Using feedthrough for near one-step-ahead control of inversely unstable plants

The one-step-ahead (OSA) control law is modified by the use of feedthrough to accommodate unstable plant zeros. An nth-order discrete-time system is guaranteed to track the desired input in one timestep. This is accomplished by subtracting the denominator dynamics and algebraically canceling the numerator dynamics. A problem occurs with OSA control when the plant has unstable zeros, that is, zeros that are outside the z-plane unit circle. In this case, an unstable zero is canceled and the resulting controller will be unstable. The authors address this problem. The approach taken is specific to OSA control