Cross-coupling control (CCC), which acts on contour error, is intended to improve contouring precision of multiaxis servosystems. The contour error estimate (CEE) significantly affects contouring ...precision. Conventional CEE methods rely on static single-point techniques to reconstruct contour error using current position error and an estimate of the reference map at the lead point. The performance of such static CEE methods deteriorates dramatically with increasing contour feedrate and at sharp corners. Hence, a dynamic CEE algorithm based on the Newton update algorithm is proposed to achieve high-precision CEE. Since the convergence rate of the Newton algorithm is user assignable and independent of the reference contour, the proposed CEE stays almost identical to the contour error for vastly different feedrates or sharp corners. Multiaxis cross-coupling adds more design steps for the position control loops. Therefore, in this paper, feedback signals are modified such that a separate cross-coupling controller is no longer needed. It has been shown, analytically and experimentally, that the modified feedback in combination with integral sliding mode control provides simpler design and fewer steps in comparison to conventional CCC designs. Moreover, the proposed CEE and the concept of modified feedback together result in reduced contour error. Various experiments are reported to show the effectiveness of the proposed algorithm at high feedrates and for sharp corners.
Component swapping modularity (CSM) refers to distributed modular control design in networks of swappable smart components. CSM reduces control design effort and complexity in platform-based systems. ...Existing CSM methods achieve promising results for low order multi-input-multi-output systems. However, the lack of generalization, heavy computational burden, and to a lower extent, designer's involvement limit the applications of the existing CSM methods. Thus, this brief utilizes linear matrix inequalities (LMIs) to present an almost automatic CSM algorithm which converges rapidly and is easy to generalize to 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 <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_{2} </tex-math></inline-formula> optimization and robust <inline-formula> <tex-math notation="LaTeX">\mathcal {H}_\infty </tex-math></inline-formula> optimization to obtain a distributed control composed of parts with prescribed orders and partially tunable parameters. The designer's involvement is dramatically reduced to the iterative tuning of two scalar parameters to optimize the fixed part of the controller. 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 example.
Time-delay systems Yi, Sun; Yi, Sun; Nelson, Patrick W ...
2010., 2010, 2010-06-25
eBook
This book comprehensively presents a recently developed novel methodology for analysis and control of time-delay systems. Time-delays frequently occurs in engineering and science. Such time-delays ...can cause problems (e.g. instability) and limit the achievable performance of control systems.
Prior works use numerical simulations to verify component swapping modularity (CSM) for various systems. Moreover, current CSM algorithms do not investigate control parameter allocation for a ...realistic control configuration when the control consists of multiple parts. Thus, this work primarily focuses on presenting and experimentally validating an empirical methodology to allocate and calibrate various parts of the controller to improve CSM in a precision multiaxis servo-system. As a secondary contribution, the concept of the modified reference contour is introduced to simplify control allocation and to improve the modularity of the cross-coupling control (CCC), which is utilized to achieve high-precision contouring. First, the unified linear CCC algorithm is presented for multiaxis servo-systems. Initially, the sensitivity of the contouring algorithm versus the control parameters is studied numerically. Then, empirical calibration and sensitivity analysis are conducted to obtain the optimal set of control parameters. Hence, the lowest feasible contour error is obtained for possible configurations of the servo-system. It is shown that the results of the empirical analysis are consistent with those of the numerical analysis. Despite dramatic differences between the servo-system variants, experimental results show that full CSM is achieved with the same controller for the variants of the servo-system.
The estimation of the decay function (i.e.,
Ke
α
t
Φ
; see equation (2)) for time delay systems has been a long-standing problem. Most existing methods focus on dominant decay rate (i.e., α) ...estimation, i.e., the estimation of the rightmost eigenvalue. Although some frequency domain approaches, such as bifurcation or finite dimensional approximation approaches are able to approximate the optimal decay rate computationally, the estimation of the factor, K, requires knowledge of the system trajectory over time and cannot be obtained from the frequency domain alone. The existing time domain approaches, such as matrix measure/norm or Lyapunov approaches, yield conservative estimates of decay rate. Furthermore, the factor K in the Lyapunov approaches is typically not optimized.
A new Lambert W-function-based approach for estimation of the decay function for time delay systems is presented. This new approach is able to provide a closed-form solution for time delay systems in terms of an infinite series. Using this solution form, the optimal decay rate, α, and an estimate of the corresponding factor, K, can be obtained. Less conservative estimates of the decay function can lead to more accurate description of the exponential behavior of time delay systems, and more effective control design based on those results. The method is illustrated with several examples, and results compare favorably with existing methods for decay function estimation.
Reconfigurable manufacturing systems (RMS) address challenges in modern manufacturing systems arising from product variety and from rapid changes in product demand. This paper considers an arch-type ...reconfigurable machine tool (RMT) that has been built to demonstrate the basic concepts of RMT design. The arch-type RMT was designed to achieve customized flexibility and includes a passive degree-of-freedom, which allows it to be reconfigured to machine a family of parts. The kinematic and dynamic capabilities of the machine are presented, including the experimental frequency response functions (FRFs) and computed stability lobes of the machine in different configurations. A comparison of FRFs and stability lobes of the arch-type RMT reveals almost similar dynamic characteristics at different reconfiguration positions. These similar characteristics arise because the dominant mode where chatter occurs is due to the spindle–tool–tool holder assembly. Consequently, to ensure consistent dynamic behavior regardless of reconfiguration, a desirable dynamic design feature for RMTs is that the machine's structural frequencies are less dominant than the structural frequencies of the spindle, tool and tool holder.
The stability problem for uncertain piecewise affine (PWA) time-delay systems is investigated in this article. It is assumed that there exists a known constant time delay in the system and the ...uncertainly is norm-bounded. Sufficient conditions for the stability of nominal systems and the stability of systems subject to uncertainty are derived using the Lyapunov-Krasovskii functional with a triple integration term. This approach handles switching based on the delayed states (in addition to the states) for a PWA time-delay system, considers structured as well as unstructured uncertainty and reduces the conservativeness of previous approaches. The effectiveness of the proposed approach is demonstrated by comparing with the existing methods through numerical examples.
During recent decades, controllability and observability of linear time delay systems have been studied, including various definitions and corresponding criteria. However, the lack of an analytical ...solution approach has limited the applicability of the existing theory. Recently, the solution to systems of linear delay differential equations has been derived in the form of an infinite series of modes written in terms of the matrix Lambert W function. The solution form enables one to put the results for point-wise controllability and observability of systems of delay differential equations to practical use. We derive the criteria for point-wise controllability and observability, obtain the analytical expressions for their Gramians in terms of the parameters of the system, and develop a method to approximate them for the first time using the matrix Lambert W function-based solution form.
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