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NASA NTRS1997

Recursive Deadbeat Controller Design

This paper presents a recursive algorithm for a deadbeat predictive controller design. The method combines together the concepts of system identification and deadbeat controller designs. It starts with the multi-step output prediction equation and derives the control force in terms of past input and output time histories. The formulation thus derived satisfies simultaneously system identification and deadbeat controller design requirements. As soon as the coefficient matrices are identified satisfying the output prediction equation, no further work is required to compute the deadbeat control gain matrices. The method can be implemented recursively just as any typical recursive system identification techniques.

Juang, Jer-Nan↗

NASA NTRS2003

Flux-Based Deadbeat Control of Induction-Motor Torque

An improved method and prior methods of deadbeat direct torque control involve the use of pulse-width modulation (PWM) of applied voltages. The prior methods are based on the use of stator flux and stator current as state variables, leading to mathematical solutions of control equations in forms that do not lend themselves to clear visualization of solution spaces. In contrast, the use of rotor and stator fluxes as the state variables in the present improved method lends itself to graphical representations that aid in understanding possible solutions under various operating conditions. In addition, the present improved method incorporates the superposition of high-frequency carrier signals for use in a motor-self-sensing technique for estimating the rotor shaft angle at any speed (including low or even zero speed) without need for additional shaft-angle-measuring sensors.

Kenny, Barbara H.↗

NASA NTRS1997

Broadband Noise Control Using Predictive Techniques

Predictive controllers have found applications in a wide range of industrial processes. Two types of such controllers are generalized predictive control and deadbeat control. Recently, deadbeat control has been augmented to include an extended horizon. This modification, named deadbeat predictive control, retains the advantage of guaranteed stability and offers a novel way of control weighting. This paper presents an application of both predictive control techniques to vibration suppression of plate modes. Several system identification routines are presented. Both algorithms are outlined and shown to be useful in the suppression of plate vibrations. Experimental results are given and the algorithms are shown to be applicable to non- minimal phase systems.

Eure, Kenneth W.↗

NASA NTRS1997

Deadbeat Predictive Controllers

Several new computational algorithms are presented to compute the deadbeat predictive control law. The first algorithm makes use of a multi-step-ahead output prediction to compute the control law without explicitly calculating the controllability matrix. The system identification must be performed first and then the predictive control law is designed. The second algorithm uses the input and output data directly to compute the feedback law. It combines the system identification and the predictive control law into one formulation. The third algorithm uses an observable-canonical form realization to design the predictive controller. The relationship between all three algorithms is established through the use of the state-space representation. All algorithms are applicable to multi-input, multi-output systems with disturbance inputs. In addition to the feedback terms, feed forward terms may also be added for disturbance inputs if they are measurable. Although the feedforward terms do not influence the stability of the closed-loop feedback law, they enhance the performance of the controlled system.

Juang, Jer-Nan↗

NASA NTRS1990

Time optimal feedback control of discrete systems with bounded inputs

Deadbeat control theory gives a feedback solution to the time optimal control of discrete time systems. Experience has shown the results to be impractical because they ignore bounds on the actuator strength. This paper develops two algorithms for generating time optimal control in feedback form for discrete systems with bounded controls. The results are also applicable for generating recovery regions and the set of reachable states. For multiple control problems a method of generating sublayers is developed which decreases off-line and on-line computational effort. Two algorithms are presented with somewhat different computational and storage requirements. The algorithms are practical within certain dimension constraints, and are natural for implementation with parallel processing.

Chen, Xin↗

NASA NTRS2001

Stator and Rotor Flux Based Deadbeat Direct Torque Control of Induction Machines

A new, deadbeat type of direct torque control is proposed, analyzed, and experimentally verified in this paper. The control is based on stator and rotor flux as state variables. This choice of state variables allows a graphical representation which is transparent and insightful. The graphical solution shows the effects of realistic considerations such as voltage and current limits. A position and speed sensorless implementation of the control, based on the self-sensing signal injection technique, is also demonstrated experimentally for low speed operation. The paper first develops the new, deadbeat DTC methodology and graphical representation of the new algorithm. It then evaluates feasibility via simulation and experimentally demonstrates performance of the new method with a laboratory prototype including the sensorless methods.

