Parameter Identification of Second-Order Systems Using Least Squares and Recursive Least Squares Methods

This paper presents parameter identification of second-order systems using both ordinary least squares (OLS) and recursive least squares (RLS) methods. These approaches significantly enhance system stability and identification accuracy while offering practical applicability. The implementation typically involves formulating the system as a linear regression model y = φθ, where y represents the output, φ contains the regressor matrix of past inputs and outputs, and θ denotes the parameter vector to be estimated. For OLS, the solution is computed using the normal equation θ = (φᵀφ)⁻¹φᵀy, which provides a batch processing approach suitable for offline analysis. The RLS algorithm implements a recursive update mechanism through equations: K(k) = P(k-1)φ(k)[λ + φᵀ(k)P(k-1)φ(k)]⁻¹, θ(k) = θ(k-1) + K(k)[y(k) - φᵀ(k)θ(k-1)], and P(k) = [I - K(k)φᵀ(k)]P(k-1)/λ, where λ represents the forgetting factor for handling time-varying systems. The author also discusses potential application scenarios and future research directions to further explore the method's advantages and limitations. Overall, parameter identification using OLS and RLS methods serves as a powerful tool with broad applications across various engineering domains, particularly in system modeling, adaptive control, and real-time parameter tracking applications.