Control of Linear Second-Order Systems by Fuzzy Logic-Based Algorithm

Abstract

The control of e exible structures employing the passivity approach has been extended to systems having noncollocated input/output pairs by introducing an observer that incorporates the nominal dynamical model of the plant. The passive observer-based control is applied to the American Control Conference benchmark problem, whereby, the control force emulates a dynamic vibration absorber attached to a virtual wall with passive control elements (spring, mass, and dashpot ). The springs and mass elements of the controller are constant, whereas the damping coefe cients are selected as time dependent in an attempt to choose continuously the most appropriate amount of damping in compliance with the design goals. A novel approach is introduced, whereby the passive observer-based control law is modie ed by varying the damping coefe cient of the virtual dashpot by means of an adaptive fuzzy logic algorithm. This modie ed system exhibits quick settling times and desirable performance characteristics. Results from the statistical robustness analysis for the developed controller are compared to 10 other(linear)solutionsofthebenchmarkproblem.Thecomparisonisbasedonrobuststability,robustperformance (settling time ), and control effort. The results obtained by the adaptive fuzzy logic algorithm are superior to those obtained by all other methods, and, consequently, further application of the fuzzy algorithm is advocated.