Friction-induced limit cycling deteriorates system performance in a wide variety of mechanical systems. In this paper, we study the way in which essential friction characteristics affect the occurrence and nature of friction-induced limit cycling in an experimental drill-string set-up. This study is performed on the level of a Lyapunov-based stability analysis and on the level of both numerical and experimental bifurcation analyses. The synthesis of these results confirms that friction-induced limit cycling is due to a subtle balance between negative damping at lower velocities and viscous friction at higher velocities. Moreover, it is shown how these essential friction characteristics depend on physical conditions such as temperature and normal forces in the frictional contact in the experimental set-up.

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SUMMARYThis article focuses on the synthesis of computationally friendly sub-optimal nonlinear model predictive control (NMPC) algorithms with guaranteed robust stability. To analyse the robustness of the MPC closed-loop system, we employ the input-to-state stability (ISS) framework. To design ISS sub-optimal NMPC schemes, a new Lyapunov-based method is proposed. ISS is ensured via a set of constraints, which can be specified as a finite number of linear inequalities for input affine nonlinear systems. Furthermore, the method allows for online optimization over the ISS gain of the resulting closed-loop system. The potential of the developed theory for the control of fast nonlinear systems, with sampling periods below 1 ms, is illustrated by applying it to control a Buck-Boost DC-DC converter.

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For bonding silicon carbide optics, which require extreme stability, hydroxide catalysis bonding is considered [Rowan, S., Hough, J. and Elliffe, E., Silicon carbide bonding. UK Patent 040 7953.9, 2004. Please contact Mr. D. Whiteford for further information: D.Whiteford@admin.gla.ac.uk]. This technique is already used for bonding silicate-based materials, like fused silica and Zerodur. In application with silicon carbide, the technique is highly experimental and the aim is to test the strength of the bond with silicon carbide. The silicon carbide is polished to λ/10 PV flatness and then oxidized at 1100 • C in a wet environment prior to bonding to form a necessary layer of SiO 2 on the surface. The bonding is performed in clean room conditions. After bonding the pieces are sawed into bars to determine the strength in a four-point bending experiment. The oxidization process shows many different color changes indicating thickness variations and contamination of the oxidization process. The bonding has been performed with success. However, these bonds are not resistant against aqueous cooling fluids, which are used during sawing. Several bars have survived the sawing and a maximum strength of 30 N mm −2 has been measured.

A method is described for the synchronization of nonlinear discrete-time dynamics. The methodology consists of constructing observer–receiver dynamics that exploit at each time instant the drive signal and buffered past values of the drive signal. In this way, the method can be viewed as a dynamic reconstruction mechanism, in contrast to existing static inversion methods from the theory of dynamical systems. The method is illustrated on a few simulation examples consisting of coupled chaotic logistic equations. Also, a discrete-time message reconstruction scheme is simulated using the extended observer mechanism.

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The paper deals with the problem of robust synchronization of dynamical systems. The design procedure is based on the concept of observers with absolutely stable error dynamics. In the general case of nonlinear time-varying error dynamics the procedure requires exact knowledge of a Lyapunov function while in case of the linearizable error dynamics frequency domain conditions which ensure existence of such a function can be employed. Two examples are considered: synchronization of two Lorenz systems and Rössler systems.