The problem of robust multiloop proportional-integral-derivative (PID) controller tuning for multivariable processes is addressed in this paper. The problem is formulated in the H∞ control framework, and the controller parameters are determined based on both user-specified performance and robust stability. The PID settings are computed by solving a nonlinear optimization problem with matrix ine...

Two methods are presented for approximating the costate of optimal control problems in integral form using orthogonal collocation at Legendre–Gauss (LG) and Legendre–Gauss–Radau (LGR) points. It is shown that the derivative of the costate of the continuous-time optimal control problem is equal to the negative of the costate of the integral form of the continuous-time optimal control problem. Us...

The purpose of this paper is to propose a GSA-tuning IPD control technique for magnetic suspension systems. An educational demonstration on a magnetic-field sensed magnetic suspension system is examined for effectiveness. For the magnetic-field sensed magnetic suspension system (FSMSS), the current transducer is employed for measuring the electromagnetic coil current, and a Hall effect device i...

Proximity sensing applications requires the detection of small changes in capacitance (typically on the order of a few femtofarads) around the noise floor. There are many ways to process the data to determine whether a target was detected or not. So how do you choose? This application note describes a simple algorithm that can be used for proximity sensing or capacitive touch button application...

In the field of control, various control methodologies and strategies have been devised, tested and implemented in process control and other such control applications. Favourite examples of controllers are proportional, Integral and derivative in parallel and/ or series combinations so far. Controller tuning is also an important aspect of process control. Speaking on control techniques, there a...

In this paper, a hybrid neuro-fuzzy controller (NFC) is presented for the speed control of brushless DC motors to improve the control performance of the drive under transient and steady state conditions. In the hybrid control system, proportional-derivative (PD) type neuro-fuzzy controller (NFC) is the main tracking controller, and an integral compensator is proposed to compensate the steady st...

In this paper, the author analyzes the characteristics of the temperature control systems in industry, which have long delay time, large time constants and strong couple affects. The author then introduces a Proportional, Integral and Derivative neural networks (PIDNN) and lets PIDNN be a multivariable controller. The simulation results for a three-stage heater in a plastic injection machine ar...

A stochastic calculus similar to Malliavin’s calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener f...

In this paper, the generalized Taylor’s expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzyfractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessarythat we prove them in details. In application, the fractional Euler’s method is derived for solving fuzzy fractionaldifferential equations in the sense of Caputo...

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...