使用电路定理对RL一阶电路进行建模，并写在S-fun中；并与依据实际模型搭建电路相对比，观察其输出是否一致。
1.一阶RL建模
首先给出LR一阶电路
依据电路原理，可得：
那么就是要求i，也就是电感电流
2.一阶RL写S-fun
输入量是电压，输出量是电感电流。
写入S函数，得到LR模块
function [sys,x0,str,ts,simStateCompliance] = LR(t,x,u,flag)
%SFUNTMPL General MATLAB S-Function Template
% With MATLAB S-functions, you can define you own ordinary differential
% equations (ODEs), discrete system equations, and/or just about
% any type of algorithm to be used within a Simulink block diagram.
%
% The general form of an MATLAB S-function syntax is:
% [SYS,X0,STR,TS,SIMSTATECOMPLIANCE] = SFUNC(T,X,U,FLAG,P1,...,Pn)
%
% What is returned by SFUNC at a given point in time, T, depends on the
% value of the FLAG, the current state vector, X, and the current
% input vector, U.
%
% FLAG RESULT DESCRIPTION
% ----- ------ --------------------------------------------
% 0 [SIZES,X0,STR,TS] Initialization, return system sizes in SYS,
% initial state in X0, state ordering strings
% in STR, and sample times in TS.
% 1 DX Return continuous state derivatives in SYS.
% 2 DS Update discrete states SYS = X(n+1)
% 3 Y Return outputs in SYS.
% 4 TNEXT Return next time hit for variable step sample
% time in SYS.
% 5 Reserved for future (root finding).
% 9 [] Termination, perform any cleanup SYS=[].
%
%
% The state vectors, X and X0 consists of continuous states followed
% by discrete states.
%
% Optional parameters, P1,...,Pn can be provided to the S-function and
% used during any FLAG operation.
%
% When SFUNC is called with FLAG = 0, the following information
% should be returned:
%
% SYS(1) = Number of continuous states.
% SYS(2) = Number of discrete states.
% SYS(3) = Number of outputs.
% SYS(4) = Number of inputs.
% Any of the first four elements in SYS can be specified
% as -1 indicating that they are dynamically sized. The
% actual length for all other flags will be equal to the
% length of the input, U.
% SYS(5) = Reserved for root finding. Must be zero.
% SYS(6) = Direct feedthrough flag (1=yes, 0=no). The s-function
% has direct feedthrough if U is used during the FLAG=3
% call. Setting this to 0 is akin to making a promise that
% U will not be used during FLAG=3. If you break the promise
% then unpredictable results will occur.
% SYS(7) = Number of sample times. This is the number of rows in TS.
%
%
% X0 = Initial state conditions or [] if no states.
%
% STR = State ordering strings which is generally specified as [].
%
% TS = An m-by-2 matrix containing the sample time
% (period, offset) information. Where m = number of sample
% times. The ordering of the sample times must be:
%
% TS = [0 0, : Continuous sample time.
% 0 1, : Continuous, but fixed in minor step
% sample time.
% PERIOD OFFSET, : Discrete sample time where
% PERIOD > 0 & OFFSET < PERIOD.
% -2 0]; : Variable step discrete sample time
% where FLAG=4 is used to get time of
% next hit.
%
% There can be more than one sample time providing
% they are ordered such that they are monotonically
% increasing. Only the needed sample times should be
% specified in TS. When specifying more than one
% sample time, you must check for sample hits explicitly by
% seeing if
% abs(round((T-OFFSET)/PERIOD) - (T-OFFSET)/PERIOD)
% is within a specified tolerance, generally 1e-8. This
% tolerance is dependent upon your model's sampling times
% and simulation time.
%
% You can also specify that the sample time of the S-function
% is inherited from the driving block. For functions which
% change during minor steps, this is done by
% specifying SYS(7) = 1 and TS = [-1 0]. For functions which
% are held during minor steps, this is done by specifying
% SYS(7) = 1 and TS = [-1 1].
