09-10Chapter 6_6 Performance characteristics(2)

09-10Chapter 6_6 Performance characteristics(2) -...

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Performance characteristics-part 2 Principle of Automatic Control CHAPTER 6 oot Locus(P200 Ch 7) By Hui Hui Wang Wang Root Locus(P.200, Ch.7) 浙江大学控制科学与工程学系
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Performance characteristics-part 2 Outline of Chapter 6 troduction 9 Introduction 9 Basic Concepts of Root Locus Method 9 Geometrical Properties (Construction Rules) 9 Generalized Root Locus erformance characteristics art 1 9 Performance characteristics-part 1 9 Performance characteristics-part 2 9 ……… 2
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Performance characteristics 1. General Introduction 2 Plot f haracteristic r ots f r < <1 . o o cc e s c oo s o 0 ζ 3. Variation of Roots with ζ >=0 4. Higher-Order Systems 5. Synthesis 6. Additional Poles and Zeros 7. Controller Synthesis 理安寺 控制科学与工程学系
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Performance characteristics-part 2 OOT LOCUS ROOT LOCUS Performance characteristics 5. Synthesis (See P240-243) 问题: (1)如果由根轨迹不能得到满意的响应? (2)如何提高控制系统的性能? 为了提高系统性能而进行的系统校正 (modifying) 或根轨迹改 (reshape) 称为“补偿 (compensation)” 补偿的目的是使系统稳定,具有满意的动态响应,以及有足 够大的增益保证稳态误差不超过某个给定的最大值。 补偿器的位置参见 P320 ,图 10.1 4
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Performance characteristics-part 2 OOT LOCUS ROOT LOCUS Performance characteristics 5. Synthesis (See P240-243) 5
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Performance characteristics-part 2 OOT LOCUS onsider e stem hich ntains ominant mplex oles nd n ROOT LOCUS Performance characteristics 6.1 Additional poles (See 10.3) Consider the system which contains dominant complex poles and an additional real pole p 3 , as Fig., the close-loop transfer function is C(t) ) )( 2 ( ) ( ) ( 3 2 2 p s s s K s R s C n n + + = ω ζω σ j ω p 1 p 3 3 2 p K n = t p 2 ith nit ep put e me sponse With a unit step input the time response is ( ) t p n t n e A t e A t c 3 3 2 1 1 sin 2 1 ) ( + + + = φ ζ (10.17) 0 2 ) 2 ( 3 2 2 2 3 2 2 3 2 3 < + + = + + = = = p s n n n p s n n n s s s s s p A 6
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Performance characteristics-part 2 OOT LOCUS ROOT LOCUS Performance characteristics 6.1 Additional poles (See 10.3) j ω C(t) C(t) The time response isas following ( ) t p n t n e A t e A t c 3 3 2 1 1 sin 2 1 ) ( + + + = φ ζ ω ζω σ p 1 p p σ j ω p 1 p 3 t 2 3 t p 2 ¾ As thepole p 3 moves to the right , the magnitudeof A 3 increases and the overshoot becomes smaller . ¾ As p approaches but is still to the left of the complex poles, the first 3 maximum in the time response is less than the final value. The largest overshoot can occur at the second or a later maximum 7
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Performance characteristics-part 2 OOT LOCUS ROOT LOCUS Performance characteristics 6.1 Additional poles (See 10.3) j ω C(t) p 1 p 3 j ω C(t) p 1 p 3 σ t p 2 σ t p 2 When p 3 is located at the real-axis projection of the complex poles, the r sponse i monotonic( i here i no vershoot This r presents espo se s oo t o c ( 单调) ; .e., tee s o ove s oot. s ep ese ts the critically ( 临界) damped situation, the complex poles may contribute a “ripple ”( 波纹)
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This note was uploaded on 12/01/2011 for the course EE 400 taught by Professor Hui during the Spring '11 term at Zhejiang University.

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09-10Chapter 6_6 Performance characteristics(2) -...

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