An Efficient on‐Line Parameter Identification Algorithm for Nonlinear Servomechanisms with an Algebraic Technique for State Estimation

Abstract

This paper presents a methodology for on-line closed-loop identification of a class of nonlinear servomechanisms. First, a system is defined with the same structure as the actual servomechanism, but using time-varying estimated parameters. No coupling between the actual and the estimation systems is present. Position, velocity and acceleration errors, defined as the difference of the actual respective signals and the signals coming from the estimation system, are required in the identification method. Then, a recursive algorithm for on-line identification of the system parameters is derived from a cost function depending on a linear combination of all the estimation errors. Velocity and acceleration estimates, required in the proposed parameter identification algorithm, are obtained by using an algebraic methodology. The identification algorithm is compared by means of real-time experiments with an on-line least squares algorithm with forgetting factor and an off-line least squares algorithm with data preprocessing. Experimental results show that the proposed approach has a performance comparable to that obtained with the off-line least squares algorithm, but with the advantage of avoiding any preprocessing.

Closed‐loop parameter identification of second‐order non‐linear systems: a distributional approach using delayed reference signals

“…The controller closing the loop must stabilise the system with relatively low tracking error. Besides, this controller must not depend on the system parameters [4, 37]. These features allow selecting controllers consisting of a linear combination of , , and/or .…”

“…This absence may be cumbersome because are required for calculating , and . There are many solutions for computing these signals such as algebraic differentiators [4], sliding modes differrentiators [41], or the dirty derivative. In general, the worst estimation results are obtained using the dirty derivative [4].…”

“…An online parameter identification scheme usually computes the system parameters employing each new measurement, which allows generating a new set of parameters in real time [4, 6]. The off‐line techniques use all the collected input–output data, usually have a pre‐processing data stage, and then estimate the system parameters [8].…”

“…For instance, relay‐based techniques have been applied for parameter identification of DC servomechanisms [5, 16, 17]. Other works dealing with parameter identification of DC servomechanisms using the least‐squares (LS) algorithm or similar approaches can be found in [4, 7, 17–22].…”

A Data-Driven Multi-Scale Online Joint Estimation of States and Parameters for Electro-Hydraulic Actuator in Legged Robot

“…Colorado has proposed a novel on-line closed-loop parameter identification algorithm for second order nonlinear systems, designed a cost function based on the optimization method by using a linear combination of the actual and an estimation system, and used algebraic techniques to estimate the velocity and acceleration signals, avoiding noise processing problems. This method converges faster than the online and off-line least squares algorithms, and has strong robustness against disturbance, but without requiring any type of data pre-processing [30], [31]. In addition, he has also proposed a first integrals and adaptive parameter identification method for conservative Hamiltonian systems, and discussed the parameter identification problem as an optimization one [32].…”