%
% SIMSTATECOMPLIANCE = Specifices how to handle this block when saving and
% restoring the complete simulation state of the
% model. The allowed values are: 'DefaultSimState',
% 'HasNoSimState' or 'DisallowSimState'. If this value
% is not speficified, then the block's compliance with
% simState feature is set to 'UknownSimState'.
% Copyright 1990-2010 The MathWorks, Inc.
%
% The following outlines the general structure of an S-function.
%
switch flag,
%%%%%%%%%%%%%%%%%%
% Initialization %
%%%%%%%%%%%%%%%%%%
case 0,
[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;
%%%%%%%%%%%%%%%
% Derivatives %
%%%%%%%%%%%%%%%
case 1,
sys=mdlDerivatives(t,x,u);
%%%%%%%%%%
% Update %
%%%%%%%%%%
case 2,
sys=mdlUpdate(t,x,u);
%%%%%%%%%%%
% Outputs %
%%%%%%%%%%%
case 3,
sys=mdlOutputs(t,x,u);
%%%%%%%%%%%%%%%%%%%%%%%
% GetTimeOfNextVarHit %
%%%%%%%%%%%%%%%%%%%%%%%
case 4,
sys=mdlGetTimeOfNextVarHit(t,x,u);
%%%%%%%%%%%%%
% Terminate %
%%%%%%%%%%%%%
case 9,
sys=mdlTerminate(t,x,u);
%%%%%%%%%%%%%%%%%%%%
% Unexpected flags %
%%%%%%%%%%%%%%%%%%%%
otherwise
DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag));
end
% end sfuntmpl
%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes
%
% call simsizes for a sizes structure, fill it in and convert it to a
% sizes array.
%
% Note that in this example, the values are hard coded. This is not a
% recommended practice as the characteristics of the block are typically
% defined by the S-function parameters.
%
sizes = simsizes;
sizes.NumContStates = 1; %%%%%%表示这个是一阶电路，只有一个状态变量iL
sizes.NumDiscStates = 0;
sizes.NumOutputs = 1; %%%%%%%设计的输出就是iL，这个状态变量
sizes.NumInputs = 1; %%%%%%%电路的输入是一个量，即电压
sizes.DirFeedthrough = 1;
sizes.NumSampleTimes = 1; % at least one sample time is needed
sys = simsizes(sizes);
%
% initialize the initial conditions
%
x0 = [0]; %%%%%%%%%%%%%%通常初始状态设为0
%
% str is always an empty matrix
%
str = [];
%
% initialize the array of sample times
%
ts = [0 0];
% Specify the block simStateCompliance. The allowed values are:
% 'UnknownSimState', < The default setting; warn and assume DefaultSimState
% 'DefaultSimState', < Same sim state as a built-in block
% 'HasNoSimState', < No sim state
% 'DisallowSimState' < Error out when saving or restoring the model sim state
simStateCompliance = 'UnknownSimState';
% end mdlInitializeSizes
%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%主要就是编写这里
function sys=mdlDerivatives(t,x,u)
%三个输入u(1)电压，
iL=x(1);
%电路的三个参数
L=3.99e-5;
C=0.18;
R=5;
%写入微分方程
diL=(1/L)*(u-R*iL)
sys = [diL];%%作为输出
% end mdlDerivatives
%
%=============================================================================
% mdlUpdate
% Handle discrete state updates, sample time hits, and major time step
% requirements.
%=============================================================================
%
function sys=mdlUpdate(t,x,u)
sys = [];
% end mdlUpdate
%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function sys=mdlOutputs(t,x,u)
sys = x;
% end mdlOutputs
%
%=============================================================================
% mdlGetTimeOfNextVarHit
% Return the time of the next hit for this block. Note that the result is
% absolute time. Note that this function is only used when you specify a
% variable discrete-time sample time [-2 0] in the sample time array in
% mdlInitializeSizes.
%=============================================================================
%
function sys=mdlGetTimeOfNextVarHit(t,x,u)
sampleTime = 1; % Example, set the next hit to be one second later.
sys = t + sampleTime;
% end mdlGetTimeOfNextVarHit
%
%=============================================================================
% mdlTerminate
% Perform any end of simulation tasks.
