Lebesgue‐ p NORM Convergence OF Fractional‐Order PID‐Type Iterative Learning Control for Linear Systems

Monotone systems are dynamical systems whose solutions preserve an ordering, relative to the initial data. This paper focuses on the set‐point regulation problem for excitable‐transparent‐monotone single‐input single‐output systems with well‐defined static characteristics. The suggested technique for designing a static feedback controller is inspired from the Hirsch Theorem for monotone autonomous systems. It is shown that the closed‐loop system is strongly monotone and its generic solution converges to the desired set‐point. A remark is given on the application of the suggested design methodology to delay systems, as well as to systems with reaction‐diffusion equations. A simulation example from the biological world demonstrates the effectiveness of the proposed control strategy in real applications.

Section: Monotone Systems: Revisitedmentioning

confidence: 99%

Application of the Hirsch Generic Convergence Statement to the Set‐Point Regulation of Excitable‐Transparent‐Monotone Systems

Agahi

2018

“…In 2001, [13] first proposed the D -type ILC and extended the application of ILC to fractional-order systems. For fractional-order linear or nonlinear systems, fruitful achievements on the performance of fractional-order iterative learning control (FOILC) have been made over the last 18 years [14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

PD^α‐type iterative learning control for fractional‐order linear continuous‐time switched systems

Zhang

Peng

2019

For a class of fractional‐order linear continuous‐time switched systems specified by an arbitrary switching rule, this paper proposes a PDα‐type fractional‐order iterative learning control algorithm. For systems disturbed by bounded measurement noise, the robustness of PDα‐type algorithm is first discussed in the iteration domain and the tracking performance is analyzed. Next, a sufficient condition for monotone convergence of the algorithm is studied when external noise is absent. The results of analysis and simulation illustrate the feasibility and effectiveness of the proposed control algorithm.

“…Nangrani and Bhat propose a fractional order proportional integral controller (FOPI) based on state feedback for precise and robust control of such undesirable behavior [13]. Lei Li discusses firstand second-order fractional-order PID-type iterative learning control strategies for a class of Caputo-type fractional-order linear time-invariant systems [14]. Gandomi et al use chaotic mapping to improve the firefly algorithm for setting the parameters β and γ in this algorithm [15].…”

Section: Introductionmentioning

confidence: 99%

Optimum Design of Fractional Order Pid Controller Using Chaotic Firefly Algorithms for a Control CSTR System

Ravari

Yaghoobi

2018

A fractional‐order PID controller is a generalization of a standard PID controller using fractional calculus. Compared with the standard PID controller, two adjustable variables, “differential order” and “integral order”, are added to the PID controller. Fractional‐order PID is more flexible, has better responses, and the precise adjustment closed‐loop system stability region is larger than that of a classic PID controller. But the design and stability analysis is more complicated than for the PID controller. Therefore, the optimal setting of parameters is very important. A firefly algorithm in standard mode has only local optimization and accuracy is low. In order to fix this flaw an improved chaotic algorithm firefly is proposed for a design controller FOPID. To evaluate the performance of the proposed controller, it has been used in the control of a CSTR system with a variety of fitness functions. Simulations confirm the optimal performance of the proposed controller.