Robert J. Veillette

Reliable linear-quadratic state-feedback control

Abstract This paper introduces a procedure for the design of modified linear-quadratic (LQ) state-feedback controls that tolerate actuator outages. The controls improve on the known stability gain-margin properties of the standard LQ regulator by tolerating the insertion of any independent gains from zero to infinity into selected feedback loops. They also guarantee a given performance bound despite the insertion of gains from zero to two into those loops. The reliable LQ design is shown to be equivalent to a standard LQ-optimal design with a modified performance index. Thus, the design procedure is seen as a means of choosing a particular quadratic performance index for which the optimal control will possess the desired reliability properties.

A charge controller for linear operation of a piezoelectric stack actuator

This paper examines the position control problem of piezoelectric stack actuators and presents a method for overcoming the hysteresis nonlinearity between the applied voltage and the actuator displacement. An inverting charge control circuit is implemented to linearize the stack actuator movement by taking advantage of the linear relationship between charge and displacement. The charge control feedback loop is analyzed in detail. It incorporates an operational amplifier to provide high loop gain, a high-voltage amplifier (HVA) to drive the stack actuator, and a lead compensator to ensure stability. Experiments were conducted to compare the responses of the stack actuator under voltage and charge control. The experimental data show that the charge control provides linear actuator operation from 1 Hz-10 Hz over approximately 35% of the actuator operating range, and from 1 Hz-20 Hz over approximately 19% of the operating range.

Design and performance analysis of sliding-mode observers for sensorless operation of switched reluctance motors

This paper presents an analytical and experimental evaluation of the sliding-mode observer (SMO) for eliminating position and speed sensors in switched reluctance motor (SRM) drives. Design guidelines are derived for the SMO to guarantee an upper bound on the observer error for all time. An analysis is presented to demonstrate that the SMO also possesses an automatic adaptation property with respect to the intensity of the measurement noise. The SMO approach is shown, in simulations and in experiments, to provide accurate position and speed estimates under various operating conditions. The resolution and reliability of the scheme are shown to be superior to those obtained using standard state observers. The results demonstrate the applicability of the SMO-based sensorless controllers for SRM drives.

Robust stabilization and disturbance rejection for systems with structured uncertainty

A method based on the algebraic Riccati equation is presented for designing state- and output-feedback control laws for plants with structured uncertainty. The designs provide both robust stability and disturbance rejection with robust H/sub infinity /-norm bounds. The design method consists of incorporating information on the plant uncertainty into the algebraic Riccati equations used for nominal H/sub infinity / disturbance-rejection designs.<<ETX>>

A methodology for FPGA-based control implementation

When used for digital compensator implementation, field-programmable gate arrays (FPGAs) allow the use of a short sampling period, and of a customized fixed-point hardware definition wherein each coefficient and each state variable may be represented using a different number of bits. A methodology is presented based on the control system L/sub 1/ or l/sub 1/ norms for computing the appropriate number of bits to represent each quantity. The methodology is shown to be effective for designing hardware for both traditional shift-form and delta-form representations of the compensator. The methodology is applied to the implementation of a magnetic bearing control system. In this example, a delta-form realization requires less hardware than a shift-form realization, and provides a closer approximation to the original analog compensator. The results show that the methodology is useful for the comparison of competing digital compensator structures.

Simulation and Control of an Active Tilting-Pad Journal Bearing

This study developed an active tilting-pad journal bearing with a feedback control system to regulate the orbit of a rotating shaft. The control is implemented by means of linear actuators installed behind the pivot of each pad, which allow the radial motion of the pads in real time. The control design uses the linear feedback of the state variables of the bearing-rotor system, with the feedback gains determined by the optimization of a quadratic performance index. The optimization is based on a linear spring-mass model that incorporates the direct stiffness and damping elements associated with each of the bearing pads. This linear model is found by the simulation of the system under small perturbations using a nonlinear Reynolds equation model. The nonlinear model is capable of simulating the radial motions of the pads by the actuators and is used to verify the effectiveness of the feedback control. It is shown that certain design parameters in the quadratic performance index may be used to determine both the stiffness and the damping of the closed-loop bearing system and that the shaft orbit can be thereby suitably regulated.

Determining appropriate precisions for signals in fixed-point IIR filters

This paper presents an analytical framework for the implementation of digital infinite impulse response filters in fixed-point hardware on field programmable gate arrays. This analysis is necessary because FPGAs, unlike fixed register size digital signal processors, allow custom bit widths. Within the framework, the designer determines the number of bits necessary for representing the constant coefficients and the internal signals in the filter. The coefficient bit widths are determined by accounting for the sensitivity of the filters pole and zero locations with respect to the coefficient perturbations. The internal signal bit widths are determined by calculating theoretical bounds on the ranges of the signals, and on the errors introduced by truncation in the fixed-point hardware. The bounds tell how many bits are required at any point in the computation in order to avoid overflow and guarantee a prescribed degree of accuracy in the filter output. The bounds form the basis for a methodology for the fixed-point digital filter implementation. The methodology is applied to the implementation of a second-order filter used as a compensator in a magnetic bearing control system.

Energy storage and loss in fractional-order circuit elements

The efficiency of a general fractional-order circuit element as an energy storage device is analysed. Simple expressions are derived for the proportions of energy that may be transferred into and then recovered from a fractional-order element by either constant-current or constant-voltage charging and discharging. For a half-order element, it is shown that the efficiency of the charging phase of the cycle is equal to the efficiency of the discharging phase. The results demonstrate the duality of the fractional capacitive and inductive elements, in that the efficiency of one under constant-current cycling is the same as the efficiency of the other under constant-voltage cycling, and vice-versa.

FPGA-based implementation of digital control for a magnetic bearing

An FPGA-based digital controller is presented for a magnetic bearing control application. A side-by-side comparison of the FPGAand DSP-based controllers demonstrates the advantages of using an FPGA in terms of design procedures, performance, and hardware utilization. The FPGA-based controller runs two orders of magnitude faster than the DSP-based controller does. The flexibility to customize the bit-widths of the internal variables makes the FPGA-based implementation more accurate than the DSPbased implementation, without increasing total register space. The increased accuracy in the control computation is especially important as fast sampling causes increased computational sensitivity.

Robust Stabilization and Disturbance Rejection for Uncertain Systems by Decentralized Control

This paper develops a decentralized control design which provides robust H ∞ disturbance rejection for a plant with structured uncertainty in a bounded admissible set. The design consists of an observer in each control channel, which includes estimates of the controls generated in the other channels and of the worst disturbance as determined by a state-feedback H ∞ solution. The observer gains are computed from a positive-definite solution of a Riccati-like algebraic equation. A convexity property of a matrix Riccati function is used to compute for the closed-loop system an H ∞-norm bound smaller than the predetermined bound, and to find an enlarged admissible set of plant uncertainities.