Kenny, Barbara H.↗

NASA NTRS2002

Stator and Rotor Flux Based Deadbeat Direct Torque Control of Induction Machines

Kenny, Barbara H.↗

NASA NTRS2003

Stator and Rotor Flux Based Deadbeat Direct Torque Control of Induction Machines

A new, deadbeat type of direct torque control is proposed, analyzed and experimentally verified in this paper. The control is based on stator and rotor flux as state variables. This choice of state variables allows a graphical representation which is transparent and insightful. The graphical solution shows the effects of realistic considerations such as voltage and current limits. A position and speed sensorless implementation of the control, based on the self-sensing signal injection technique, is also demonstrated experimentally for low speed operation. The paper first develops the new, deadbeat DTC methodology and graphical representation of the new algorithm. It then evaluates feasibility via simulation and experimentally demonstrates performance of the new method with a laboratory prototype including the sensorless methods.

Kenny, Barbara H.↗

NASA NTRS1983

On the stabilizability of multivariable systems by minimum order compensation

In this paper, a derivation is provided of the necessary condition, mp equal to or greater than n, for stabilizability by constant gain feedback of the generic degree n, p x m system. This follows from another of the main results, which asserts that generic stabilizability is equivalent to generic solvability of a deadbeat control problem, provided mp equal to or less than n. Taken together, these conclusions make it possible to make some sharp statements concerning minimum order stabilization. The techniques are primarily drawn from decision algebra and classical algebraic geometry and have additional consequences for problems of stabilizability and pole-assignability. Among these are the decidability (by a Sturm test) of the equivalence of generic pole-assignability and generic stabilizability, the semi-algebraic nature of the minimum order, q, of a stabilizing compensator, and the nonexistence of formulae involving rational operations and extraction of square roots for pole-assigning gains when they exist, answering in the negative a question raised by Anderson, Bose, and Jury (1975).

Byrnes, C. I.↗

NASA NTRS1986

A class of fast staircase algorithms for generalized state-space systems

Several methods are presented for defining generalized state space models (GSSM), with emphasis on 'fast' techniques for transforming GSSMs to condensed state space models (SSM). The fast forms are configured to yield invariant transfer functions. Details of the decomposition process are summarized in terms of the determination of eigenvalues which are separated within staircase matrices. Applications of the techniques are illustrated through implementation of a unimodular transformation which does not affect the finite eigenvalues, by demonstrating deadbeat control of a GSSM, which the definition of a reduced observer of a GSSM, and by embedding a polynomial matrix into a unimodular matrix.

Beelen, T.↗

NASA NTRS2003

NASA Tech Briefs, March 2003

Topics covered include: Tool for Bending a Metal Tube Precisely in a Confined Space; Multiple-Use Mechanisms for Attachment to Seat Tracks; Force-Measuring Clamps; Cellular Pressure-Actuated Joint; Block QCA Fault-Tolerant Logic Gates; Hybrid VLSI/QCA Architecture for Computing FFTs; Arrays of Carbon Nanotubes as RF Filters in Waveguides; Carbon Nanotubes as Resonators for RF Spectrum Analyzers; Software for Viewing Landsat Mosaic Images; Updated Integrated Mission Program; Software for Sharing and Management of Information; Update on Integrated Optical Design Analyzer; Optical-Quality Thin Polymer Membranes; Rollable Thin Shell Composite-Material Paraboloidal Mirrors; Folded Resonant Horns for Power Ultrasonic Applications; Touchdown Ball-Bearing System for Magnetic Bearings; Flux-Based Deadbeat Control of Induction-Motor Torque; Block Copolymers as Templates for Arrays of Carbon Nanotubes; Throttling Cryogen Boiloff To Control Cryostat Temperature; Collaborative Software Development Approach Used to Deliver the New Shuttle Telemetry Ground Station; Turbulence in Supercritical O2/H2 and C7H16/N2 Mixing Layers; and Time-Resolved Measurements in Optoelectronic Microbioanal.

