IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 2, APRIL 2002 207 Computerized Investigation of Robust Measurement Systems Nikolay Petkov Kolev, Snejana Todorova Yordanova, and Plamen Marinov Tzvetkov Abstract—This paper deals with the development of software for investigating the robust properties of measurement systems and for their design and tuning in order to improve their robustness. The software constitutes Simulink models and m-files as extensions of the libraries of MATLAB. The investigations on continuous mea- surement systems (a self-balancing system) and discrete systems (ADCs) with improved robustness by using the internal model con- troller technique revealed new properties—fast dynamics, high ac- curacy, and discretization error reduction via multiple measure- ments. Index Terms—Computer investigation, measurement systems, robustness. I. INTRODUCTION R OBUSTNESS is the property of a system to preserve its characteristics with acceptable tolerance about its desired (nominal) characteristics for a given level of model uncertainties (perturbations due to aging of material, drift of the zero, and am- bient influences such as noise, disturbances, temperature, dust, etc.). All measurement systems are designed to be robust as a rule. A special class is developed to further improve the dynamic re- sponse speed and the accuracy of measuring systems through a robustness feedback on the basis of a simplified reference model of the system. Such an approach is an extension of the internal model control for achieving robustness to perturbations, noise, and disturbances [1], [2]. The aim of this paper is to develop software, investigate mea- surement systems, and improve their robustness. The software concerns the continuous and the discrete parts of measurement channels, including case studies from these parts (self-balancing systems, ADCs, etc.). It is based on the building of Simulink models, m-files using MATLAB and Control Toolbox [3], and Assembler real-time measurement and control modules. II. THEORETICAL BACKGROUND The robustness of a dynamic system can be estimated by the robust stability or robust performance criteria [1], [2]. The ro- bust stability ensures preservation of the stability of the system for a given multiplicative system uncertainty, defined as , where and are the transfer Manuscript received November 22, 2001; revised January 3, 2002 The authors are with the English Language Department of Engineering, Tech- nical University of Sofia, Sofia, Bulgaria. Publisher Item Identifier S 0018-9456(02)02916-9. Fig. 1. Block diagram of a measurement system with internal model controller. functions of the measurement system and of its simplified ref- erence model, respectively. The robust performance criterion requires minimization of the -norm of the error in the mea- surement system. It is estimated by the transfer function of the system and its sensitivity. The design of high accuracy measurement systems requires the use of various techniques and schemes to achieve the nec- essary robustness—compensation and protection circuits, ther- mostats, shielding, etc. [4], [5]. The most effective is the feed- back approach. In this case, the robust stability criterion is ex- pressed as , where is the frequency characteristic of the closed-loop system with nom- inal parameters, and with denoting the significant frequency range [6], [7]. The robust performance criterion takes the form , where is the sensitivity of the closed-loop system with respect to disturbances and system model uncertainties, and is the frequency characteristic of a filter that shapes the disturbance in the Laplace transformation [2]. In the fre- quency range of interest in most cases of disturbances, is assumed to be within the range [0.3–0.9] [2]. The measurement system with internal model controller is a class of the feedback measurement system, which is based on the introduction of a simplified internal model of the system and a specially designed controller as shown in Fig. 1. The transfer function of the controller is , where is the stable part of the inverse reference model. The filter is added to make proper [2], and for step input signals it has the form: (1) The equivalent controller has the transfer function (2) 0018-9456/02$17.00 © 2002 IEEE