%=============================================================================
%
function sys=mdlTerminate(t,x,u)
sys = [];
% end mdlTerminate
3.一阶RL仿真验证
两者进行对比。
4.二阶RLC建模
得到：
5.二阶RL写S-fun
function [sys,x0,str,ts,simStateCompliance] = RLC(t,x,u,flag)
%SFUNTMPL General MATLAB S-Function Template
% With MATLAB S-functions, you can define you own ordinary differential
% equations (ODEs), discrete system equations, and/or just about
% any type of algorithm to be used within a Simulink block diagram.
%
% The general form of an MATLAB S-function syntax is:
% [SYS,X0,STR,TS,SIMSTATECOMPLIANCE] = SFUNC(T,X,U,FLAG,P1,...,Pn)
%
% What is returned by SFUNC at a given point in time, T, depends on the
% value of the FLAG, the current state vector, X, and the current
% input vector, U.
%
% FLAG RESULT DESCRIPTION
% ----- ------ --------------------------------------------
% 0 [SIZES,X0,STR,TS] Initialization, return system sizes in SYS,
% initial state in X0, state ordering strings
% in STR, and sample times in TS.
% 1 DX Return continuous state derivatives in SYS.
% 2 DS Update discrete states SYS = X(n+1)
% 3 Y Return outputs in SYS.
% 4 TNEXT Return next time hit for variable step sample
% time in SYS.
% 5 Reserved for future (root finding).
% 9 [] Termination, perform any cleanup SYS=[].
%
%
% The state vectors, X and X0 consists of continuous states followed
% by discrete states.
%
% Optional parameters, P1,...,Pn can be provided to the S-function and
% used during any FLAG operation.
%
% When SFUNC is called with FLAG = 0, the following information
% should be returned:
%
% SYS(1) = Number of continuous states.
% SYS(2) = Number of discrete states.
% SYS(3) = Number of outputs.
% SYS(4) = Number of inputs.
% Any of the first four elements in SYS can be specified
% as -1 indicating that they are dynamically sized. The
% actual length for all other flags will be equal to the
% length of the input, U.
% SYS(5) = Reserved for root finding. Must be zero.
% SYS(6) = Direct feedthrough flag (1=yes, 0=no). The s-function
% has direct feedthrough if U is used during the FLAG=3
% call. Setting this to 0 is akin to making a promise that
% U will not be used during FLAG=3. If you break the promise
% then unpredictable results will occur.
% SYS(7) = Number of sample times. This is the number of rows in TS.
%
%
% X0 = Initial state conditions or [] if no states.
%
% STR = State ordering strings which is generally specified as [].
%
% TS = An m-by-2 matrix containing the sample time
% (period, offset) information. Where m = number of sample
% times. The ordering of the sample times must be:
%
% TS = [0 0, : Continuous sample time.
% 0 1, : Continuous, but fixed in minor step
% sample time.
% PERIOD OFFSET, : Discrete sample time where
% PERIOD > 0 & OFFSET < PERIOD.
% -2 0]; : Variable step discrete sample time
% where FLAG=4 is used to get time of
% next hit.
%
% There can be more than one sample time providing
% they are ordered such that they are monotonically
% increasing. Only the needed sample times should be
% specified in TS. When specifying more than one
% sample time, you must check for sample hits explicitly by
% seeing if
% abs(round((T-OFFSET)/PERIOD) - (T-OFFSET)/PERIOD)
% is within a specified tolerance, generally 1e-8. This
% tolerance is dependent upon your model's sampling times
% and simulation time.
%
% You can also specify that the sample time of the S-function
% is inherited from the driving block. For functions which
% change during minor steps, this is done by
% specifying SYS(7) = 1 and TS = [-1 0]. For functions which
% are held during minor steps, this is done by specifying
% SYS(7) = 1 and TS = [-1 1].
