Alexis Castelan-Perez

Disturbances in dynamical systems pose a major challenge for parameter identification, particularly in the presence of unknown initial conditions and uncertain external influences. To address this issue, this paper proposes an algebraic parameter estimation methodology that incorporates fractional-order calculus in the Laplace domain for controlled linear engineering systems. The proposed approach eliminates the influence of unknown initial conditions and considers external disturbances that admit a local polynomial representation through Taylor series expansions over sufficiently small time intervals, while avoiding explicit numerical differentiation in the time domain. The manuscript includes analytical, numerical, and experimental validations to highlight the benefits of incorporating fractional-order differentiation in the derivation of algebraic estimators for online parameter estimation. The method is experimentally validated on two linear differentially flat electrical circuits, whose flat representations enable the proposed algebraic formulation under distinct disturbance signals. The results demonstrate that the fractional differentiation order acts as an additional tuning parameter, and that appropriately selected fractional orders can improve estimation accuracy, yielding parameter estimates consistently closer to their true values when compared with the conventional integer-order algebraic formulation.

The accurate estimation of parameters in dynamical systems stands for an open key research issue in modeling, control, and fault diagnosis. The presence of noise in input and output signals poses a serious challenge for accurate real-time dynamical system parameter estimation. This paper proposes a new robust algebraic parameter estimation methodology for integer-order dynamical systems that explicitly incorporates the signal filtering dynamics within the estimator structure and enhances noise attenuation through fractional differentiation in frequency domain. The introduced estimation methodology is valid for Liouville-type fractional derivatives and can be applied to estimate online the parameters of differentially flat, oscillating or vibrating systems of multiple degrees of freedom. The parametric estimation can be thus implemented for a wide class of oscillating or vibrating, nth-order dynamical systems under noise influence in measurement and control signals. Positive values are considered for the inertia, stiffness, and viscous damping parameters of vibrating systems. Parameter identification can be also used for development of actuators and control technology. In this sense, validation of the algebraic parameter estimation is performed to identify parameters of a differentially flat, permanent-magnet direct-current motor actuator. Parameter estimation for both open-loop and closed-loop control scenarios using experimental data is examined. Experimental results demonstrate that the new parameter estimation methodology combining signal filtering dynamics and fractional calculus outperforms other conventional methods under presence of significant noise in measurements.

Parameter identification in dynamical systems is a well-known problem with many applications in control design, system monitoring, and fault detection. As these systems are increasingly integrated into complex and demanding environments, challenges such as rapid response, uncertainty handling, and disturbance rejection must be addressed. This paper presents a real-time estimation technique for parameters and load torque in brushless DC (BLDC) motors. These electrical machines are extensively used in engineering applications and often operate under hard conditions. The proposed method is based on algebraic identification, known for its robust performance in both linear and nonlinear systems. In utilizing the mathematical model of a BLDC motor, a set of equations is derived to enable parameter estimation, assuming the availability of input and output measurements in open loop. Moreover, unknown load torque is estimated by approximating the disturbance over a short time window using Taylor series expansion polynomials. The theoretical contribution is analytically validated and is also verified through numerical evaluations revealing the effectiveness of the proposed technique for real-time parameter and disturbance estimation in BLDC motors over other important techniques. Additionally, to address potential peaks in the estimation process, a modification involving an exponent is introduced to mitigate these issues.

Brushless DC machines have demonstrated significant advantages in electrical engineering by eliminating commutators and brushes. Every year, these machines increase their presence in transportation applications. In this sense, early fault identification in these systems, specifically in the electronic speed controllers, is relevant for correct device operation. In this context, the techniques reported in the literature for fault identification based on the Hilbert–Huang transform have shown efficiency in electrical systems. This manuscript proposes a novel technique for early fault identification in electronic speed controllers based on the Hilbert–Huang transform algorithm. Initially, currents from the device are captured with non-invasive sensors in a time window during motor operation. Subsequently, the signals are processed to obtain pertinent information about amplitudes and frequencies using the Hilbert–Huang transform, focusing on fundamental components. Then, estimated parameters are evaluated by computing the error between signals. The existing electrical norms of a balanced system are used to identify a healthy or damaged driver. Through amplitude and frequency error analysis between three-phase signals, early faults caused by system imbalances such as current increasing, torque reduction, and speed reduction are detected. The proposed technique is implemented through data acquisition devices at different voltage conditions and then physical signals are evaluated offline through several simulations in the Matlab environment. The method’s robustness against signal variations is highlighted, as each intrinsic mode function serves as a component representation of the signal and instantaneous frequency computation provides resilience against these variations. Two study cases are conducted in different conditions to validate this technique. The experimental results demonstrate the effectiveness of the proposed method in identifying early faults in brushless DC motor drivers. This study provides data from each power line within the electronic speed controller to detect early faults and extend different approaches, contributing to addressing early failures in speed controllers while expanding beyond the conventional focus on motor failure analysis.