Dennis F. Wilkie

Generation of sensitivity functions for linear systems using low-order models

New proofs are given for the recently demonstrated total symmetry and complete simultaneity properties for the companion canonic form for single-input linear time-invariant controllable systems. These proofs result in a convenient closed-form expression for the complete simultaneity property. The use of these properties to generate by one n th-order sensitivity model all the sensitivity functions \frac{\partialx_{i}}{\partialv_{j}}|_v^{0}, i=1,...,n, j=1,...,r, for a single-input linear time-invariant controllable n th-order system which depends on r different parameters is reviewed. This method represents an improvement over known methods for generating the sensitivity functions, which generally require a composite dynamic system of order n(r+1) . This result is then extended to the case of multi-input normal linear systems, where, at most, 2m-1 dynamic n th-order systems are needed in addition to the system to generate all the sensitivity functions of the system state with respect to any number of parameters ( m is the dimension of u ). It is shown that the algebraic calculations that must be made in the m -input case are much less than m times the calculations needed for the single-input case. The implications of these results for the computer aided sensitivity analysis of systems are discussed.

Analysis of Motion of Magnetic Levitation Systems: Implications for High‐Speed Vehicles

To study the motion of a magnetically suspended high‐speed vehicle, a simple example (the long wire above a thin conducting plate) is considered in detail. The lift and drag forces on the magnet (long wire) are derived for arbitrary motion above the plate. The stability of the system is analyzed for typical parameters (velocity = 300 mph, height = 0.1 m). By using a Laplace‐transform technique, it is shown that two types of modes occur (in the linearized equations of motion). One mode is a vertical oscillation with an amplitude that grows slowly in time. The other mode is an unbounded increase in the horizontal velocity error. This latter instability results from the fact that the drag force decreases with increasing velocity at high speeds. In this connection, an error is pointed out in a recent publication in which it was claimed that the system is stable. Detailed consideration of the effects of horizontal acceleration and vertical velocity on the magnetic forces is given. The effects of aerodynamic dr...

DYNAMICS, CONTROL AND RIDE QUALITY OF A MAGNETICALLY LEVITATED HIGH SPEED GROUND VEHICLE

MAGNETIC MEANS OF SUSPENDING VEHICLES HAVE BEEN PROPOSED FOR USE IN HIGH SPEED GROUND TRANSPORTATION SYSTEMS. HOWEVER, THE MOTION OF SUCH SUSPENSION (LEVITATION) SYSTEMS USING MAGNETIC REPULSION FORCES WHEN THEY ARE PERTURBED FROM EQUILIBRIUM IS OSCILLATORY WITH A FREQUENCY OF THE ORDER OF 1 HZ AND A VERY LONG DAMPING TIME. ONE MEANS OF OBTAINING MORE DAMPING IS BY FEEDBACK CONTROL OF THE MAGNET CURRENTS. IN THIS PAPER, THE RIDE QUALITY RESULTING FROM ALTERNATIVE CONTROL STRATEGIES USING FEEDBACK PROPORTIONAL TO VEHICLE-TRACK CLEARANCE, VERTICAL VELOCITY AND ACCELERATION ARE CONSIDERED. IT IS FOUND THAT GOOD RIDE QUALITY CAN BE OBTAINED OVER A TRACK EQUIVALENT TO A MODERATELY GOOD HIGHWAY WITH A HIGH CLEARANCE MAGNETIC SUSPENSION. THE DYNAMICS OF A VEHICLE IN ALTERNATIVE GUIDEWAYS WHICH SUPPLY LATERAL GUIDANCE AS WELL AS LIFT FORCES ARE ANALYZED. IT IS SEEN THAT A GUIDEWAY CONFIGURATION WHICH PROVIDES ORTHOGONAL SURFACES FOR GUIDANCE AND LEVITATION FORCES LEADS TO INHERENTLY MORE STABLE VEHICLE MOTION AND ALLOWS THE USE OF SIMPLE INDEPENDENT CONTROL STRATEGIES ON ALL LIFT AND GUIDANCE MAGNETS. /AUTHOR/

On the sensitivity of the linear state regulator

The sensitivity of the optimal response of a linear system with quadratic performance index to changes in the weighting factors in the performance index is determined. This necessitates finding the sensitivity of the feedback gain matrix K to changes in the weighting factors. It is shown that the sensitivities of K can be obtained as the solution of a set of linear matrix differential equations. Further, for time-invariant systems and an infinite time interval, it is seen that the sensitivities of K are found more simply by solving a set of linear algebraic matrix equations.

Where does the control theorist fit into the transportation picture

The possible role of the control theorist in the development of innovative new transportation systems is discussed. In particular, it is noted that the most promising of the new systems are very dependent on automatic control and/or efficient routing and scheduling for their success. Thus, the control theorist can play a vital role in the design of new systems. It is further noted that the system theorist is well suited to help develop better techniques for analyzing the usage of potential new systems and forecasting their regional impact.