%
% SIMSTATECOMPLIANCE = Specifices how to handle this block when saving and
% restoring the complete simulation state of the
% model. The allowed values are: 'DefaultSimState',
% 'HasNoSimState' or 'DisallowSimState'. If this value
% is not speficified, then the block's compliance with
% simState feature is set to 'UknownSimState'.
% Copyright 1990-2010 The MathWorks, Inc.
%
% The following outlines the general structure of an S-function.
%
switch flag,
%%%%%%%%%%%%%%%%%%
% Initialization %
%%%%%%%%%%%%%%%%%%
case 0,
[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes;
%%%%%%%%%%%%%%%
% Derivatives %
%%%%%%%%%%%%%%%
case 1,
sys=mdlDerivatives(t,x,u);
%%%%%%%%%%
% Update %
%%%%%%%%%%
case 2,
sys=mdlUpdate(t,x,u);
%%%%%%%%%%%
% Outputs %
%%%%%%%%%%%
case 3,
sys=mdlOutputs(t,x,u);
%%%%%%%%%%%%%%%%%%%%%%%
% GetTimeOfNextVarHit %
%%%%%%%%%%%%%%%%%%%%%%%
case 4,
sys=mdlGetTimeOfNextVarHit(t,x,u);
%%%%%%%%%%%%%
% Terminate %
%%%%%%%%%%%%%
case 9,
sys=mdlTerminate(t,x,u);
%%%%%%%%%%%%%%%%%%%%
% Unexpected flags %
%%%%%%%%%%%%%%%%%%%%
otherwise
DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag));
end
% end sfuntmpl
%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes
%
% call simsizes for a sizes structure, fill it in and convert it to a
% sizes array.
%
% Note that in this example, the values are hard coded. This is not a
% recommended practice as the characteristics of the block are typically
% defined by the S-function parameters.
%
sizes = simsizes;
sizes.NumContStates = 2;
sizes.NumDiscStates = 0;
sizes.NumOutputs = 1; %输出电容电压
sizes.NumInputs = 1; %电流源
sizes.DirFeedthrough = 1;
sizes.NumSampleTimes = 1; % at least one sample time is needed
sys = simsizes(sizes);
%
% initialize the initial conditions
%
x0 = [0;0];
%
% str is always an empty matrix
%
str = [];
%
% initialize the array of sample times
%
ts = [0 0];
% Specify the block simStateCompliance. The allowed values are:
% 'UnknownSimState', < The default setting; warn and assume DefaultSimState
% 'DefaultSimState', < Same sim state as a built-in block
% 'HasNoSimState', < No sim state
% 'DisallowSimState' < Error out when saving or restoring the model sim state
simStateCompliance = 'UnknownSimState';
% end mdlInitializeSizes
%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%
function sys=mdlDerivatives(t,x,u)
%输入u电流源，
iL=x(1);
Vc=x(2);
L=0.25;
C=0.5;
R=1/3;
%可以在这个下边进行修改L
diL=(1/L)*Vc
dVc=(1/C)*(-iL- Vc/R + u)
sys = [diL;dVc];
% end mdlDerivatives
%
%=============================================================================
% mdlUpdate
% Handle discrete state updates, sample time hits, and major time step
% requirements.
%=============================================================================
%
function sys=mdlUpdate(t,x,u)
sys = [];
% end mdlUpdate
%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function sys=mdlOutputs(t,x,u)
sys = x(2);
% end mdlOutputs
%
%=============================================================================
% mdlGetTimeOfNextVarHit
% Return the time of the next hit for this block. Note that the result is
% absolute time. Note that this function is only used when you specify a
% variable discrete-time sample time [-2 0] in the sample time array in
% mdlInitializeSizes.
%=============================================================================
%
function sys=mdlGetTimeOfNextVarHit(t,x,u)
sampleTime = 1; % Example, set the next hit to be one second later.
sys = t + sampleTime;
% end mdlGetTimeOfNextVarHit
%
%=============================================================================
% mdlTerminate
% Perform any end of simulation tasks.
%=============================================================================
%
function sys=mdlTerminate(t,x,u)
sys = [];
% end mdlTerminate
6.二阶RLC仿真验证
做差：
最后
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