First order plus frequency dependent delay modeling : new perspective or mathematical curiosity?

The first-order-plus-dead-time model (FOPDT) is a popular simplified representation of higher order dynamics. However, a well known drawback is the rapid decrease of the frequency response accuracy with increasing process order. This especially applies to the higher frequency range. Literature offers solutions by extending this three parameter model with more parameters. Here, a fractional dead time is proposed. As such, a Frequency-Dependent Delay (FDD) is introduced, which offers a better approximation. As the fractional-order term introduces nonlinear coupling between the phase and the magnitude of the process, the fitting of the function becomes an iterative process, so a constrained multi-objective optimization is needed. This novel model, first-order-plus-frequency-dependent-delay or FOPFDD is fitted on a real electrical ladder network of resistors and capacitors of four and eight parts. The classic model, which is clearly a special case of the new model, is outperformed in the entire bandwidth

Active learning in control education : a pocket-size PI(D) setup

Active learning techniques have the possibility to enhance student performance. In control engineering these techniques unravel concepts such as feedback control, proportional-integral-derivative control, system dynamics, etc. This paper presents the development of pocket-size PID setups and how they are implemented in an undergraduate course of control engineering. The setup makes use of an electrical circuit which has the capability of mimicking a wide range of processes, thus appealing to the multidisciplinary character of the student group. Custom-made analog PID printed circuit boards are developed, making each part of the controller transparent. Open-source software is used to build a graphical user interface to communicate with data-acquisition cards used in industry. It is shown in this paper that investing in mobile setups which are numerous, allows for active learning in control education. This leads to better understanding of abstract concepts and increased student performance

Bioimpedance sensor and methodology for acute pain monitoring

The paper aims to revive the interest in bioimpedance analysis for pain studies in communicating and non-communicating (anesthetized) individuals for monitoring purpose. The plea for exploitation of full potential offered by the complex (bio)impedance measurement is emphasized through theoretical and experimental analysis. A non-invasive, low-cost reliable sensor to measure skin impedance is designed with off-the-shelf components. This is a second generation prototype for pain detection, quantification, and modeling, with the objective to be used in fully anesthetized patients undergoing surgery. The 2D and 3D time-frequency, multi-frequency evaluation of impedance data is based on broadly available signal processing tools. Furthermore, fractional-order impedance models are implied to provide an indication of change in tissue dynamics correlated with absence/presence of nociceptor stimulation. The unique features of the proposed sensor enhancements are described and illustrated here based on mechanical and thermal tests and further reinforced with previous studies from our first generation prototype

Effect of social distancing for office landscape on the ergonomic illumination

In office buildings valuable energy is wasted if not properly regulated as a function of presence of humans and active demands for illumination levels. Effective and clever usage of the sunlight is essential for optimal use of energy resources in large office buildings. Additionally, productivity of the employees can be improved by maintaining a constant light intensity. In context of social distancing enforced onto landscape area structure and occupancy, they have effects in the illumination pattern and ergonomics. This paper presents the practical setup to mimic the illumination regulatory problem in landscape offices and the dynamic properties of such a system in the context of social distancing regulations. The light level control is performed with distributed predictive control, whereas a comparison is made among various situations. The original contribution of the paper is a fast, adaptive control algorithm, which can deal with changing context parameters; e.g. varying landscape office structures. Copyright (C) 2020 The Authors

First Order Plus Fractional Diffusive Delay Modeling: interconnected discrete systems

This paper presents a novel First Order Plus Fractional Diffusive Delay (FOPFDD) model, capable of modeling delay dominant systems with high accuracy. The novelty of the FOPFDD is the Fractional Diffusive Delay (FDD) term, an exponential delay of non-integer order $\alpha$, i.e. $e^{-(Ls)^{\alpha}}$ in Laplace domain. The special cases of $\alpha = 0.5$ and $\alpha = 1$ have already been investigated thoroughly. In this work $\alpha$ is generalized to any real number in the interval $]0,1[$. For $\alpha=0.5$, this term appears in the solution of distributed diffusion systems, which will serve as a source of inspiration for this work. Both frequency and time domain are investigated. However, regarding the latter, no closed-form expression of the inverse Laplace transform of the FDD can be found for all $\alpha$, so numerical tools are used to obtain an impulse response of the FDD. To establish the algorithm, several properties of the FDD term have been proven: firstly, existence of the term, secondly, invariance of the time integral of the impulse response, and thirdly, dependency of the impulse response's energy on $\alpha$. To conclude, the FOPFDD model is fitted to several delay-dominant, diffusive-like resistors-capacitors (RC) circuits to show the increased modeling accuracy compared to other state-of-the-art models found in literature. The FOPFDD model outperforms the other approximation models in accurately tracking frequency response functions as well as in mimicing the peculiar delay/diffusive-like time responses, coming from the interconnection of a large number of discrete subsystems. The fractional character of the FOPFDD makes it an ideal candidate for an approximate model to these large and complex systems with only a few parameters.Comment: 16 pages, 9 figures, under revie

Imitating a Tuned Vibration Absorber With an Euler-Lagrange Controller: Comparing Different Stability Proofs

Vibrations in mechanical systems are often undesirable. They could lead to failure and/or disruption of proper operation of the system. Hence, mitigation of vibrations is indispensable. Two major classes can observed: passive and active vibration mitigation. The former does not rely on sensors and actuators and is for that reason assumed to be less complex, more reliable with regard to failure, and more intuitive to tune. The latter allows more design flexibility, can be adaptive to changes over time, and is more compact. In the class of active vibration absorption, a feedback loop containing a control strategy is used to connect the sensors with the actuators. Many complex, mathematical controllers already exist that have proven to be very effective to decrease vibrations in a system. However, interpretability of the controller parameters can be lacking and, thus, impede an intuitive tuning strategy, because of its abstract nature and the rapid increasing number of controller parameters. The flexibility of active control allows to imitate a passive tuned vibration absorber with extra design freedom: all types of nonlinearities and interconnections can be created. This could lead to a vibration control strategy that combines the advantages of passive and active vibration mitigation. The first step in designing an active nonlinear controller is to guarantee stability. Therefore, it is necessary to proof the ranges of the controller parameters to achieve an asymptotically stable system. Different methods to proof stability can be used and will lead to different limitations for the controller. In this work, the direct method of Lyapunov is used to prove stability based on an extended Lure type Lyapunov function and a straightforward energy based Lyapunov function. Both stability proofs will be compared with respect to the interconnection system/EL-controller they yield and the corresponding controller design freedom they offer