现代控制系统chapter 3.ppt

P4.7 Solution: Let The closed loop transfer function 《自动控制原理》 第三章 控制系统的时域分析 AP4.1 A tank level regulator control is shown in Figure AP4.1(a). It is desired to regulate the level, h, in response to a disturbance change, q3. The block diagram shows small variable changes about the equilibrium conditions so that the desired hd(t) = 0. Determine the equation for the error E(s), and determine the steady-state error for a unit step disturbance when (a) G(s)=K and (b) G(s)=K/s. P235 FIGURE AP4.1 A tank level regulator. AP4.1 Solution: P236 AP4.4(a) An armature-controlled DC motor with tachometer feedback is shown in Figure AP4.4. Assume that Km = 10, J = 1, and Ra = 1. (a) Determine the required gain, K, to restrict the steady-state error to a ramp input (v(t) = t for t 0) to 0.1(assume that D(s) = 0). FIGURE AP4.4 DC motor with feedback. P236 AP4.4(a) Solution: The closed-loop transfer function is With v(t)=t, we have V(s)=1/s2. Using the final value theorem yields We desire that ess=1/10K0.1. P295 E5.2(a) The engine, body, and tires of a racing vehicle affect the acceleration and speed attainable. The speed control of the car is represented by the model shown in Figure E5.2. (a) Calculate the steady-state error of the car to a step command in speed. FIGURE E5.2 Racing car speed control. P295 E5.2(a) P297 E5.10 A system with unity feedback is shown in Figure E5.10. Determine the steady-state error for a step and a ramp input when FIGURE E5.10 Unity feedback system. P297 E5.10 Solution: P298 E5.13 A feedback system is shown in Figure E5.13. Determine the steady-state error for a unit step when K = 0.4 and Gp(s） = 1. Select an appropriate value for Gp(s) so that the steady-state error is equal to zero for the unit step input. FIGURE E5.13 Feedback system. P298 E5.13 Solution: P299 P5.3 FIGURE P5.3 Laser beam control. A laser beam can be used to weld, drill, etch, cut, and mark metals, as shown in Figure P5.3(a). Assume we have a work requirement for an a