Fractional-order feedback control of a poorly damped system

Abstract

Abstract-This study presents the design of a fractionalorder proportional-integral (FOPI) controller for a mass-springdamper system which is poorly damped. A model based design technique is used to design a FOPI controller for this system. A good performance of the closed loop control of a high order oscillatory system, such as the mass-spring-damper system, is with traditional proportional-integral (PI) controllers difficult to achieve. Therefore, a comparison between a traditional PI controller and a FOPI controller is performed by simulation. The simulation results show that the FOPI controller outperforms the classical PI controller resulting in an increased damping of the oscillations while maintaining a reasonable control effort.

Robust combined feedback/feedforward control for fractional FOPDT systems

“…A discussion about the numerical solution of the optimization problem is out of the scope of this paper. Nevertheless, it must be underlined that, for the family F, the robust boundary .j!/ can be easily obtained via (11) by gridding the allowable values of the parameters of Q G.s/. This operation may seem computationally demanding, but it is never involved in the numerical optimization because it must be performed just once, before the optimization starts.…”

“…We first aim at minimizing the worst-case settling time at 2%, with a unitary set-point value y f D 1, imposing a constraint on the maximum control variable of U max D 1:5 and one on the maximum acceptable overshoot of O max D 0:2. First, we numerically compute the robust stability boundary by gridding the process uncertainty intervals and computing for each process Q G.s/ the uncertainty (11) with respect to the real-rational model. We obtain .j!/ by upper bounding the computed uncertainties for each frequency, obtaining the results shown in Figure 4.…”

“…It is well known that the fundamental trade-off in control design is the balance between performance and robustness. In this context, fractional control has received a great attention recently because of its capability of dealing with uncertainty in an effective way [1][2][3][4][5][6][7][8][9][10][11].…”

Comparison of Various Fractional Order Controllers on a Poorly Damped System

“…Poorly damped processes feature a high-oscillatory response in the time domain with the presence of resonance peaks in the frequency domain representation of the process, increasing the difficulty of the control task. The transfer function of the classical PID controller has a single pair of zeros to compensate the poorly damped process, motivating the need of a higher order controller to compensate for the poorly damped characteristics of the plant [6]. Hence, the development of more complex tuning procedures is needed for controlling processes with poorly damped dynamics.…”

Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

“…A fractional order control based approach is proposed for piezoactuated nanopositioning stage to suppress the vibration of the low-damped resonant mode and also to minimize the tracking error for nanopositioning applications and it is proposed [20]. A fractional order proportional-integral (FOPI) controller for a mass-spring-damper system which is poorly damped is proposed and it is proved that FOPI controllers are effective compared to the classical PI controllers [21]. A fractional order (FO) controller is proposed for solving the vibration suppression problem in civil structures experimented on a laboratory scaled steel structure, with one floor, modeled as a single degree-of-freedom system proposed and investigated [22].…”