자동제어 Feedback Control of Dynamic Systems 4E Franklin 대학교재솔루션 등록

자동제어 Feedback Control of Dynamic Systems 4E Franklin 대학교재솔루션 등록

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자동제어 Feedback Control of Dynamic Systems 4E Franklin 대학교재솔루션

자동제어 Feedback Control of Dynamic Systems_4E_Franklin 솔루션

Chapter 2

Dynamic Models
Problems and Solutions for Section 2.1

1. Write the di?erential equations for the mechanical systems shown in Fig. 2.38. Solution: The key is to draw the Free Body Diagram (FBD) in order to keep the signs right. For (a), to identify the direction of the spring forces on the object, let x2 = 0 and Þxed and increase x1 from 0. Then the k1 spring will be stretched producing its spring force to the left and the k2 spring will be compressed producing its spring force to the left also. You can use the same technique on the damper forces and the other mass.

(a) m1 x1 ¨ m2 x2 ¨ = ?k1 x1 ? b1 x1 ? k2 (x1 ? x2 ) u = ?k2 (x2 ? x1 ) ? k3 (x2 ? y) ? b2 x2 u 11

12

CHAPTER 2. DYNAMIC MODELS

Figure 2.38: Mechanical systems

13

m1 x1 ¨ m2 x2 ¨

= ?k1 x1 ? k2 (x1 ? x2 ) ? b1 x1 u = ?k2 (x2 ? x1 ) ? k3 x2

m1 x1 ¨ m2 x2 ¨

= ?k1 x1 ? k2 (x1 ? x2 ) ? b1 (x1 ? x2 ) u u = F ? k2 (x2 ? x1 ) ? b1 (x2 ? x1 ) u u

2. Write the equations of motion o

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