Wu Jun, Hu Xie-he, Chen Sheng, Chu Jian
National Key Laboratory of Industrial Control Technology, Institute of Advanced Process Control, Zhejiang University, Hangzhou 310027, China.
J Zhejiang Univ Sci. 2003 Nov-Dec;4(6):651-7. doi: 10.1631/jzus.2003.0651.
The closed-loop stability issue of finite-precision realizations was investigated for digital controllers implemented in block-floating-point format. The controller coefficient perturbation was analyzed resulting from using finite word length (FWL) block-floating-point representation scheme. A block-floating-point FWL closed-loop stability measure was derived which considers both the dynamic range and precision. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable block-floating-point FWL closed-loop stability measure was then introduced and the method of computing the value of this measure for a given controller realization was developed. The optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach was adopted to solve the resulting optimal realization problem. A numerical example was used to illustrate the design procedure and to compare the optimal controller realization with the initial realization.
针对以块浮点格式实现的数字控制器，研究了有限精度实现的闭环稳定性问题。分析了使用有限字长（FWL）块浮点表示方案导致的控制器系数扰动。推导了一种考虑动态范围和精度的块浮点FWL闭环稳定性度量。为便于设计最优有限精度控制器实现，随后引入了一种计算上易于处理的块浮点FWL闭环稳定性度量，并开发了针对给定控制器实现计算该度量值的方法。最优控制器实现被定义为使相应度量最大化的解，并采用数值优化方法来解决由此产生的最优实现问题。通过一个数值例子来说明设计过程，并将最优控制器实现与初始实现进行比较。
