The Ziegler-Nichols tuning rules have been very influential and have been used extensively in process industry. This paper presents an extension of the modified Ziegler-Nichols tuning rules for fractional PI controllers. The design method consists on minimizing a frequency objective function subject to a constraint on the maximum sensitivity function M _S . In this paper it is also demonstrated that substantially better performance can be obtained using PI ^λ instead of PI controllers. An interpretation of these tuning rules as methods where one point of the Nyquist curve is positioned in a desired point is also given. These tuning rules are compared with other tuning rules and shown to give good results, especially when simplicity, performance and robustness are emphasized.

This paper aims to present a general identification procedure for fractional first-order plus dead-time (FFOPDT) models. This identification method is general for processes having S-shaped step responses, where process information is collected from an open-loop step-test experiment, and has been conducted by fitting three arbitrary points on the process reaction curve. In order to validate this procedure and check its effectiveness for the identification of fractional-order models from the process reaction curve, analytical expressions of the FFOPDT model parameters have been obtained for both situations: as a function of any three points and three points symmetrically located on the reaction curve, respectively. Some numerical examples are provided to show the simplicity and effectiveness of the proposed procedure. Good results have been obtained in comparison with other well-recognized identification methods, especially when simplicity is emphasized. This identification procedure has also been applied to a thermal-based experimental setup in order to test its applicability and to obtain insight into the practical issues related to its implementation in a microprocessor-based control hardware. Finally, some comments and reflections about practical issues relating to industrial practice are offered in this context.

This paper presents a new method for identifying dynamical systems to get fractional-reduced-order models based on the process reaction curve. This proposal uses information collected from the process. It can be applied to processes with an S-shaped step response that can be considered with fractional behavior and a fractional order range of α ∈ [0.5, 1.0]. The proposed approach combines obtaining model fractional order using asymptotic properties of the Mittag-Leffler function with time-based parameter estimation by considering two arbitrary points on the process reaction curve. The improvement in terms of accuracy of the identified FFOPDT model is obtained due to a more accurate estimation of α parameter. This method is characterized by its effectiveness and simplicity of implementation, which are key aspects when applying at an industrial level. Several examples are used to illustrate the effectiveness and simplicity of the proposed method compared to other well-established methods and other approaches based on the process reaction curve. Finally, it is also implemented on microprocessor-based hardware to demonstrate the applicability of the proposed method to identify the fractional model of a thermal process.

In this paper, the conceptualization of a control hardware architecture aimed to the implementation of integer- and fractional-order identification and control algorithms is presented. The proposed hardware architecture combines the capability of implementing PC-based control applications with embedded applications on microprocessor- and FPGA-based real-time targets. In this work, the potential advantages of this hardware architecture over other available alternatives are discussed from different perspectives. The experimental prototype that has been designed and built to evaluate the control hardware architecture proposed in this work is also described in detail. The thermal-based process taking place in the prototype is characterized for being reconfigurable and exhibiting fractional behaviour, which results in a suitable equipment for the purpose of fractional-order identification and control. In order to demonstrate the applicability and effectiveness of the proposed control hardware architecture, integer- and fractional-order identification and control algorithms implemented in various control technologies have been applied to the temperature-based experimental prototype described before. Detailed discussion about results and identification and control issues are provided. The main contribution of this work is to provide an efficient and practical hardware architecture for implementing fractional-order identification and control algorithms in different control technologies, helping to bridge the gap between real-time hardware solutions and software-based simulations of fractional-order systems and controllers. Finally, some conclusions and concluding remarks are offered in the industrial context.

This paper presents new tuning rules for fractional PI control of processes that are typically found in process control. The rules are based on characterization of process dynamics by three parameters that can be obtained from a simple step response experiment. The rules are obtained by minimizing a frequency objective function subject to a constraint on the maximum sensitivity. Comparisons with classical tuning rules show that they are very simple but give substantially better performance.