西安理工大学自动控制理论双语chap.pptx

会计学1西安理工大学自动控制西安理工大学自动控制(z dn kn zh)理论双语理论双语chap 第一页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems define:input ur output uc。we have：Example 2.1:Example 2.1:A passive circuit A passive circuit 第2页/共38页第二页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsExample 2.2:Example 2.2:A mechanism A mechanismDefine:input F，output y.We have:Compare with example 2.1:ucy,urF-analogous systems第3页/共38页第三页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems Example 2.3:Example 2.3:An operational amplifier(Op-amp)circuit An operational amplifier(Op-amp)circuitInput ur output uc(2)(3);(2)(1);(3)(1)：第4页/共38页第四页，共38页。Chapter 2 mathematical models of Chapter 2 mathematical models of systemssystems Example 2.4:Example 2.4:A DC motor A DC motorInput ua，output 1(4)(2)(1)and(3)(1):(4)(2)(1)and(3)(1):第5页/共38页第五页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsMake:第6页/共38页第六页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems Assume the motor idle:Mf=0,and neglect the friction:f=0,we have:the differential equation description of the DC motor is:Compare with example 2.1 and example 2.2:-Analogous systems第7页/共38页第七页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsExample 2.5:Example 2.5:A DC-Motor control system A DC-Motor control systemInput ur,Output;neglect the friction:第8页/共38页第八页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems（2 2）（1 1）（3 3）（4 4），），），），we havewe have：2.2.2 steps to obtain the input-output description (differential equation)of control systems1)Identify the output and input variables of the control systems.2)Write the differential equations of each systems component in terms of the physical laws of the components.*necessary assumption and neglect.*proper approximation.3)dispel the intermediate(across)variables to get the input-output description which only contains the output and input variables.第9页/共38页第九页，共38页。Chapter 2 mathematical models of Chapter 2 mathematical models of systemssystems4)Formalize the input-output equation to be the“standard”form:Input variable on the right of the input-output equation.Output variable on the left of the input-output equation.Writing the polynomialaccording to the falling-power order.2.2.3 General form of the input-output equation of the linear control systems A nth-order differential equation:Suppose:input r，output yE2.14,P2.2,P2.3,P2.7第10页/共38页第十页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems2.3 Linearization of the nonlinear components2.3.1 what is nonlinearity？The output of system is not linearly vary with the linear variation of the systems (or components)input nonlinear systems(or components).2.3.2 How do the linearization？Suppose:y=f(r)The Taylor series expansion about the operating point r0 is:第11页/共38页第十一页，共38页。Chapter 2 mathematical models of Chapter 2 mathematical models of systemssystemsExamples:Examples:Example 2.6:Elasticity equation Example 2.7:Fluxograph equationQ Flux;p pressure difference第12页/共38页第十二页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems2.4 Transfer function Another form of the input-output(external)description of control systems,different from the differential equations.2.4.1 definition Transfer function:The ratio of the Laplace transform of the output variable to the Laplace transform of the input variable with all initial condition assumed to be zero and for the linear systems,that is:第13页/共38页第十三页，共38页。Chapter 2 mathematical models of Chapter 2 mathematical models of systemssystemsC(s)Laplace transform of the output variable R(s)Laplace transform of the input variable G(s)transfer function*Only for the linear and stationary(constant parameter)systems.*Zero initial conditions.*Dependent on the configuration and coefficients of the systems,independent on the input and output variables.2.4.2 How to obtain the transfer function of a system1)If the impulse response g(t)is knownNotes:第14页/共38页第十四页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems Example 2.8:2)If the output response c(t)and the input r(t)are knownWe have:Because:We have:Then:第15页/共38页第十五页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems Example 2.9:Then:3)If the input-output differential equation is known Assume:zero initial conditions;Make:Laplace transform of the differential equation;Deduce:G(s)=C(s)/R(s).第16页/共38页第十六页，共38页。Chapter 2 mathematical models of Chapter 2 mathematical models of systemssystemsExample 2.10:Example 2.10:4)For a circuit*Transform a circuit into a operator circuit.