Limitations on maximal tracking accuracy. 2. Tracking sinusoidal and ramp signals

For part 1, see Proc. of 35th IEEE Conference on Decision and Control, p.726-31 (1996). This paper continues the earlier work on optimal tracking problems with respect to multivariable feedback systems. We examine the error between a system´s output response and its command input, which is either a sinusoidal or a ramp signal. This error is quantified under an integral square criterion, and is adopted as a measure of tracking accuracy. For both sinusoidal and ramp signals, we derive explicit expressions of the minimal tracking error attainable by all possible stabilizing controllers. These results show that the tracking accuracy may be fundamentally limited by plant nonminimum phase zeros and unstable poles together with their spatial properties, in ways dependent upon the command input signals