Optimal digital redesign of continuous-time systems using fractional-order hold

Abstract

This paper proposes a novel optimal digital redesign technique using fractional‐order hold (f.o.h.) for finding a dynamic digital control law from the available analog counterpart and for simultaneously minimizing a quadratic performance index. A method for converting the dynamic digital control law into a static one, through a tuning parameter, is also presented. The proposed technique can be applied to a system cascaded with a more general class of reference inputs than simple step inputs, and the developed digital controller can be implemented via low cost microcomputers. The superiority of using the fractional‐order hold over the zero‐order hold and the first‐order hold is exploited. © 1997 John Wiley & Sons, Ltd.

Adaptive control of printing devices using fractional-order hold circuits adjusted through neural networks

“…A FROH adjustable device drives the actuator. The control system has now a sampling period T ¼ 0.01 s, and the transfer function for the motor and pen carriage issee the detailed description of the system in [11]-…”

“…Finally, it has been shown in [10], that there exits no constraint referred to the sampling period in practice for the application of such a method, when the continuous-time system behavior can be described as a zero-free second-order plant. In addition, an attractive redesign technique using FROH for finding a dynamic digital control law from the available analog counterpart and for simultaneously minimizing a quadratic performance index is proposed in [11], and a practical approximate implementation method by using a common ZOH is studied deeply in [12,13].…”

A Review of Sample and Hold Systems and Design of a New Fractional Algorithm

“…For instance, the first-order hold (S&H-1) reconstructs signals as a piecewise linear approximations and may yield better fit at the price of a higher complexity. Other S&H are the fractional-and exponential-order holds, abbreviated as S&H-β and S&H-exp, with parameters 0 ≤ β ≤ 1 and τ > 0, respectively, that also improve the technique at the cost of a slight additional complexity [11][12][13][14]. In fact, we can take advantage of the extra parameter β and τ by tuning their values for a particular application.…”

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

“…Nevertheless, although the original continuous‐time system is stable, its discrete‐time model may be unstable if the sampling period is too small. Especially, some well‐designed methodologies for the continuous‐time system cannot or are extremely difficult to be directly extended to the digital design of discrete‐time system. For example, without solving the eigenvalues and eigenvectors of the system matrix, the multi‐stage continuous‐time optimal pole‐placement design optimally moves the poles outside the sector region (hatched) as shown in Figure (a) in the s‐plane to the desired hatched sector and keeps those original poles of the open‐loop system lying within the sector invariant that cannot be directly extended to the digital control case for the corresponding common region of a circle and a logarithmic spiral in the z‐plane (hatched) as shown in Figure (b).…”