This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 2 U+00B3 factorial experimental design for a fractional order proportional integral and derivative controller U+0028 FOPID U+0029, integer order proportional integral and derivative controller U+0028 IOPID U+0029 and the Skogestad internal model control controller U+0028 SIMC U+0029. The factors assumed in experiment are the presence of random noise, external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.

This paper presents a new design methodology for robust fractional-order controllers with more than three parameters for first-order plus dead time systems using the synthesis scheme of the ‘more flat phase’ idea for a fractional-order controller with [proportional integral derivative] (FO[PID]) structure. The stability region of the FO[PID] controller and the synthesis scheme with the ‘more flat phase’ idea are illustrated through a simulation example. The corresponding pseudo-codes of the synthesis scheme are also summarised. The implementation and approximation error of the FO[PID] controller are also discussed. Likewise, the superiority of the FO[PID] controller designed with the ‘more flat phase’ idea is verified by additional simulations and experimental results where the closed-loop system with FO[PID] controller is not sensitive to the variations of the loop gain, ensuring satisfactory control performance. Obtained results show high potential in practical industrial applications.

Developing accurate mathematical or data-driven models for effective controller design under dynamic variable conditions becomes increasingly challenging. For this reason, the concept of a digital twin (DT) as a virtual representation of a physical asset has been introduced as a tool for process modelling, design, and control implementation while providing additional knowledge of the system that can be used to enable awareness capabilities on the asset. However, digital twin models used to be complex, requiring expensive computational times depending on the application to provide the most accurate system representation, limiting its application in edge, embedded, and register transfer level computing domains. Therefore, using reduced-order digital twin models is an alternative to get DT closer to the physical asset. Considering these challenges, we propose a reduced-order FPGA-based digital twin implementation that directly sources data from the real system, operates in parallel with the virtual system, and enables awareness mechanisms to improve the systems operation. This setup removes large data transfers, cloud interfaces and expensive computational times deriving into a faster and more efficient DT. To illustrate the capabilities of this embedded digital twin, we present a case study focused on monitoring a power converter. The study involves establishing and enforcing a safe operating area (SOA) for the power converter, implementing error awareness mechanisms, and enabling machine learning models to predict converter load conditions and fault events detection. Thus, we aim to showcase the effectiveness of our proposed FPGA-based digital twin approach in addressing real-time control challenges towards smart control engineering.

This paper presents the identification, control and robustness analysis for a robotic system of 1 degree of freedom using fractional and integer PID controllers. Initially, an ADAMS-MATLAB co-simulation model is built to simulate the dynamic model of robotic system. The identification of the dynamic model parameters of the system employs the recursive least-squares method. The controller design uses a linearized model of the robotic system obtained by the method of input-output linearization, and then, the fractional PID and integer PID controllers are designed based on it. The robustness of the PID controllers is analyzed in the frequency and the time domain. The robustness analysis in the frequency domain uses The Gang of Four (sensibility, complementary sensibility, sensibility of the plant and sensibility of the controller effort). The time domain analysis uses the ADAMS-MATLAB co-simulation model, considering external disturbances, noise in the feedback loop, parametric uncertainty and set-point variation, using as performance criteria ISE, average value and standard deviation of the control action. The tests are performed for positioning and tracking tasks. The obtained results show that the fractional PID controller has a better behavior in presence of external disturbances and lower energy consumption.