Source record↗

NASA NTRS2003

NASA Tech Briefs, April 2003

Topics include: Tool for Bending a Metal Tube Precisely in a Confined Space; Multiple-Use Mechanisms for Attachment to Seat Tracks; Force-Measuring Clamps; Cellular Pressure-Actuated Joint; Block QCA Fault-Tolerant Logic Gates; Hybrid VLSI/QCA Architecture for Computing FFTs; Arrays of Carbon Nanotubes as RF Filters in Waveguides; Carbon Nanotubes as Resonators for RF Spectrum Analyzers; Software for Viewing Landsat Mosaic Images; Updated Integrated Mission Program; Software for Sharing and Management of Information; Optical-Quality Thin Polymer Membranes; Rollable Thin Shell Composite-Material Paraboloidal Mirrors; Folded Resonant Horns for Power Ultrasonic Applications; Touchdown Ball-Bearing System for Magnetic Bearings; Flux-Based Deadbeat Control of Induction-Motor Torque; Block Copolymers as Templates for Arrays of Carbon Nanotubes; Throttling Cryogen Boiloff To Control Cryostat Temperature; Collaborative Software Development Approach Used to Deliver the New Shuttle Telemetry Ground Station; Turbulence in Supercritical O2/H2 and C7H16/N2 Mixing Layers; and Time-Resolved Measurements in Optoelectronic Microbioanal.

Source record↗

NASA NTRS1968

Design of low sensitivity sample-data control systems.

Minimum sensitivity deadbeat sampled data control system design by frequency domain technique, using two controllers

Bennett, J. E.↗

NASA NTRS2003

New Technique of High-Performance Torque Control Developed for Induction Machines

Two forms of high-performance torque control for motor drives have been described in the literature: field orientation control and direct torque control. Field orientation control has been the method of choice for previous NASA electromechanical actuator research efforts with induction motors. Direct torque control has the potential to offer some advantages over field orientation, including ease of implementation and faster response. However, the most common form of direct torque control is not suitable for the highspeed, low-stator-flux linkage induction machines designed for electromechanical actuators with the presently available sample rates of digital control systems (higher sample rates are required). In addition, this form of direct torque control is not suitable for the addition of a high-frequency carrier signal necessary for the "self-sensing" (sensorless) position estimation technique. This technique enables low- and zero-speed position sensorless operation of the machine. Sensorless operation is desirable to reduce the number of necessary feedback signals and transducers, thus improving the reliability and reducing the mass and volume of the system. This research was directed at developing an alternative form of direct torque control known as a "deadbeat," or inverse model, solution. This form uses pulse-width modulation of the voltage applied to the machine, thus reducing the necessary sample and switching frequency for the high-speed NASA motor. In addition, the structure of the deadbeat form allows the addition of the high-frequency carrier signal so that low- and zero-speed sensorless operation is possible. The new deadbeat solution is based on using the stator and rotor flux as state variables. This choice of state variables leads to a simple graphical representation of the solution as the intersection of a constant torque line with a constant stator flux circle. Previous solutions have been expressed only in complex mathematical terms without a method to clearly visualize the solution. The graphical technique allows a more insightful understanding of the operation of the machine under various conditions.

Kenny, Barbara H.↗

NASA NTRS1993

Noncolocated Structural Vibration Suppression Using Zero Annihilation Periodic Control

The Zero Annihilation Periodic (ZAP) controller is applied to the problem of vibration control of a noncolocated flexible structure. It is shown that even though the transfer function is nonminimum-phase, a plant inverse controller can be designed which elicits a deadbeat closed-loop response.

periodic control noncolocated systems non-minimum ↗

NASA NTRS1984

State deadbeat response and observability in multi-modal systems

Two aspects of multimodal systems are examined. It is shown that any completely controllable system with state dimension n not exceeding three allows a choice of feedback matrices resulting in a state deadbeat response. Some of the results presented here are valid for arbitrary n, and it is suggested that for all n the state deadbeat response can be obtained under the hypothesis of complete controllability. The controllability canonical form for a multimodal system is refined by introducing a notion of observability which is dual to controllability for these systems.

Conner, L. T., Jr.↗

NASA NTRS1996

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Balakrishnan, A. V.↗

NASA NTRS1991

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

An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. 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 gives 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. Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure.

Juang, Jer-Nan↗