Patent GB-840123-A (GB)
Title: Improvements in on-off type control systems
Inventor: COALSE JOHN FLAVELL
IPC: G05D3/14
Filed: 1955-05-20
Abstract: 840,123. Electric correspondence control systems. NATIONAL RESEARCH DEVELOPMENT CORPORATION. May 18, 1956 [May 20, 1955], No. 14689/55. Class 40 (1). [Also in Group XXXVI] In an on-off control system responsive to input signals, having two or more stable states for governing the action of a controlled mechanism, e.g. a motor, wherein a control signal applied, e.g. to such motor is generated to have at least two discrete values each representing a respective stable state of such controlled mechanism, a computer operating on a time scale fast in relation to the operative time constant of the controlled mechanism repetitively extrapolates into future time from the present the data (e.g. position and velocity) represented by the input signals and by output signals similarly representing the action of the controlled mechanism, to derive future signals; a signal is fed to the computer representing the present discrete value of the control signal; and a comparison element generates signals representing errors between the corresponding extrapolated input and output signals at successive future instants of time; each comparison giving rise to a resultant signal which is reapplied to the computer as a correction factor for extrapolation of the output data, until the resultant signal is brought to a value which is operative to effect a changeover of the control signal from one discrete value to another, whereby the controlled mechanism is changed over from one stable state to the other at a critical optimum future instant of time such that the input signals are followed without hunting or overshoot. It is shown by mathematics that in an on-off type of control system responsive to a specific signal at any instant, a single switchover of torque is necessary at a unique future time t 1  in order to make the trajectory of the representative point of the state of the system (as defined by the input/output error e and its first derivative e) intersect the origin of the phase/plane defined by e plotted against e (Figs. 1, 2, not shown), and that t 1  may be computed continuously on a fast time scale and used in selfadjusting manner to control the switch-over to take place when t 1  becomes zero in present time. The following switching rules for the dynamic operation of such a system in response to a varying input signal are developed mathematically. (a) After changeover at time s 1  of a computing cycle, error e is observed when error derivative e is zero for the first time after changeover, and at the end of the sweep if e does not pass through zero. (b) If the controlled mechanism is in its forward stable state, e less than zero necessitates an earlier and e greater than zero a later instant of changeover, and vice versa if the mechanism is in its reverse stable state. In a second older control system (Fig. 3) wherein a motor and load M are driven through a power control relay Y from source W in correspondence with an input signal x so that in response to variations of the latter the motor is switched from full torque in one direction to full torque in the opposite direction at a critical future time so that the instantaneous load deflection corresponds with the instantaneous input signal without hunting or overshoot, the present output position and velocity parameters X, X are continuously fed as signals to an analogue simulator S together with a signal representing the calculated optimum changeover time S 1  on a fast computing time scale, to yield repetitive future position and velocity signals X(s), X(s) computed on this time scale. Present signals representing input position velocity and acceleration signals x 0 , x 0  and x 0 , are obtained from differentiator D and applied to input predictor P to produce repetitive future values of position and velocity input signals x(s) and x(s) on the computing time scale, under synchronism with master timer T also controlling the analogue simulator S. Subtractors G1 and G2 produce position and velocity error signals e 8  and e s  from x(s), x(s), X(s) and X(s), of which e(s) energizes a pulse generator K operating pulse when e(s) reaches zero, at the repetitive computing frequency N. A selection circuit H is operated by each pulse to derive a signal e(s 0 ) representing the value of e(s) at time s=S 0 , or at the end of a computing cycle if e(s) does not reach zero during such cycle, in accordance with rule (a) above. The impulsed signal e(s 0 ) is integrated at I to a voltage signal S 1  which is fed to the simulator S and also operates a power relay Y (providing the control signal for the driven mechanism) switching the output of power source W to motor and load M when S 1  passes through zero or a critical value, to reverse the motor torque. The motor and load time constant is long compared with the duration of a computer cycle, and the output position and velocity signals X 0 , X 0  are derived from a rotary potentiometer, associated with a differentiator or tachometer. Simulator S (Fig. 4), representing the performance of the motor load, and power relay, solves the differential equation where In is the moment of inertia; F(X) is the Coulomb friction; G(X) is the viscous friction; L is the applied torque; in response to signals x 0 , X 0  from the motor; Œ A denoting the operational state of the power relay and signal s 1  representing on the computing time scale the calculated future time at which the relay must reverse the motor torque for coincidence. Operation is synchronized from master timer T. A high-gain D.C. amplifier A1, shunted by capacitance C and resistance R is fed with current Œ L(S 1 )/R 1  over resistance R 1 , derived R 1  from a torque simulating bi-stable multivibrator (not shown) set at the beginning of each computing cycle to agree with the setting of the power relay in response to signal, and after a time S 1  in each computing sweep adapted to changeover correspondingly to the torque reversal in response to a trigger pulse generated at equality between the output of a Miller timebase (synchronized from T) with the input voltage signal S 1 . A further current ŒF(#X)/R 2  is applied to the input over resistance R 2  from a direct coupled amplifier-multivibrator MA fed with the computed value of the output velocity X(s) at future time s, while at the end of each computing cycle, contact J1 closes to restart the integrating action of amplifier A1 from a level representing the output velocity signal X 0  derived from tachometer or differentiator TG. It is shown that the output X s  is given by which by correct choice of components is equivalent to equation (1) above for the performance of the motor and load on the computing time scale, so that the output X s  represents the predicted value of output velocity at future time S. This is applied over resistance R 0  to D.C. amplifier A2 shunted by capacitance C 0  and normally open contact J2 (the whole having a time constant greater than the period of the computing cycle) and is combined with the output position signal X 0  in summation amplifier A3 to derive signal X(s) according to equation The contacts J1, J2 are closed during a resetting period equal to and following each computing cycle so that the latter restarts from an output value of X s  equal to X 0  and an output X s  from A2 equal to zero; the signal X 0  being added thereto in amplifier A3. To simulate a thirdorder motor load system wherein a delay term occurs due to the build-up time of motor field current, the input signal Œ A(s 1 ) from the power relay is applied to integrating D.C. amplifier AX shunted with resistance, capacitance, and a normally open contact J5 in series with a motor field current simulating signal F; the contact being closed at the beginning of each computing cycle to restart the next cycle of generation of signal Œ L 81  from a level representing the motor field current. The input predictor P and differentiator D may comprise (Fig. 5) a D.C. amplifier A4 fed with input signal x(t) over a series resistance and capacitance Cr to generate signal - x 0 (t) feeding D.C. amplifier A5 over series resistance and capacitance Cr<SP>1</SP> to generate signal x 0 (t). Integrating amplifier A6 shunted by capacitance and normally open diode or mechanical switch J3 receives x 0 (t) to develop a signal - X 0 (s) combined with a signal -x 0 (t) at summation amplifier A7 to yield a signal x(s)=x(o)+x o (s). This is also phase-inverted by D.C. amplifier A8 and integrated by D.C. amplifier A9 shunted by capacitance and normally open diode or mechanical switch J4 to give a signal x 0 (s) + ¢x 0 (s<SP>2</SP>) which is combined with signal x 0  in summation amplifier A10 to yield signal - x(s) = - x 0  - x 0 (s) - ¢x 0 (s<SP>2</SP>). The switches are closed from timer T to restore the integrators at the end of each computing cycle; the period of each of which is small compared with the operating time of the control system. It is shown that since x 0 , x 0  and x 0  are substantially constant over each computing cycle, the equations represent the predicted values of input position and velocity signals at a future time s defined on the computing time scale. The pulse generator circuit K and selection circuit H (Fig. 3) comprise a comparator E (Fig. 6) wherein when signal Ú(s) passes through zero (or at the end of a computing cycle if it does not reach zero) a sharpened output pulse triggers multivibrator M1 which generates a corresponding short rectangular pulse, but which is disabled until elapse of the computed changeover time S 1  by a voltage signal Œ A(S 1 ) derived from simulator S. Multivibrator M2, triggered from timer T generates a sharp pulse just prior to the end of each computing cycle to trigger multivibrator M3 to generate a short rectangular pulse which together with the pulse from multivibrator M1 is fed to buffer circuit B, which generates an output pulse at the end of each comp