Analytical structures and analysis of the simplest fuzzy PD controllers

Abstract

This paper deals with simplest fuzzy PD controllers which employ only two fuzzy sets on the universe of discourse of each input variable, and three fuzzy sets on the universe of discourse of output variable. First, analytical structures of the simplest fuzzy PD controllers are derived via triangular membership functions for fuzzification, intersection T-norm, Lukasiewicz OR and Zadeh (1965) OR T-conorms, Mamdani's minimum, Larsen's product and drastic product inference methods, and center of area method for defuzzification. Properties of such fuzzy PD controllers are investigated. Based on these properties a comparative study is made on fuzzy controllers derived, and also on the fuzzy controllers and their counterpart-conventional linear PD controller. Finally, sufficient conditions for bounded-input bounded-output stability of fuzzy PD control systems are established using the well known small gain theorem.

Derivation and stability analysis of the analytical structures of the interval type-2 fuzzy PID controller

“…The nature of this issue is the same as when deriving the analytical structure of the T1-FLCs whose fuzzy rules involve the Zadeh AND operator [29,30]. We consider the case, when E * (k) is inside [− L 1 − P 1 , L 1 + P 1 ], and V * (k) is inside [− L 2 − P 2 , L 2 + P 2 ] for brevity.…”

“…As shown in Eqs. (25), (29) and (33), the IT2F-PID is a nonlinear PID type controller because its structure is the same as the discrete form of the linear PID controller. The controller gains are composed of the IT2F-PID parameters G e1 , G v1 , G e2 , G v2 , G u and G u .…”

“…The mathematical relationship between inputs and outputs may assist the research community to understand the configurations of the fuzzy controllers. For the type-1 fuzzy logic controllers (T1-FLCs), the analytical structures of the T1F-PD controller [29] and the T1F-PI controller [30] have been performed and proved to be equivalent to nonlinear PD and PI controllers with variable gains. The analytical structure derivation depends on the configuration of the fuzzy controller, particularly, which kind of the fuzzy AND operator is used.…”

A Novel Design of Fuzzy PID Controllers for Dual-Sensor Cardiac Pacemaker Systems

“…In addition to the above, the fuzzy PID pacing rate is then defuzzified using the standard center of area (COA) method [37] yielding the subsequent pacing rate provided by the pacemaker and applied on the heart corresponding to the current actual heart rate.…”

Heart Rate Control During Treadmill Exercise

“…It has been shown that a fuzzy controller can be very effective for controlling a system of unknown structure and nonlinear behavior [4] [5] . In this paper, both conventional PID and fuzzy PI [6] control algorithm have been applied for controller design. Fuzzy PI control resulted in better control performance.…”