Adaptive sampling frequency for sampled-data control systems

Sampled-data control systems generally have fixed sampling frequencies which must be set high enough to give satisfactory performance for all anticipated conditions. A study is made here of an adaptive system which varies the sampling frequency by measuring a system parameter. It is shown that a sampler followed by a zero-order hold whose sampling period is controlled by the absolute value of the first derivative of the error signal will be a more "efficient" sampler than a fixed-frequency sampler. That is, over a given time interval, fewer samples are needed with the variable-frequency system than with a fixed-frequency system while maintaining essentially the same response characteristics. Analog computer studies of simple Type I and Type II sampled-data servo systems with error sampling and unity feedback verified the method. Standard analog computer components were used to set up a simulated servo system, a rate detector, absolute-value detector, a voltage-controlled oscillator, and a sampler and zero-order hold. The system described reduced the number of samples required for response to a step input to about three-quarters that required in a fixed-sampling-frequency system. Over a long period of time savings in the number of samples required can be expected to be between 25 and 50 per cent. In many applications the savings produced by reducing the over-all number of samples required may outweigh the added complexity of the adaptive-sampling-frequency system.