Lucas G. Horta

Identification of observer/Kalman filter Markov parameters - Theory and experiments

This paper discusses an algorithm to compute the Markov parameters of an observer or Kalman filter from experimental input and output data. The Markov parameters can then be used for identification of a state-space representation, with associated Kalman or observer gain, for the purpose of controller design. The algorithm is a nonrecursive matrix version of two recursive algorithms developed in previous works for different purposes, and the relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and offers bounds on the proper choice of observer order. It is shown that if one uses data containing noise and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. The results of the paper are demonstrated in numerical studies and experiments on the Bubble space telescope.

A slewing control experiment for flexible structures

A hardware setup has been developed to study slewing control for flexible structures including a steel beam and a solar panel. The linear optimal terminal control law is used to design active controllers that are implemented in an analog computer. The objective of this experiment is to demonstrate and verify the dynamics and optimal terminal control laws as applied to flexible structures for large-angle maneuver. Actuation is provided by an electric motor while sensing is given by strain gages and angle potentiometers. Experimental measurements are compared with analytical predictions in terms of modal parameters of the system stability matrix, and sufficient agreement is achieved to validate the theory.

Improvement of Observer/Kalman Filter Identification (OKID) by Residual Whitening

This paper presents a time-domain method to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data. The identified filter has the properties that its residual is minimized in the least squares sense, orthogonal to the time-shifted versions of itself, and to the given input-output data sequence. The connection between the state space model and a particular auto-regressive moving average description of a linear system is made in terms of the Kalman filter and a deadbeat gain matrix. The procedure first identifies the Markov parameters of an observer system, from which a state space model of the system and the filter gain are computed. The developed procedure is shown to improve results obtained by an existing observer/Kalman filter identification method, which is based on an auto-regressive model without the moving average terms. Numerical and experimental results are presented to illustrate the proposed method.

Effects of Atmosphere on Slewing Control of a Flexible Structure

Air drag forces are introduced into the equations for a slewing control maneuver of a flexible structure to assess the effects of atmosphere on the controller design. Simulated modal parameters and transient responses are compared with experiments in normal atmosphere and vacuum. Analytical techniques for control laws are examined and verified. Physical insight into the air damping is gained so that results in vacuum can be extrapolated from results in air.

Transitioning Active Flow Control to Applications

Active Flow Control Programs at NASA, the U.S. Air Force, and DARPA have been initiated with the goals of obtaining revolutionary advances in aerodynamic performance and maneuvering compared to conventional approaches. These programs envision the use of actuators, sensors, and controllers on applications such as aircraft wings/tails, engine nacelles, internal ducts, nozzles, projectiles, weapons bays, and hydrodynamic vehicles. Anticipated benefits of flow control include reduced weight, part count, and operating cost and reduced fuel burn (and emissions), noise and enhanced safety if the sensors serve a dual role of flow control and health monitoring. To get from the bench-top or laboratory test to adaptive distributed control systems on realistic applications, reliable validated design tools are needed in addition to sub- and large-scale wind-tunnel and flight experiments. This paper will focus on the development of tools for active flow control applications.

System Identification from Closed-Loop Data with Known Output Feedback Dynamics

This paper formulates a method to identify the open-loop dynamics of a system operating under closedloop conditions. The closed-loop excitation data and the feedback dynamics are assumed to be known. Two closed-loop configurations are considered where the system has either a linear output feedback controller or a dynamic output feedback controller. First, the closed-loop excitation data are used to compute the closed-loop Markov parameters, from which the open-loop Markov parameters are recovered from the known feedback dynamics. The Markov parameters are then used to compute a state space representation of the open-loop system. Examples are provided to illustrate the computational steps involved in the proposed closed-loop identification method.

FREQUENCY-WEIGHTED SYSTEM IDENTIFICATION AND LINEAR QUADRATIC CONTROLLER DESIGN

Application of filters for the frequency weighting of Markov parameters (pulse response functions) is described in relation to system/observ er identificatio n. The time domain identification approach recovers a model that has a pulse response weighted according to frequency. The identified model is composed of the original system and filters. The augmented system occurs in a form that can be used directly for frequencyweighted linear quadratic controller design. Data from either single or multiple experiments can be used to recover the Markov parameters. Measured acceleration signals from a truss structure are used for system identification and the model obtained is for frequency-weighted controller design. The procedure makes the identification and controller design complementary problems.

Classical control system design and experiment for the Mini-Mast truss structure

This paper describes control system design and experimental test results for the Mini-Mast truss structure located at the NASA Langley Research Center. Simple classical controllers and their ground test results are presented as a benchmark design for the Mini-Mast. The concepts of non-minimum-phase compensation and periodic disturbance rejection control are experimentally validated. The practicality, of a sensor decoupling approach for the classical single-input and single-output control design is also demonstrated. The test results that clearly indicate the undesirable effect of phase lag caused by computational delay and prefiltering are discussed.

Linear system identification via an asymptotically stable observer

This paper presents a formulation for identification of linear multivariable systems from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero corresponding to a deadbeat observer. In this formulation, the Markov parameters of the observer are first identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to realize a state space model of the system. The basic mathematical formulation is derived, and numerical examples are presented to illustrate the proposed method.

A Sequential Linear Optimization Approach for Controller Design

A linear optimization approach with a simple, real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first-order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam, finite element model for the optimal sizing and placement of active/passive structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to the initial conditions of the linear optimization approach is also demonstrated.