Pulse-width-modulating feedback control of electromagnetic actuators

A system for controlling the dynamics of a group of electromagnetic actuators, each actuator having a related armature, coil and driver, in which system an armature is displaceable from an initial position by electrical activation of the related coil, comprising:

• means for providing a coil-energizing waveform signal as a succession of pulses denoted sequentially by the index i and which being at fixed times t.sub.i with respect to the start of the activation,
• means for modulating each pulse to have a variable duration .tau..sub.i determined on-the-fly as a function of a vector state-variable errors e.sub.i observed at a pre-defined observation time t.sub.i * fixed with respect to the start of said pulse, said errors being computed by reference to an ideal trajectory which the armature should follow,
• and
• means for regulating the armature trajectory responsive to the pulse duration modulated coil-energizing waveform signal whereby the armature trajectory is urged to substantially follow the ideal trajectory.

A method for automatically deriving the control functions f.sub.i required to achieve the desired regulation of actuator dynamics, comprising the following steps:

• calibrating an ideal trajectory which an accelerating mass forming a portion of the actuator should follow, by energizing the actuator in the absence of perturbations using a nominal energizing waveform signal made up of a series of pulse having pre-defined, nominal pulse widths .tau..sub.i, whereby the ideal trajectory is energized, thereby allowing the state variable describing the ideal trajectory to be measured at the pre-defined observation times t.sub.i *, and the results of the measurements to be stored as digital statements in memory;
• performing a trial-and-error procedure for each pulse i in the energizing waveform for the purpose of obtaining experimental data describing the control function f.sub.i, in which various combinations of state-variable errors e.sub.i for pulse i are deliberately and systematically produced at the observation time t.sub.i * by means of perturbation parameters, each combination of perturbation parameters being applied while energizing the actuator a number of times with each actuation employing a slightly different width .tau..sub.i of pulse i (all subsequent pulses held fixed at their nominal widths), thereby to determine which values of pulse width .tau..sub.i counteract the given combination of state-variable errors e.sub.i with adequate success, success being defined according to an acceptance criterion in which the actuator follows the ideal trajectory within predetermined limits;
• and
• performing a statistical procedure for fitting the experimental data collected by the trial-and-error procedure, whereby the data relevant to each pulse of the energizing waveform are fit separately with a piece-wise smooth function, thereby interpolating and extrapolating the experimental data, such that during subsequent, feedback-controlled operation, the appropriate values of pulse widths .tau..sub.i may be determined for any combination of the state-variable errors e.sub.i.

A method for automatically deriving, through selective pulse-width-modulation of a succession of n pulses, the control functions f.sub.1, . . . , f.sub.n and the acceptance windows .DELTA..sub.1, . . . , .DELTA..sub.n-1, to achieve desired regulation of actuator dynamics comprising the following steps:

• (a) deriving an ideal trajectory which an accelerating mass forming a portion of the actuator should follow in terms of a succession of n pulses having pre-defined widths;
• (b) deriving, by causing and measuring disturbances of actuator motion, a set of data points which partially describes a control function for pulse n, and at the same time circumscribes an acceptance window .DELTA..sub.n-1 ;
• (c) iterating step (b) for earlier pulses n-1, . . . , 1;
• and
• (d) providing, through regression analysis, a complete description of the control functions f.sub.1, . . . , f.sub.n ;
• whereby pulse-width modulation of the n pulses according to the control functions causes the actuator trajectory to substantially follow the ideal trajectory with an acceptable deviation.