Fundamental limitations of monotonic tracking systems
Provides foundational theoretical bounds for control engineers designing monotonic tracking systems.
The paper establishes necessary and sufficient conditions for monotonic tracking in linear systems, revealing fundamental limitations including feasible zero locations, minimum controller order, and fastest decay rate, with a geometric interpretation for complex-conjugate zeros.
We consider the monotonic tracking control problem for continuous-time single-input single-output linear systems using output-feedback linear controllers in this paper. We provide the necessary and sufficient conditions for this problem to be solvable and expose its fundamental limitations: the exact feasible locations of the plant zeros, the minimum controller order possible, and the fastest decay rate achievable for the closed-loop system. The relationship between these bounds is explained by a simple geometric shape for plants with a pair of complex-conjugate zeros.