Constant-Gain Linear Feedback Control of Piecewise Linear Structural Systems via Nonlinear Normal Modes

Abstract

We present a technique for using constant-gain linear position feedback control to implement eigenstructure assignment of n-degrees-of-freedom conservative structural systems with piecewise linear nonlinearities. We employ three distinct control strategies which utilize methods for approximating the nonlinear normal mode (NNM) frequencies and mode shapes. First, the piecewise modal method (PMM) for approximating NNM frequencies is used to determine n constant actuator gains for eigenvalue (pole) placement. Secondly, eigenvalue placement is accomplished by finding an approximate single-degree-of-freedom reduced model with one actuator gain for the mode to be controlled. The third strategy allows the frequencies and mode shapes (eigenstructure) to be placed by using a full n 1 n matrix of actuator gains and employing the local equivalent linear stiffness method (LELSM) for approximating NNM frequencies and mode shapes. The techniques are applied to a two-degrees-of-freedom system with two distinct types of nonlinearities: a bilinear clearance nonlinearity and a symmetric deadzone nonlinearity.

RETRACTED: A critical review of structural system control by the large-scaled neural network linear-deferential-inclusion-based criterion

“…semi-active static output feedback VSC system is superior to that of the optimally passive damping and maximum damping variety. Butcher and Lu (2004) presented a technique for using constant-gain linear position feedback control with piecewise linear nonlinearities to implement the eigenstructure assignment of n-degrees-of-freedom conservative structural systems. They employed three distinct control strategies which utilize different methods for approximating the nonlinear normal mode (NNM) frequencies and mode shapes.…”

A review of non-linear structural control techniques

“…Single/low-degree-offreedom systems are often used in models for active suspension systems, which has seen a considerable amount of research and Williams [92] gives a review of this area. Linear techniques such as optimal control [93][94][95], pole placement [96], and H-infinity [54] have been modified to be used in active structural control. Non-linear problems have also been considered using techniques such as sliding mode control [97][98][99], Lyapunov control design [73], particle filters [100], and adaptive approaches [101] (discussed in Section 6)see reference [102] for a review of techniques used for active aeroelastic control.…”

Control of a class of nonsmooth dynamical systems

“…For instance, dry friction, impact and backlash in mechanical systems, diode elements in electrical circuits, bangbang controllers which switch discontinuously between maximum and minimum values in optimal control problems. Also, nonsmooth nonlinearities exist in many mechanical systems either by design or as the result of wearing or failure (Butcher and Lu, 2004). It is necessary to know that one of the most common problems in mechanics is nonsmoothness.…”