*Deduce the C(s)/R(s)in terms of the circuits theory.第17页/共38页第十七页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems Example 2.11:Example 2.11:For a electric circuit:For a electric circuit:第18页/共38页第十八页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsExample 2.12:Example 2.12:For a op-amp circuitFor a op-amp circuit第19页/共38页第十九页，共38页。Chapter 2 mathematical models of Chapter 2 mathematical models of systemssystems5)For a control system5)For a control system Write the differential equations of the control system;Make Laplace transformation,assume zero initial conditions,transform the differential equations into the relevant algebraic equations;Deduce:G(s)=C(s)/R(s).Example 2.13the DC-Motor control system in Example 2.5第20页/共38页第二十页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems In In Example 2.5Example 2.5,we have written down the differential equations,we have written down the differential equations as:as:Make Laplace transformation,we have:(2)(1)(3)(4),we have:第21页/共38页第二十一页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsE2.2,E2.6,E2.15,E2.19,E2.20,E2.27,P2.7,P2.8第22页/共38页第二十二页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems2.5.1 Proportioning elementRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:amplifier,gear train,tachometer2.5 Transfer function of the typical elements of linear systems A linear system can be regarded as the composing of several typical elements,which are:第23页/共38页第二十三页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems2.5.2 Integrating element2.5.2 Integrating elementRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:Integrating circuit,integrating motor,integrating wheel第24页/共38页第二十四页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems2.5.3 Differentiating element2.5.3 Differentiating elementRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:differentiating amplifier,differential valve,differential condenser第25页/共38页第二十五页，共38页。2.5.4 Inertial element2.5.4 Inertial elementChapter 2 mathematical models of systemsChapter 2 mathematical models of systemsRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:inertia wheel,inertial load(such as temperature system)第26页/共38页第二十六页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems2.5.5 Oscillating element2.5.5 Oscillating elementRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:oscillator,oscillating table,oscillating circuit第27页/共38页第二十七页，共38页。2.5.6 Delay element2.5.6 Delay elementChapter 2 mathematical models of systemsChapter 2 mathematical models of systemsRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:gap effect of gear mechanism,threshold voltage of transistors第28页/共38页第二十八页，共38页。.2.6.1 Block diagram representation of the control systems2.6.1 Block diagram representation of the control systemsChapter 2 mathematical models of systemsChapter 2 mathematical models of systemsExamples:2.6 block diagram models(dynamic)Portray the control systems by the block diagram models more intuitively than the transfer function or differential equation models第29页/共38页第二十九页，共38页。Example 2.14Example 2.14 Chapter 2 mathematical models of Chapter 2 mathematical models of systemssystemsFor the DC motor in Example 2.4 In Example 2.4,we have written down the differential equations as:Make Laplace transformation,we have:第30页/共38页第三十页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsDraw block diagram in terms of the equations(5)Draw block diagram in terms of the equations(5)(8):(8):Consider the Motor as a whole:1)(12+ffemmeeTsTTTsTTC1)()(12+ffemmemmeTsTTTsTTTsTTJUa(s)(sW)(sM-第31页/共38页第三十一页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsExample 2.15Example 2.15The water level control system in Fig 1.8:第32页/共38页第三十二页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsThe block diagram model is:The block diagram model is:第33页/共38页第三十三页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsExample 2.16Example 2.16The DC motor control system in Fig 1.9第34页/共38页第三十四页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systemsThe block diagram model is:The block diagram model is:第35页/共38页第三十五页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems2.6.2 Block diagram reduction purpose:reduce a complicated block diagram to a simple one.2.6.2.1 Basic forms of the block diagrams of control systemsChapter 2-2.ppt第36页/共38页第三十六页，共38页。Chapter 2 mathematical models of systemsChapter 2 mathematical models of systems第37页/共38页第三十七页，共38页。感谢您的观看感谢您的观看(gunkn)！第38页/共38页第三十八页，共38页。