Approximate solutions of Volterra integral equations by an interpolation method based on ramp functionsVolterra integral equationSingular kernelRamp functionCollocation methodConvergence analysisIn the present paper we develop a numerical collocation scheme for integral equations based on the interpolation method ...
Consider the piecewise linear ramp function, with the step occurring over a domain of length 0.1, given by: $$\begin{aligned} f(x)=\left\{ \begin{array}{ll} 0&{} \hbox {if } 0<x<4.9\\ 10(x-4.9)&{} \text{ if } 4.9\le x\le 5\\ 1&{} \text{ if } 5.0<x<10. \end...
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This was motivated by the observation that the initial open-loop response of lag-dominant processes, such as tray temperature in high-purity distillation columns, resembles that of a delayed ramp variable. This study compares the behaviour of several PID λ-tuning rules with the Skogestad internal...
Unlike the proportional control system where valve position was a direct function of float position, this control system sets the speed of the motor-driven valve according to the float position. The further away from the setpoint the liquid level is, the faster the valve moves open or closed....
To describe the evolution equations of the state variables and , we introduce an endurance surface , defined by an endurance function . The state evolves according to the initial value problems (IVPs), [12], [17] (2a)(2b) where is the unit ramp function, , is the Heaviside step function...
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The system undergoes nonlinearity when encountering sudden ramp up to such a high step input. All the system responses converge, however the proposed is seen to converge faster compared to the others. This is due to the consistent steady state value of the integral term of the controller, ...
Controller 10 may include a proportional type electrohydraulic valve having a modulation control input applied from a periodic on-off type modulation source, whereby the resultant brake torque applied to a braked wheel may be perturbed in a ramp function fashion or alternately increased and decreased...
but permitting rotation of the other member through a predetermined arc. The other member is stepped to define a shoulder thereon which faces the shoulder provided on the bore. Camming means are disposed between the members, so that, when the other member is rotated, the one member is urged...