We have introduced a novel approach to competency-based education in mechatronics from the undergraduate to the postgraduate level. What distinguishes this approach is the integration of modeling and control of sampled systems right from the beginning of the undergraduate education. It is achieved by changing the structure of the first-semester Calculus course to focus on discrete-time systems: emphasizing numerical differentiation and integration and difference equations. The curriculum is enriched by interdisciplinary homework project assignments that, given in subsequent courses throughout the education, are tied to the same quarter-vehicle model but vary in theoretical complexity. It demonstrates multiple dimensions of the same engineering problem, leading to a deeper understanding. Based on the discrete-time modeling studied in Calculus, students can solve the problem at a basic level and verify the results with measurements. Later, they can compare these solutions with those obtained using more advanced tools. This approach creates a synergy between different subjects ranging from the basics to the advanced control theory. This article focuses primarily on the mathematical toolkit that facilitates the achievement of our didactic goals.

Modeling of various phenomena in engineering work is always a kind of simplification of real processes, aiming at a model where a certain level of mathematical theory and computational procedures is sufficient. If the complexity of the required theory corresponds to the general mathematical competence of engineers, then technical problems can be treated separately in engineering (or physical) models without regard to the mathematical background. However, in some advanced engineering fields, the harmonized development of engineering and mathematical models and toolboxes is necessary to find efficient solutions. For example, modeling variable structure systems in ideal sliding mode requires a mathematical toolbox that goes far beyond general engineering competence through the theory of discontinuous right-hand-side differential equations. Although sliding mode control is popular in practice and the concept of sliding mode allows a significant reduction of model complexity, its exact mathematical description is rarely encountered. The problem of friction compensation of a micro-telemanipulator using sliding mode control demonstrates a harmonized application of the mathematical and engineering approaches. Based on Filippov’s theory, the ideal sliding mode can be discussed. Although an ideal system cannot be implemented in reality, the real systems can be kept close enough to it; therefore, the discussion of the solution of the ideal model is important for practical applications. Although several elements of the topic are available in the literature, in this paper a unique complex approach is given for users of sliding mode control with experimental considerations, different engineering models, and codes. The paper concludes that sliding mode control is a case where engineering and mathematical modeling are inseparable and requires the competence of both fields.

Nowadays, our students are required to use more and more mathematical tools with the help of user-friendly software. As a result, they are able to move to higher levels of abstraction in system modeling and control. One such tool is poly topic modeling, which is taught in the postgraduate advanced control course. Its mathematical description can be intimidating for students at first, but we provide them with utilities that can be used even by students who cannot or do not want to delve into the mathematical depths. We provide these students with semi-finished models, e.g. a model of a linearized quarter vehicle, which they learn in a previous course. Here, the minimum requirement is to add nonlinear friction to the simple linearized quarter vehicle model and construct a poly topic model from the resulting more compact model, and use it to apply the simple pole placement learned in the state space description of linear systems. The advantage of the poly topic modeling presented in this paper is that it can be generated directly from the measurement data of a system.