In this work, we introduce and use an innovative approach for adaptive piecewise linear interval approximation of sensor characteristics, which are differentiable functions. The aim is to obtain a discreet type of inverse sensor characteristic, with a predefined maximum approximation error, with minimization of the number of points defining the characteristic, which in turn is related to the possibilities for using microcontrollers with limited energy and memory resources. In this context, the results from the study indicate that to overcome the problems arising from the resource constraints of smart devices, appropriate “lightweight” algorithms are needed that allow efficient connectivity and intelligent management of the measurement processes. The method has two benefits: first, low-cost microcontrollers could be used for hardware implementation of the industrial sensor devices; second, the optimal subdivision of the measurement range reduces the space in the memory of the microcontroller necessary for storage of the parameters of the linearized characteristic. Although the discussed computational examples are aimed at building adaptive approximations for temperature sensors, the algorithm can easily be extended to many other sensor types and can improve the performance of resource-constrained devices. For prescribed maximum approximation error, the inverse sensor characteristic is found directly in the linearized form. Further advantages of the proposed approach are: (i) the maximum error under linearization of the inverse sensor characteristic at all intervals, except in the general case of the last one, is the same; (ii) the approach allows non-uniform distribution of maximum approximation error, i.e., different maximum approximation errors could be assigned to particular intervals; (iii) the approach allows the application to the general type of differentiable sensor characteristics with piecewise concave/convex properties.

The paper presents a theoretical and experimental investigation of a thermo-mechanical model of an actuator composed of a shape memory alloy wire arranged in series with a bias spring. The developed mathematical model considers the dynamics of the actuator in the thermal and mechanical domains. The modelling accuracy is increased through the developed algorithm for modelling the minor and sub minor hystereses, thus removing the disadvantages of the classical model. The algorithm improves the accuracy, especially when using pulse-width modulation control, for which minor and sub minor hystereses are likely to occur. Experimental studies show that the system is very sensitive, and there are physical factors whose presence cannot be considered in the mathematical model. The experimental research has shown that setting constant values of the duty cycle is impossible to obtain a stable value of displacement and force. The comparison between the developed mathematical model results and the experimental results shows that the differences are acceptable. The improved modelling serves as a basis for designing such actuators and creating an improved automatic feedback control system to maintain a given displacement (force) or trajectory tracking.

We consider a nonlinear control system with a bang-bang hysteresis control, which is a simplified model of a thermal energy harvester. We obtain conditions on the controller and the system parameters guaranteeing the existence of a periodic mode in the system.

We study the existence of oscillatory modes in a controlled nonlinear system closed by a feedback in the form of a bistable hysteretic switch. The system is a simplified mathematical model of a thermal energy harvester. Conditions on the controller and on the system parameters are established that guarantee the existence of oscillatory modes in this system.

The popularity of smart sensors and the Internet of Things (IoT) is growing in various fields and applications. Both collect and transfer data to networks. However, due to limited resources, deploying IoT in real-world applications can be challenging. Most of the algorithmic solutions proposed so far to address these challenges were based on linear interval approximations and were developed for resource-constrained microcontroller architectures, i.e., they need buffering of the sensor data and either have a runtime dependency on the segment length or require the sensor inverse response to be analytically known in advance. Our present work proposed a new algorithm for the piecewise-linear approximation of differentiable sensor characteristics with varying algebraic curvature, maintaining the low fixed computational complexity as well as reduced memory requirements, as demonstrated in a test concerning the linearization of the inverse sensor characteristic of type K thermocouple. As before, our error-minimization approach solved the two problems of finding the inverse sensor characteristic and its linearization simultaneously while minimizing the number of points needed to support the characteristic.