strategy is applied to discrete-time systems which are affected by faults and stochastic noises. We present a multi-objective design strategy of the observer that fixes the trade-offs between practical engineering parameters regarding the noise attenuation and the ability to track each kind of fault dynamics considered by the augmented observer. They study the influence of the order of the observer on the steady-state and transient performance of the estimation of different types of faults. Finally, a numerical example is given to illustrate the effectiveness of the proposed observer, design and characterisation

What is Time? A New Mathematico- Physical and Information Theoretic Approach

A New Mathematico-Physical and Information Theoretic Approach Examination of the available hard core information to firm up the process of unification of quantum and gravitational physics leads to the conclusion that for achieving this synthesis, major paradigm shifts are needed as also the answering of `What is Time?' The object of this submission is to point out the means of achieving such a grand synthesis. Currently the main pillars supporting the edifice of physics are: (i) The geometrical concepts of space- time-gravitation, (ii) The dynamic concepts involving quantum of action, (iii) Statistical thermodynamic concepts, heat and entropy, (iv) Mathematical concepts, tools and techniques serving both as a grand plan and the means of calculation and last but not least v)Controlled observation, pertinent experimentation as the final arbiter. In making major changes the author is following Dirac's dictum "....make changes without sacrificing the existing superstructure". It is shown that time can be treated as a parameter rather than an additional dimension. A new entity called "Ekon" having the properties of both space and momentum is introduced along with a space called "Chalachala". The requisite connection with Einstein's formulation and mathematical aperatus required have been formulated which is highly suited for the purpose. The primacy of the Plancks quantum of action and its representation geometrically as a twist is introduced. The practical and numerical estimates have been made and applied to evaluation of the gravitational constant in a a seperate submission "Estimations of gravitational constant from CMBR data".Comment: 29 pages, pdf fil