西安理工大学自动控制理论双语课件chap-.ppt

西安理工大学自西安理工大学自动控制理控制理论双双语课件件chap Chapter 2 mathematical models of systems2.2.1 Examples2.1.4 types 1)Differential equations 2)Transfer function 3)Block diagram、signal flow graph 4)State variables2.2 The input-output description of the physical systems differential equations The input-output descriptiondescription of the mathematical relationship between the output variable and the input variable of physical systems.Chapter 2 mathematical models of systems define:input ur output uc。we have：Example 2.1:A passive circuit Chapter 2 mathematical models of systemsExample 2.2:A mechanismDefine:input F，output y.We have:Compare with example 2.1:ucy,urF-analogous systemsChapter 2 mathematical models of systems Example 2.3:An operational amplifier(Op-amp)circuitInput ur output uc(2)(3);(2)(1);(3)(1)：Chapter 2 mathematical models of systems Example 2.4:A DC motorInput ua，output 1(4)(2)(1)and(3)(1):(4)(2)(1)and(3)(1):Chapter 2 mathematical models of systemsMake:Chapter 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 systemsChapter 2 mathematical models of systemsExample 2.5:A DC-Motor control systemInput ur,Output;neglect the friction:Chapter 2 mathematical models of systems（2）（1）（3）（4），），we 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.Chapter 2 mathematical models of systems4)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,P2.7Chapter 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:Chapter 2 mathematical models of systemsExamples:Example 2.6:Elasticity equation Example 2.7:Fluxograph equationQ Flux;p pressure differenceChapter 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:Chapter 2 mathematical models of systemsC(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:Chapter 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:Chapter 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).Chapter 2 mathematical models of systemsExample 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.Chapter 2 mathematical models of systems Example 2.11:For a electric circuit:Chapter 2 mathematical models of systemsExample 2.12:For a op-amp circuitChapter 2 mathematical models of systems5)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 2.5Chapter 2 mathematical models of systems In Example 2.5,we have written down the differential equations as:Make Laplace transformation,we have:(2)(1)(3)(4),we have:Chapter 2 mathematical models of systemsE2.2,E2.6,E2.15,E2.19,E2.20,E2.27,P2.7,P2.8Chapter 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:Chapter 2 mathematical models of systems2.5.2 Integrating elementRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:Integrating circuit,integrating motor,integrating wheelChapter 2 mathematical models of systems2.5.3 Differentiating elementRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:differentiating amplifier,differential valve,differential condenser2.5.4 Inertial elementChapter 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)Chapter 2 mathematical models of systems2.5.5 Oscillating elementRelationship between the input and output variables:Transfer function:Block diagram representation and unit step response:Examples:oscillator,oscillating table,oscillating circuit2.5.6 Delay elementChapter 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.2.6.1 Block diagram representation of the control 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 modelsExample 2.14 Chapter 2 mathematical models of systemsFor the DC motor in Example 2.4 In Example 2.4,we have written down the differential equations as:Make Laplace transformation,we have:Chapter 2 mathematical models of systemsDraw block diagram in terms of the equations(5)(8):Consider the Motor as a whole:1)(12+ffemmeeTsTTTsTTC1)()(12+ffemmemmeTsTTTsTTTsTTJUa(s)(sW)(sM-Chapter 2 mathematical models of systemsExample 2.15The water level control system in Fig 1.8:Chapter 2 mathematical models of systemsThe block diagram model is:Chapter 2 mathematical models of systemsExample 2.16The DC motor control system in Fig 1.9Chapter 2 mathematical models of systemsThe block diagram model is:Chapter 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.pptChapter 2 mathematical models of systems医学资料仅供参考,用药方面谨遵医嘱