第二章ech22015.ppt

Example x2 = a12 x1 + a32 x3 x3 = a23 x2 + a43 x4 x4 = a24 x2 + a34 x3 + a44 x4 x5 = a25 x2 + a45 x4 把内部变量结构和相互关系描述的 一清二楚 G1(s) G2(s) G1 G2 G 2 G1 G1 G2 G1 G2 G1 G2 G1 G2 * 课堂练习：化简下面结构图 G1 G2 G3 G4 Y(s) G6 - G5 G7 - R(s) - A * A点后移 G1 G2 G3 G4 Y(s) G6 - G5 G7 - R(s) - A 1/G4 G1 G2 G3 G4 Y(s) G6 - G5 G7 - R(s) - A * Y(s) G1 G2 G3G4 1+G3G4G5 G6/G4 - G7 - R(s) Y(s) G1 G2G3G4 1+G3G4G5 1+ G6G3G4G2 G4(1+G3G4G5) - G7 Y(s) R(s) 反馈公式 反馈公式 反馈公式 Y(s) G1 G2 G3G4 G6/G4 - G5 - G7 - R(s) * * 2-5 Signal-flow graph (信号流图) * Signal-Flow Graph Models Signal-flow graph: A diagram that consists of nodes connected by several directed branches and that is a graphical representation of a set of linear relations. Nodes: The input and output points or junctions branch * 信号流图 信号流图是线性代数方程组的一种图形表达。 设:一组线性方程式如下： 信流图的表示形式 a43 a44 x1 a12 x2 x3 x4 x5 a23 a34 a45 a24 a25 a32 * ZPK TF sys = zpk（z，p, k） [z, p,k] = tfdata (sys) Conversion of the types of TF [z, p, k] = tf2zp(num, den) * How poles and zeros relate to system response Why we strive to obtain mathematical models? Why control engineers prefer to use TF model? How to use TF model to analyze and design control systems? we start from the relationship between the locations of zeros and poles of TF and the output responses of a system * -a j i 0 Q: Where is the zero? 0 Position of poles and zeros Transfer function Time-domain impulse response * -a j i b 0 0 Position of poles and zeros Transfer function Time-domain impulse response * j i b 0 0 Position of poles and zeros Transfer function Time-domain impulse response * -a j i 0 Transfer function Time-domain impulse response Position of poles and zeros * TF： -a j i b 0 0 Time-domain impulse response Position of poles and zeros * A summary of pole position and system dynamic response * Transfer function of typical components－1 元件 微分方程 传递函数 * Example：RC circuit Ta