Optimal Selection of Basis Functions for Minimum-Effort Tracking Control of Nonminimum Phase Systems Using Filtered Basis Functions
Optimal Selection of Basis Functions for Minimum-Effort Tracking Control of Nonminimum Phase Systems Using Filtered Basis Functions
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DOI：
10.1115/1.4044355
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
Keval S. Ramani;Molong Duan;C. Okwudire;A. Galip Ulsoy
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文献类型：
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作者：
Keval S. Ramani;Molong Duan;C. Okwudire;A. Galip Ulsoy
非最小相位（NMP）系统的精确跟踪是众所周知的，需要大量的控制工作。因此，最小化实现NMP系统的期望水平的跟踪精度所需的努力具有实用价值。有越来越多的兴趣在使用的滤波基函数（FBF）方法跟踪控制的线性NMP系统，因为它具有明显的性能优势，比其他方法。FBF方法将控制输入表示为用户定义的基函数的线性组合。通过对象的动态特性对基函数进行前向滤波，并选择系数以使跟踪误差最小化。有各种各样的基函数，可以使用的FBF方法，但一直没有工作到目前为止，如何选择最好的基函数集。为了选择最佳的基函数，Frobenius范数的提升系统表示（LSR）的动态提出了一个很好的度量评估的线性时变（LTV）离散时间跟踪控制器的性能，如FBF，独立于期望的轨迹被跟踪。使用的度量，一组最佳的基函数，最大限度地减少控制的努力，而不牺牲跟踪精度。在仿真和实验中显示，与流行的基函数（如B样条）相比，最佳基函数集显着减少了控制工作，同时保持或提高了跟踪精度。
Accurate tracking of nonminimum phase (NMP) systems is well known to require large amounts of control effort. It is, therefore, of practical value to minimize the effort needed to achieve a desired level of tracking accuracy for NMP systems. There is growing interest in the use of the filtered basis functions (FBF) approach for tracking the control of linear NMP systems because of distinct performance advantages it has over other methods. The FBF approach expresses the control input as a linear combination of user-defined basis functions. The basis functions are forward filtered through the dynamics of the plant, and the coefficients are selected such that the tracking error is minimized. There is a wide variety of basis functions that can be used with the FBF approach, but there has been no work to date on how to select the best set of basis functions. Toward selecting the best basis functions, the Frobenius norm of the lifted system representation (LSR) of dynamics is proposed as an excellent metric for evaluating the performance of linear time varying (LTV) discrete-time tracking controllers, like FBF, independent of the desired trajectory to be tracked. Using the metric, an optimal set of basis functions that minimize the control effort without sacrificing tracking accuracy is proposed. The optimal set of basis functions is shown in simulations and experiments to significantly reduce control effort while maintaining or improving tracking accuracy compared to popular basis functions, like B-splines.