Some benefits of random variables in switched control systems
Recent advances in semiconductor technology have greatly increased the performance and range of application of switched mode circuits. Periodic switching can give rise to acoustic noise [Y.-S. Lai, Random switching techniques for inverter control, Electronics Letters 33 (9) (1977) 747749] or undesirable electromagnetic radiation. These problems can be reduced through the use of random switching policies [S.Y.R. Hui, S. Sathiakumar, K.-K. Sung, Novel random pwm schemes with weighted switching decision, IEEE Transactions on Power Electronics 12(0885-8993) (1997) 945951], but it is not always clear how this could be done without affecting other performance measures, such as RMS ripple or stability. We use the buck/boost regulator as an example for analysis and determine some simple techniques for choosing appropriate component values. The circuit is simulated and it is shown that strict adherence to the formal limits of stability, suggested by control theory, does not always guarantee a satisfactory output. We demonstrate that if switching is performed quickly enough then a state-space averaged model may be used for the buck/boost controller. This model is stable within wide bounds. It is possible to use some of this freedom to optimise EMC performance through the use of a control law which is random within certain limits. In the popular mind, the idea of randomness seems to be completely opposed to the idea of control. We show that not necessarily the case. Some randomness can beneficial, from the point of view of minimising the maximum power spectral density of the noise waveforms in the output current. This can be done without compromising the stability of the system.
random control switched mode stochastic resonance