The discrete time Biquad State Space structure: Low latency with high numerical fidelity

State space models of highly flexible systems can present severe numerical issues. The models derived from physical principles often lack structure. Canonical form models, are compact, but obscure any physical structure and can have coefficients that are highly sensitive to model parameters. What is needed is a form that has the compact representation of the canonical forms, the physicality of the forms derived from physical equations, and maintain numerical accuracy and physical intuition, even after discretization. This paper presents a new state space form, the Biquad State Space (BSS), based on the multinotch structure [1], [2]. We will will show that the BSS captures the endearing characteristics of the multinotch while providing the flexibility of model based control. This paper will present the basic structure in discrete time form which most closely matches the multinotch. Forms not specific to minimum latency control, including a continous time version, will be discussed in [3].