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The paper discusses the quadratic neural unit QNU and highlights its attractiveness for industrial applications such as for plant modeling, control, and time series prediction. Linear systems are still often preferred in industrial control applications for their solvable and single solution nature and for the clarity to the most application engineers. Artificial neural networks are powerful cognitive nonlinear tools, but their nonlinear strength is naturally repaid with the local minima problem, overfitting, and high demands for application-correct neural architecture and optimization technique that often require skilled users. The QNU is the important midpoint between linear systems and highly nonlinear neural networks because the QNU is relatively very strong in nonlinear approximation; however, its optimization and performance have fast and convex-like nature, and its mathematical structure and the derivation of the learning rules is very comprehensible and efficient for implementation. These advantages of QNU are demonstrated by using real and theoretical examples.