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证明了在相同指标要求下δ离散域的反馈控制应完全等同于 Z 域的反馈控制,导出了δ域二次型最优解;证明了在相同加权下当采样周期 T→0时,δ域的最优增益趋近于连续域最优解,从而可以通过解连续域的 Riccati 方程直接得到离散控制律,δ域的闭环特性比 Z 域更接近连续域的闭环特性.并对几种方法进行了比较研究,验证了上述结论.
It is proved that the feedback control of δ-discrete domain under the same index requirement should be completely equivalent to the feedback control of Z-domain, and the quadratic optimal solution of δ-domain is derived. It is proved that when the sampling period T → 0 under the same weighting, The optimal gain approaches to the optimal solution of the continuous domain, so that the discrete control law can be directly obtained by solving the Riccati equation of the continuous domain. The closed-loop characteristics of the δ-domain are closer to the closed-loop characteristics of the continuous domain than the Z domain. A comparative study verified the above conclusion.