This paper considers a quadratic stabilization problem by an H1 controller. The controller is constructed by a linear fractional transformation on contractive time-varying gains. The controller parameterization is given in terms of contractive time-varying gains. This free parameter can be used to improve the closed-loop response. A tuning method of time-varying gains is chosen so that a Lyapun...

*Correspondence: [email protected] 1College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China Full list of author information is available at the end of the article Abstract In this paper, we put forward a fractional-order survival red blood cells model and study the dynamics through the Hopf bifurcation. When the delay transcends the threshold, a...

In this paper, a simple and effective stabilization method for integrating time delay systems using fractional order PD controllers μ s k k s C d p + = ) ( is proposed. The presented method is based on finding the stability regions according to the fractional orders of the derivative element in the range of (0, 2). These regions are computed by using three stability boundaries: Real Root Bounda...

Cantilever beams have an important role in day to day life in bridges, towers, buildings and aircraft wings, making active vibration suppression a highly researched field. The purpose of this paper is to detail the design of fractional order PID controllers for smart beams. A novel tuning procedure is proposed based on solving a set of nonlinear complex equations that directly aim at reducing t...

This paper applies fractional order PID controller to torsional system’s backlash vibration suppression control, in which the order k of D controller can not only be integer but also be any real number. In order to improve control system’s robustness against backlash non-linearity, several methods have been proposed. However their design processes are very complicated. In this paper, a clear an...

In this work, a class of fractional order controller (FOPID) is tuned based on internal model control (IMC). This tuning rule has been obtained without any approximation of time delay. Moreover to show usefulness of fractional order controller in comparison with classical integer order controllers, an industrial PID controller tuned in a similar way, is compared with FOPID and then robust stabi...

This paper presents a new application of a fractional order control system which controls the input energy to a three phase electric arc furnace. Graphite electrodes are used to convert electrical energy into heat via phase electric arcs. Constant arc length is desirable as it implies steady energy transfer from the graphite electrodes to the metallic charge in the furnace bath. With the charge...

Design of fractional order PID (FOPID) controller for DC motor is proposed in this paper. A FOPID (PID) is a PID controller whose derivative and integral orders are fractional numbers rather than integers. Design stage of such controller consists of determining six parameters – proportional constant (Kp), integral constant (Ki), derivative constant (Kd), filter time constant (τd), integral orde...

In the context of reaching best way to control movement autonomous cars linearly and angularly, making them more stable balanced on different roads ensuring that they avoid road obstacles, this manuscript chiefly aims reach optimal approach for a fractional-order PID controller (or PIγDρ-controller) instead already classical one used provide smooth automatic parking electrical cars. The PIγDρ-c...

The EVs battery has the ability to enhance the balance between the load demand and power generation units. The EV aggregators to manage the random behaviour of EV owners and increasing EVs participation in the ancillary services market are employed. The presence of aggregators could lead to time-varying delay in load frequency control (LFC) schemes. The effects of these delays must be considere...