On-Line Fast Algebraic Parameter and State Estimation for a DC Motor Applied to Adaptive Control G. Mamani, J. Becedas and V. Feliu-Batlle * † Abstract—This paper presents an adaptive position control scheme for DC motors based on an on-line closed loop continuous-time identification method. A fast, non-asymptotic, algebraic identification method is used to estimate simultaneously the unknown sys- tem parameters and the unmeasured states to update an adaptive position control scheme. Keywords: Algebraic Identification, System Identifica- tion, Adaptive Control, States Estimation 1 INTRODUCTION In recent years, the importance of the continuous-time model identification problem has been recognized in the areas of identification and self tuning adaptive control. A survey on identification of continuous-time systems is [1]. Parameter estimation has been an important topic in system identification literature. The traditional theory is well developed in [2].The advantages of direct continuous time estimation in relation to its discrete-time alternative are defined in [3]. It is well known that for an observable system, represented in state space, the state estimation problem is intimately related to the computation of time derivatives of the output signals, in a sufficient number. Adaptive control covers a set of techniques which attain the control performance when the plant dynamics is un- known or changes in time. There are several survey pa- pers [4], [5] and books [6] and [7] among others. The adaptive control scheme proposed in [8] was used to con- trol a DC servomotor based on speed control method, this approach is only used to control first order systems. In that paper the method is implemented in discrete time. In [9], the multiple model adaptive system of the DC mo- tor was proposed. This is based upon the indirect adap- tive control and more than one identifier (to estimates the unknown parameters of the plant) are incorporated. * G. Mamani, J. Becedas and V. Feliu-Batlle are with Universidad de Castilla La Mancha, ETSI Industri- ales, Av. Camilo Jos´ e Cela S/N., 13071 Ciudad Real, Spain. Jonathan.Becedas@uclm.es, glmamani@uclm.es, Vicente.Feliu@uclm.es † This research was supported by the Junta de Comunidades de Castilla-La Mancha, Spain via Project PBI-05-057 and the Euro- pean Social Fund. The main contribution of our article is that we use an on-line closed loop algebraic method of continuous-time nature for the estimation of the unknown parameters and unmeasured states of a DC servomotor model in order to implement an adaptive position control scheme. Our ap- proach uses the model of the system which is well known. The advantages of the method are that it does not need any statistical knowledge of the noises corrupting the data; the estimation does not require initial conditions or dependence between the system input and output; and the algorithm is computed on-line in a closed loop and in real time. The motor parameters and states are simulta- neously estimated. The only measured variables are the motor position, as given by an encoder, and the input voltage to the armature circuit of the motor. After the estimates of the motor inertia, viscous friction, velocity and acceleration are obtained, the Coulomb’s friction co- efficient is instantaneously estimated. The importance of this coefficient estimation is explained in [10] in or- der to appropriately control the system by compensat- ing this non-linearity. The identification method is based on elementary algebraic manipulations of the following mathematical tools: module theory, differential algebra and operational calculus, see [11]. Recently, the alge- braic method has been applied in [12]. In this work the algebraic method independence to the input signal design is also demonstrated. Finally, we mention that the alge- braic method has also been applied in [13] in the area of signal processing applications, and [14] in flexible robots. This paper is structured as follows: In section 2 the DC servo motor model and the algebraic identification method are presented. The identification of Coulomb’s friction coefficient is attempted. In Section 3 the closed loop adaptive PD controller design is explained. These results are verified via simulation in Section 4. Finally, Section 5 is devoted to concluding remarks. 2 MOTOR MODEL AND IDENTIFI- CATION PROCEDURE This section is devoted to explain the linear model of the DC motor and the algebraic identification method. Proceedings of the World Congress on Engineering 2008 Vol II WCE 2008, July 2 - 4, 2008, London, U.K. ISBN:978-988-17012-3-7 WCE 2008