Optimal finite wordlength digital control with skewed sampling

Optimum controller designs are developed which take account of the digital round-off errors in the controller implementation and in the A/D and D/A converters for the case of uniform skewed sampling. Skewing the control samples allows the computational delay in the control computer to be accommodated in the optimization problem. These results provide a very general extension to the LQG theory since they reduce to the standard LQG controller when infinite precision computation is used, and there is no computational delay (the sampling is synchronous). Penalties are added to the cost function to penalize the sum of the wordlengths used to compute the fractional parts of the controller state variables, and the wordlengths of the A/D and D/A converters. Hence, controller complexity is traded with performance. Control design for a large flexible structure at the Jet Propulsion Laboratory demonstrates the performance improvement of the proposed methodology versus the standard LQG approach.