Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications

Abstract

In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractional-order PID (FOPID). Commonly, after tuning the parameters of FO-PID controller, its transfer function is discretized (for realization purposes) using the so-called generating function. This discretization is the origin of some errors and unexpected results in feedback systems. It may even happen that the controller obtained by discretizing a FOPID controller works worse than a directly-tuned discrete-time classical PID controller. Moreover, FOPID controllers cannot directly be applied to the processes modeled by, e.g., the ARMA or ARMAX model. The aim of this paper is to propose a discrete-time version of the FOPID controller and discuss on its properties and applications. Similar to the FOPID controller, the proposed structure applies nonlocal operators (with adjustable memory length) to the error signal. Two methods for tuning the parameters of the proposed controller are developed and it is shown that the proposed controller has the capacity of solving complicated control problems.

Eigenvalue Analysis and Case Study Examples of Fractional Order Generalised Predictive Control

“…Minimisation of the associated discrete-time cost function yields a controller with the same structural form as GPC, i.e. it is defined by equations (7)- (9). The main difference is that, whilst the GPC weighting matrices Γ and Λ are defined explicitly via the cost function (3), or more commonly in practice via the scalar input weight λ as described above, FGPC defines these weights implicitly via the two scalar tuning terms, α and β.…”

Meliorating the performance of heating furnace using the FOPID controller

“…IOPID stands for the integer order proportional derivative which [1] is mathematically defined as, where, Kp is gain of proportional ity, K; is gain ofIntegral, Kd is gain of Derivative, e is the Error (SP-PV), t is instantaneous time and T is variable of integration that takes on the time values from 0 to the present t. On performing the Laplace transform of the equation (1) which is the PID controller equation is, (2) FOPID stands for the fractional order proportional integral derivative. Numerically the FOPID controller can be defined as,…”

“…On performing the Laplace transform ofthe equation (3) we get [2], (6) where, Kp is gain ofproportionality, K; is gain ofIntegral, Kdis gain of Derivative and A and J.l are the differential-integral's order for FOPID controller.…”

A novel optimal PID controller autotuning design based on the SLP algorithm

“…Many controller methods have been proposed for system control, such as the feedback linearization method, sliding model control, and adaptive control (Wang, Wang, Yuan, & Yang, ), but proportional integral derivative (PID) control is still widely applied in many applications, such as chemical processing, industrial applications, power plants, and automatic control (Freire, Moura Oliveira, & Solteiro Pires, ; Merrikh‐Bayat, Mirebrahimi, & Khalili, ). Approximately 90% of industrial applications use a PID controller for the actual control (Saridhar, Ramrao, & Singh, ) because its characteristics include good performance, low cost, high effectiveness, and a simple structure.…”