A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process

Abstract

In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the classical approach, we design a non-fractional high-gain observer, and then we compare the performance of both observers. We consider three scenarios: The first one considers the estimation of the system states by measuring only one output with no noise added on it and under ideal conditions. Second, we add noise to the measured output and then reconstruct the system states, and, third, in addition to the noise, we increase the gain parameter in both observers (non-fractional and fractional) due to the fact that we want to prove that the robustness changes in this parameter. The results showed that, using our approach, the estimated states can be recovered under noise circumstances in the measured output and under parameter change in the observer, contrary to using classical (non-fractional) observers where the states cannot be recovered. In all our tests, we used the normalized root-mean-square, integral square error, and integral absolute error indices, resulting in a better performance for our approach than that obtained using the classical approach. We concluded that our fractional multi-order high-gain observer is more robust to input noise than the classical high-gain observer.

Fractional-Order Sliding Mode Observer for Actuator Fault Estimation in a Quadrotor UAV

“…Several researchers have demonstrated the significant efficacy of FOC in designing dynamical observers [35,36]. For instance, in [37], the authors highlight the robustness to noise of a fractional-order high-gain observer in a heat exchanger process. A fractionalorder sliding mode control based on a nonlinear disturbance observer aimed at reducing chattering and improving transient response in an electric drive system is presented in [38].…”

Advances in Thermal Process Engineering and Simulation

“…For engineering applications, a comparison of numerical and analytical methods is developed to generate a solution to the three-dimensional heat diffusion equation [11]. The analytical solution is based on an infinite set of polynomials and an exponential-type function.…”