基于模糊PID控制的电阻炉炉温系统的研究.docx

1、基于模糊PID控制的电阻炉炉温系统的研究北京联合大学毕业设计外文原文及译文题目： 基于模糊PID控制的电阻炉炉温系统的研究 专业： 电气工程与自动化 指导教师： 张兆莉 学院： 自动化学院 学号： 24 班级： 0710031104 姓名： 杨京伟 一、外文原文Stability of Linear Control Systems1.1 INTRODUCTIONFrom the studies of linear differential equations with constant coefficients of SISO systems, we learned that the homo

2、geneous solution that corresponds to the transient response of the system is governed by the roots of the characteristic equation. Basically, the design of linear control systems may be regarded as a problem of arranging the location of the poles and zeros of the system transfer function such that t

3、he system well perform according to the prescribed specifications. Among the many forms of performance specifications used in design, the most important requirement is that the system must be stable. An unstable system is generally considered to be useless.When all types of systems are considered-li

4、near, nonlinear, time-invariant, and time-varying-the definition of stability can be given in many different forms. We shall deal only with the stability of linear SISO time-invariant systems in the following discussions.For analysis and design purposes, we can classify stability as absolute stabili

5、ty and relative stability. Absolute stability refers to the condition whether the system is stable or unstable; it is a yes or no answer. Once the system is found to be stable, it is of interest to determine how stable it is, and this degree of stability is a measure of relative stability.In prepara

6、tion for the definition of stability, we define the two following types of responses for linear time-invariant systems:1.Zero-state response. The zero-state response is due to the input only; all the initial conditions of the system are zero. 2.Zero-input response. The zero-input response is due to

7、the initial conditions only; all the inputs are zero.From the principle of superposition, when a system is subject to both inputs and initial conditions, the total response is writtenTotal response=zero-state response + zero-input responseThe definitions just given apply to continuous-data as well a

8、s discrete-data systems.1.2 BOUNDED-INPUT, BOUNDED-OUTPUT (BIBO), STABILITY-CONTINUOUS-DATA SYSTEMSLet u(t), y(t), and g(t) be the input, output, and the impulse response of a linear time-invariant system, respectively. With zero initial conditions, the system is said to be BIBO (bounded-input bound

9、ed-output) stable, or simply stable, if its output y(t) is bounded to a bounded input u(t).The convolution integral relating u(t), y(t), and g(t) isy(t)= 0u(t-)g()d (1-1)Taking the absolute value of both sides of the equation, we gety(t)=0u(t-)g()d (1-2)ory(t)0u(t-) g() d (1-3)If u(t) is bounded,u(t

10、)M (1-4)where M is a finite positive number. Then,y(t)M0g()d (1-5)Thus, if y(t) is to be bounded, ory(t)N (1-6)where N is a finite positive number, the following condition must hold:M0g()dN (1-7)Or for any finite positive Q,0g()dQ (1-8)The condition given in Eq.(6-8) implies that the area under the

11、g()-versus-curve mustbe finite.1.2.1 Relationship between Characteristic Equation Roots and StabilityTo show the relation between the roots of the characteristic equation and the condition in Eq. (6-8) we write the transfer function G(s), according to the Laplace transform definition, as G(s)=g()= 0

12、g()e-stdt (1-9)Taking the absolute value on both sides of the last equation, we haveG(s)=0g(t)e-stdt0g(t)e-stdt (1-10)Since e-st=e-t, where is the real part of s. When s assumes a value of a pole of G(s), G(s)=, Eq. (1-10) becomes0g(t)e-tdt (1-11)If one or more roots of the characteristic equation a

13、re in the right-half s-plane or on the j-axis, 0, thene-tM=1 (1-12)Equation (1-11) becomes0Mg(t)dt=0g(t)dt (1-13)which violates the BIBO stability requirement. Thus, for BIBO stability, the roots of the characteristic equation, or the poles of G(s), cannot be located in the right-half s-plane or on

14、the j-axis, in other words, they must all lie in the left-half s-plane. A system is said to be unstable if it is not BIBO stable. When a system has roots on the j-axis, say, at s= j0 and s=- j0, if the input is a sinusoid, sin0t, which is unbounded, and the system is unstable.1.3 ZERO-INPUT AND ASYM

15、PTOTIC STABILITY OF CONTINUOUS-DATA SYSTEMSIn this section we shall define zero-input stability and asymptotic stability, and establish their relations with BIBO stability.Zero-input stability refers to the stability condition when the input is zero, and the system is driven only by its initial conditions. We shall show that the zero-input stability also depends on the roots of the characteristic equation.Let the input of an nth-order system be zero, and the output due to the initial conditions be y(t). Then, y(t) can be expressed as (1-14)Where