Study of the effects of discretizing quantitative feeddback theory analog control system designs

This paper examines the feasibility of using the Pseudo Continuous Time (PCT) modelling approach for a sampled-data system in extending continuous domain (analog) Quantitative Feedback Theory (QFT) flight control system designs to the discrete domain. The results of two analog designs are studied for digital implementation. They are for a transport aircraft with robust analog fixed compensators for three different flight conditions and for a fighter aircraft, with inherent reconfiguration real-time requirements. For the transport aircraft, the analog compensators are discretized using two transformation techniques after they are modified to reflect the effects of the sampler and zero-order-hold. Simulation results for the transport aircraft show that the Tustin transformaiton with PCT modelling provides good results using a sampling rate of 40Hz. For the fighter aircraft, results are obtained with a sampling rate of 60Hz, but only for two out of four flight conditions. Sampling and finite wordlength effects are also considered. A computer program is developed to simulate the effects of finite wordlength. It is sufficiently general to allow the specification of rounding or truncation, controller wordlength and placement of the radix point. Simulations are conducted using various wordlengths, radix positions and appropriately quantized controller coefficients. The conclusion drawn from this study is that the Tustin transformation with PCT modelling provides good discrete system performance in transforming the continuous QFT design for a variety of operational modes.