现代控制系统

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,*,*,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,现代控制系统,Solution:,Drawing the Bode Diagram of open-loop system,K=100,-20,-40,-60,0.1 1 10 80 100,K=1,A Compensator is an additional component or circuit that is inserted into a control system to compensate for a deficient performance.,1.Several types of compensation (P 583),Compensator,process,-,(a)Cascade Compensation,process,-,(b)Feedback Compensation,process,Compensator,-,(c)Output or load Compensation,Compensator,(d)Input Compensation,-,10.2 Approaches to System Design,Performance measures,(1)time-domain performance measures,(2)Frequency domain performance measures,10.3 Cascade Compensation Networks,The network may be chosen to have a transfer function,(1)Consider the first order compensator with the transfer function,the network is called a phase-lead network,The compensation network of the form of Equation(10.2)is a differentiator-type network,The pole was negligible,(10.3)has the following frequency characteristic,and a phase angle of+,From Eq.(10.2)is,where,The angle of the frequency characteristic is,The Bode Diagram of formula(10.5)is as follow,let,z,P,0,+,+,-,-,c,The transfer function of this network is,1.phase-lead network,We let,The phase lead compensation,Bode diagram is as above,Maximum phase angle versus for a phase lead network is shown in Fig 10.5 on page P587,z,P,0,10,20,The phase angle readily obtainable from this network is not much greater than,2.The phase-lag network,-,-,C,The transfer function of the phase-lag network is,We have the phase-lag compensation transfer function,The Bode diagram of the phase-lag network is obtained from the transfer function,Notes:phase-lead network aims at promoting the transient performance of control system(stability,swiftness),phase-lag network aims at promoting the steady-state accuracy of system,by means of promoting the system gain K,10.4 Phase-lead design using the Bode Diagram,We determine compensation network by completing the following steps:,(1).According to the requirement of,to determine the open-gain K,(2).Using the open-gain K to calculate the angle-margin,(3).Let ,according to the requirement of to calculate of phase-lead network,Example 1 A control system is as follow,requirements:when r(t)=t,to design the cascade phase-lead network.,-,Solution,(2)Draw the Bode Diagram,20,0,40,-20,0.1 1 10 100,-20dB/dec,-40dB/dec,are all lower than the requirements,so we adopt the phase-lead network,(4)To calculate the angle-margin,Let discuss the physics realization,10.8 Phase-lag design using the Bode diagram,We determine compensation network by completing the following steps:,(1).According to the requirement of,to determine the open-gain K,(2).Using the open-gain K to calculate cut frequency the phase-margin,(3).According to the requirement of phase margin to select the cut frequency of compensated system(Allow for phase lag from the phase-lag network when determining the new crossover frequency ),Note:,is phase margin of the uncompensated system,at frequency,(4).Place the zero of the compensator one decade below the new crossover frequency,(5).Calculate by noting that the attenuation introduced by the phase-lag network is,Example 10.8 Design of a phase-lag network,The open-loop transfer function is:,Requirement:when r(t)=t,Solution,To draw the Bode diagram as follow,20,0,40,-20,0.1 1 1.5 2 10 100,-20dB/dec,-40dB/dec,26,where,The frequency response of the compensated system is:,Check the phase margin:,Example 10.8 The open-loop transfer function of the uncompensated system is:,The open-loop frequency characteristics is:,Requirement:,Drawing the Bode diagram is as follow:,Solution,20,0,40,-20,0.1 1 1.5 10 100,-20dB/dec,-60dB/dec,26,where,we let,The frequency response of the compensated system is:,Check the phase margin:,谢谢大家！,