The rotating disk has many engineering applications as in floppy, hard, compact, laser, and recently optical disk drives. This paper (Part II) considers the application of a finite element method ...presented in a companion paper (Part I) to the analysis of rotating disks. The critical speed of the disk is obtained to validate the problem formulation and solution method. Dynamic responses are obtained as parameterized by the rotating speed. Effects of the temperature distribution and material system are also observed. Thermal effects are crucial in the analysis of rotating disks, since the variation of temperature can be significant. This is especially true for equipment in which a heat source is used as a means of recording or erasing data and for equipment in which the amount of generated or transferred heat is significant. The specially orthotropic material properties of a laminated disk can have a large effect on the overall dynamic behavior.
The Frobenius norm of the lifted system representation of tracking error dynamics is proposed as a metric for evaluating the tracking performance of discrete-time linear time invariant (LTI) and ...linear time varying (LTV) controllers. The proposed metric is introduced here in the context of feedforward tracking control of LTI single-input single-output (SISO) nonminimum phase (NMP) systems, though it is more broadly applicable. It is shown that the filtered basis functions (FBF) approach, an LTV tracking control technique studied by the authors in prior work, is the optimal solution to the rank constrained minimization of the proposed metric. Moreover, for the FBF controller, the metric is independent of plant dynamics, which is not the case for most other tracking controllers; it is also independent of the type of basis functions employed in the FBF controller. The effectiveness of the proposed metric as a tracking performance evaluation tool for both LTI and LTV tracking controllers is demonstrated analytically and numerically on LTI plants with different zero locations.
Precision displacement measurement is a critical element to achieve active control for high-precision (e.g. 5 μm) flexible line boring. Since current measurement methods are difficult to apply in ...this application, a new measurement method has been developed. This paper presents a new strain-gauge-based method for the high-precision vibration measurement of a beam. This method is based on the fact that the vibration displacement can be expressed in terms of an infinite number of vibration modes and be related to the measured strains through the strain–displacement relationship. By placing multiple sets of strain gauges, multiple modes can be taken into account to achieve high-precision measurement. Both simulation and experimental results were obtained and are provided for validation. From these results, it can be concluded that this new measurement method is applicable to high-precision flexible line boring, enabling active control to compensate for the tool-tip displacement to achieve a high-precision machining process.
This paper presents an optimal policy, based on Markov decision theory for the capacity management problem in a firm facing stochastic market demand. The firm implements a reconfigurable ...manufacturing system and faces a delay between the times capacity changes are ordered and the times they are delivered. Optimal policies are presented as optimal boundaries representing the optimal capacity Expansion and reduction levels. TO increase the robustness of the optimal policy to unexpected events, the concept of feedback control is applied to address the capacity management problem. It is shown that feedback provides sub-optimal solutions to the capacity management problem which are more robust under unexpected disturbances in market demand and unexpected events.
Design for component swapping modularity (CSM) is experimentally verified for a precision contouring algorithm. Prior work focuses on developing CSM algorithms for various systems and verifying the ...results using numerical simulations 1, 3, 8. This work uses empirical and analytical methods to support the effectiveness of CSM in precision distributed manufacturing systems. The concept of a modified reference contour is introduced, which provides a fully modular cross-coupling control (CCC), to facilitate CSM design. First, the unified linear CCC algorithm with proven stability is presented for multi-axis servo-systems. Then, an empirical calibration and sensitivity analysis is conducted such that the optimal control configuration, which achieves the lowest feasible contour error, is obtained for all possible configurations of the servo-system. Despite dramatic differences between the servo-system variants, it is shown experimentally that full CSM is achieved with the same controller for all the variants of the servo-system.
The problem of component swapping modularity (CSM) refers to distributed control design in networks of smart components such that specific design constraints are satisfied. The CSM intends to reduce ...control design effort and complexity in platform-based systems. Existing CSM methods achieve promising results for low order multi-input-multi-output (MIMO) systems. However, lack of generalization, heavy computational burden, and, to a lower extent, the level of designer involvement limit the applications of the existing CSM methods. Thus, this paper presents a generalized CSM algorithm using linear matrix inequalities (LMIs) such that almost full automatic control distribution is achieved for an arbitrary linear system. The LMI-based CSM is designed to maintain both disturbance attenuation and quadratic stability. Also, it is desired to satisfy specific time response criteria. Thus, the proposed algorithm combines H 2 optimization and robust H ∞ optimization to satisfy given design constraints. The designer involvement is dramatically reduced to iterative tuning of two scalar parameters in the robust H ∞ problem. The proposed algorithm incorporates reference tracking. Also, stability measures and design criteria are checked numerically at each step. The LMI-based CSM algorithm has been numerically verified using an engine idle speed control (ISC) example.
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