Patent GB-916526-A (GB)
Title: Apparatus for predicting the future value of a variable
IPC: G06G7/625
Filed: 1960-12-14
Abstract: 916,526. Electric analogue calculating. WAYNE KERR LABORATORIES Ltd., and GOURIET G. G. Dec. 12, 1961 [Dec. 14, 1960], No. 43015/60. Class 37. Apparatus predicting the future value of an electrical variable comprises plural differentiating circuits of equal gain and time constant connected in tandem so that each differentiates the output of its predecessor, means feeding a variable signal into the first circuit, and an adding circuit combining the input signal with variable proportions of the outputs of successive differentiating circuits, delay means applying a delay equal to the prediction time to the output signal, and means for comparing the delayed and the input signals so as to control the proportions of the signals combined in the adding circuit to minimize the mean square of the difference between the input signal and the delayed predicted signal. It is shown by mathematics that a normalized transfer function   where # 1 , # 2 , # 3 , # 4  are constants and # is the operator d/dt, is reducible to   where K is a constant and #= 1/# 1    and that the corresponding normalized group delay is unity for K = 3/7 so that the transfer function   is then given by  for a maximally flat delay characteristic. In Fig. 1 an input signal is amplified at 71 and applied to tandem differentiating circuits 12, 13, 14, 15 comprising amplifiers 16 with capacitance inputs 17 and feed-back resistors 18. Their time constants are adjustable simultaneously by continuous or stepwise ganged variation of resistors 18 and/or capacitors 17, and the outputs of amplifier 11 and the successive differentiators energize variable potentiometers 21 to 25 whose outputs are additively combined over resistances 29 at the input of feed-back amplifier 27 operating indicator or recorder 30. Adjustment of the respective potentiometers to the coefficients of equation (3) develop an output signal at 30 representing the predicted value of the input signal at a future time dependent on the differentiation time constant; provided that the input has a uniform power spectrum over a given frequency band. More generally, the coefficients must be chosen so as to minimize the integral where F(j#) is the Fourier spectrum of the input signal and f(j#,#) is the transfer function of the predictor circuit, which is stated to be expressible as derivable from equation (2). In Fig. 2, the input signal is fed to predictor 41 as in Fig. 1, whose output operates recorder 30 and energizes delay unit 42, which may be an electrical network or a loop of magnetic tape co-operaiing with spaced recording and replay heads. The output delayed by the prediction time is compared at 43 with the input signal and the instantaneous error signal is fed to mean square integrator 44 incorporating a thermocouple or the circuit described in Specification 909,346 which produces a signal representing the RMS value of its input. This operates stepping switch 45 to control the values of K in automatically setting the coefficient potentiometers of the predictor circuit according to equation (5) above, so as to minimize the mean square of the error signal represented by equation (4) above. In Fig. 3, the input signal is applied to predictor 51 as in Fig. 1 whose output operates recorder 30 and delay unit 52 similar to that in Fig. 2; the latter supplying comparator 54 through variable bandwidth low-pass filter 53 together with the input signal through identical variable low-pass filter 55. The comparator instantaneous error is fed to mean square integrator 56 whose output controls the coefficient setting of predictor 51 in a sequence automatically regulated by a timing device 57, together with the settings of filters 53, 55. The transfer function of the predictor is stated to be and the cut-offs of the filters are adjusted to be low with respect to the input bandwidth after which A 1  is adjusted for minimum error. The filters are then set to progressively higher cut-off frequencies for successive adjustment of A 2 , A 8  and A 4  for minimum error. Resetting may be automatically repeated at intervals. In Fig. 4 a delay unit 62 is constructed similarly to the predictor of Fig. 1, shown as 61, which operates recorder 30 and energizes successive variable coefficient differentiating units 63, 64, 65, 66 from which the input and the first, second, third, and fourth derivatives are obtained over coefficient potentiometers and combined at 67 with the signs of the first and third derivatives reversed, to produce a delay with a mean square error identical to that of the predictor circuit 61. The resultant signal is compared with the input signal applied to 61 and a mean square difference signal obtained from integrator 69 is applied to control the coefficients of the predictor 61 and the delay unit 62 in the same manner as in Fig. 2 or Fig. 3.