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Linear Systems: Block Diagrams and Laplace Transforms
Published in Richard J. Jagacinski, John M. Flach, Control Theory for Humans, 2018
Richard J. Jagacinski, John M. Flach
For example, suppose the problem was to integrate a unit step function. A step function is a function that is zero for times less than zero and is one for times equal to zero or greater. This function was introduced in chapter 4 in the context of Fitts’ Law. The positioning task used in Fitts’ experiments could be modeled as responding to a step input. The appearance of the target is considered time zero. The distance to the target is the size of the step. Using the conventions of calculus, the problem of integrating a unit step would be represented as: () ∫0t1du
Analysis of the interaction between the Yangtze River and Poyang Lake, China based on Chaos theory
Published in Silke Wieprecht, Stefan Haun, Karolin Weber, Markus Noack, Kristina Terheiden, River Sedimentation, 2016
Jing Hu, Zhi-li Wang, Yong-Jun Lu
Where H is the Heaviside step function, defined as: () H(x)={x<0,0x≥0,1
Signals and their functional representation
Published in Alexander D. Poularikas, ®, 2018
Note: To plot a unit step function, we introduce values for t, and if the number in parentheses is 0 or positive, we set the value of the function equal to 1, and if the value is negative, we set the value of the function equal to 0.
Teaching transfer functions without the Laplace transform
Published in European Journal of Engineering Education, 2022
Imad Abou-Hayt, Bettina Dahl, Camilla Østerberg Rump
Moreover, the authors find Simulink's use of the Laplace notation for the integration process (Figure 5) unfortunate for two reasons: The input signal, the numerical integration itself and the output signal are all in the time domain.The expression is also the Laplace transform of the unit-step function (Figure 3(a)): beside being the integral operator itself (Dorf and Bishop 2011, p. 82):