Prony Series Digital Filter Implementation for Real Time Accelerometer Drift Compensation
Real-time Prony series filters model structural MEMS relaxation as discrete state poles to strip low-frequency drift before velocity integration.
State Space Realization
Matrix Representation
Matrix representation of a dynamic system provides a set of first order differential equations to describe internal behavior. A state space realization provides a framework for representing the coupling between inputs and outputs in a compact matrix form. This method allows for the analysis of multi input systems that are difficult to handle with traditional transfer functions.
Transformation Property
Conversion from a transfer function to a matrix representation is not unique, meaning several different structures can represent the same input to output behavior. A specific state space realization might be chosen to minimize computational complexity or to improve numerical stability in fixed point hardware. Common forms include the controllable canonical form and the observable canonical form.
System Analysis
Controllability and observability matrices are derived from the system matrices to determine if the internal states can be manipulated or recovered from the outputs. If a state space realization is not minimal, it contains redundant states that do not contribute to the input to output mapping. Engineers use these models to design state observers and feedback controllers for complex robotic or industrial processes.
Software Integration
Modern control software packages automate the process of building these models from physical parameters or experimental data.