Comprehensive Quantitative Tuning Method for Multiple LADRCs in High Order Plus Time Delay Processes

In response to the challenge posed by the limitations of current active disturbance rejection controllers (ADRCs) in parameter tuning and restricted control efficacy for
$K{{e}^{-\tau s}}/{{\left( Ts+1 \right)}^{n}}$
-type high-order processes, two improved linear active disturbance rejection controllers (LADRCs) are proposed in this paper: model-aided delay LADRC (MDLADRC) and compound LADRC (CLADRC). Utilising frequency domain analysis, comprehensive quantitative parameter tuning rules for LADRCs are derived, based on principles of robust stability. The aim of the rules is to address the issue of parameter tuning for both existing LADRCs and the two newly proposed variants. The simulation and comparison results demonstrate the superiority of the improved LADRCs and the tuning rules, and reveal the relationship between the order of LADRCs and their time domain indices. Experimental results on the Peltier temperature system, water tank, and superheated steam temperature (SST) system further verify the engineering applicability of the proposed method. Furthermore, these results illustrate the promising potential of the proposed method for application in process control practice. Additionally, the quantitative parameter tuning rules are also applicable to high-order inertia and first-order plus time delay (FOPTD) processes.
Note to Practitioners
—In this study, an investigation is conducted into linear active disturbance rejection control (LADRC) with improved controllers for high-order plus time-delay (HOPTD) systems and the parameter tuning method. Consequently, the innovations are characterized by their improved structures and quantitative parameter tuning rules. From the perspective of the controllers’ structures, the large inertia and time delay of HOPTD process pose significant challenges for the design of many LADRCs and other types of controllers. In order to overcome the aforementioned problems, based on the existing 5 types of LADRCs for high-order processes, model-aided delay LADRC (MDLADRC) and compound LADRC (CLADRC) are designed. Compared with the existing improved LADRCs, the disturbance observation accuracy has been found to be higher, with a faster system response speed. From the perspective of the quantitative parameter tuning rules, the relationship between the initial value of the open-loop system in the frequency domain and the controllers’ parameters is determined by means of open-loop frequency domain analysis. At the same time, general parameter tuning rules based on the robust stability of the system are proposed to comprehensively solve the parameter tuning problems of the described 7 types of LADRCs. Meanwhile, the maximum sensitivity is adopted to constrain the parameter range of the controllers. Finally, the application of various experimental scenarios are applied to verify the superiority of the two proposed improved LADRCs and the universality of the parameter tuning rules. Notably, the proposed method is compatible with other types of controllers and processes, as well as backwards compatible with high-order inertial and first-order plus time delay (FOPTD) processes. In the future, further investigations should be conducted into the proposed parameter optimisation rules and the low lag filter.