# Article

## Robot Drives Diagnostics by Identifiability Criterion Based on State Matrix

Trefilov, S. A., Nikitin, Yu. R.

Article language: English

Abstract. The paper discusses robot drives diagnostics and optimal decision-making algorithm according to the identifiability criterion based on discrete digital control model. We consider discrete control algorithm for quality criterion that minimizes the energy of control and displacement. The optimal control algorithm is based on the Riccati equation solving for control system with modified state and control matrices. The criteria of observability, controllability and identifiability of robot drives are considered as rank function of the extended matrix with measurement matrix. An algorithm is proposed for calculating the criterion for identifiability of nonlinear control system in discrete linearization variant is proposed. Decision theory is applied for the robot drives diagnosis. It is suggested or we suggest to use identification in terms of mathematical model compliance to object operation results. A robot drives control using discrete vector-matrix algorithm involves calculating the state matrix at each step. Consequently, the expanded matrix determinant is calculated at each step and is compared with some constant that numerically divides the space of state matrices. Therefore, robot drives operation allows its identification. As the identification algorithm optimality criterion was chosen the optimal decision making criterion in combination with the identifiability criterion for the optimal control algorithm by the quadratic form criterion minimum. The vector-matrix model of robot drives in the state space is presented, taking into relative account state measuring accuracy of the information-measuring subsystem of robot drives. The drive model was developed in the Russian software pack-age “Dynamic Simulation of Technical Systems SimInTech”. It proposed to determine the identifiability criterion for practical tasks. The criterion of optimal decision making (threshold) can be chosen depending on the a priori data on the loss matrix and the probabilities of the hypothesis about the object mathematical model correspondence to the results of operation and the alternative - not about the correspondence of the model and experiment. In this paper, the identifiability conditions are considered not only in relation to the rank of the extended matrix [C, AC, ...], but also as a condition for ensuring the accuracy of the model with respect to the object. It is proposed to model the identifiability threshold by exhaustive search of the object states for this model.

Keywords: identification, diagnostics, robot drives, state space, discrete model, optimal algorithm, Riccati equation, Cauchy matrix, Bayes criterion

Pages: 105–114Total pages: 10

Funding, support: The reported study was funded by RFBR, project number 18-08-00772 A.

Year of publication: 2019