《自动控制原理胡寿松第7章.ppt

离散系统的z传递函数 线性离散系统的z传递函数的特点： z传递函数的形式与采样开关的个数和位置有关 输出变量处可以设一个虚拟的采样开关 离散拉氏变换可以提到z变换符号之外 4. 若输入信号未经采样就输入到含有零点或极点的环节，则不能求出z传递函数，而只能求出输出的z变换式。 注意：P. 343 表7-3 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. C(s) R(s) - 例3.试求取如图所示线性数字系统的闭环传函 解: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. P.382 7-10 求系统脉冲传递函数 (1)式Z变换： (2)式Z变换： (3)式Z变换： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (6)： (8)代入(4)： (7)代入(9)： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. (5)代入(10)，整理： Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 7.5 稳定性分析 一.s平面与z平面的映射关系 结论：s平面的稳定区域在z平面上的映射是单位圆内部区域 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. H(s) G1(s) G2(s) C(s) R(s) - Y(s) 二.线性离散系统稳定的充要条件 闭环系统特征方程： 2 1 0 ) ( 1 = + z H G G 线性离散系统稳定的充要条件是 脉冲传函的全部极点即系统特征方程的根均位于Z平面的单位圆内,或全部特征根的模小于1 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例1.试分析特征方程为z2-z+0.632=0的系统的稳定性. 解: 系统是稳定的 1 795 . 0 618 . 0 5 . 0 | | | z | 618 . 0 5 . 0 528 . 1 5 . 0 5 . 0 2 632 . 0 4 1 1 z 2 2 2 1 1,2 \ = + = = ± = - ± = x - ± = z j Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 三.Routh稳定判据 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 例2.设闭环采样系统的特征方程为D(z)=45z3-117z2-39=0判断其稳定性. 解: Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. r(t) - T 例3.判断如图所示系统的稳定性,采样周期T=0.2(秒) 解: Evaluation only. Created with Aspose.