Digital implementation of time-optimal attitude control

An experimental single-axis, time-optimal attitude control computer was designed and built using digital differential analyzer (DDA) techniques. A relatively simple digital implementation of the control functions was obtained while holding the computational errors within predetermined limits. To evaluate the capabilities, limitations and accuracy attainable in digital implementarion of such a system, tests were conducted in which an analog computer was used to simulate the dynamics of the controlled vehicle. It was shown that the digital control system performed its function properly, providing a true time-optimal control, and that the computation errors were kept below the design limit. The primary concern of this paper is to show how basic DDA techniques can be used to implement the control functions required in attitude control of a space vehicle and to present the system characteristics resulting from such a design approach. Techniques used for reducing DDA computational errors are also given consideration. It will be seen that the truncation errors can be minimized and limited to a zero-averaged error to prevent hysteresis or drift effects. Unlike truncation errors, round-off errors cannot be completely eliminated and can cause localized irreversibility of computations (hysteresis effects). In spite of this, harmful drifts or accumulated errors are not produced because of the closed-cycle nature of the control problem as viewed in the error phase plane.