Matlab 中S-函数的使用 sfuntmpl
function [sys,x0,str,ts,simStateCompliance] = sfuntmpl(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 = 0; sizes.NumDiscStates = 0; sizes.NumOutputs = 0; sizes.NumInputs = 0; sizes.DirFeedthrough = 1; sizes.NumSampleTimes = 1; % at least one sample time is needed sys = simsizes(sizes); % % initialize the initial conditions % x0 = []; % % 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) sys = []; % 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 = []; % 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
S-函数的几个概念:
1） 直接馈通
在编写S-函数时，初始化函数中需要对sizes.DirFeedthrough 进行设置，如果输出函数mdlOutputs或者对于变采样时间的mdlGetTimeOfNextVarHit是输入u的函数，则模块具有直接馈通的特性sizes.DirFeedthrough=1;否则为0。
2） 采样时间
仿真步长就是整个模型的基础采样时间，各个子系统或模块的采样时间，必须以这个步长为整数倍。
连续信号和离散信号对计算机而言其实都是采样而来的，只是采样时间不同，连续信号采样时间可认为趋于0且基于微分方程，离散信号采样时间比较长基于差分方程。离散信号当前状态由前一个时刻的状态决定，连续信号可以通过微分方程计算得到。如果要将连续信号离散化还要考虑下信号能否恢复的问题，即香农定理。
采样时间点的确定：下一个采样时间=（n*采样间隔）+ 偏移量，n表示当前的仿真步，从0开始。
对于连续采样时间，ts可以设置为[0 0]，其中偏移量为0；
对于离散采样时间，ts假设为[0.25 0.1]，表示在S-函数仿真开始后0.1s开始每隔0.25s运行一次，当然每个采样时刻都会调用mdlOutPuts和mdlUpdate函数；
对于变采样时间，即离散采样时间的两次采样时间间隔是可变的，每次仿真步开始时都需要用mdlGetTimeNextVarHit计算下一个采样时间的时刻值。ts可以设置为[-2 0]。
对于多个任务，每个任务都可以以不同的采样速率执行S-函数，假设任务A在仿真开始每隔0.25s执行一次，任务B在仿真后0.1s每隔1s执行一次，那么ts设置为[0.25 0.1;1.0 0.1]，具体到S-函数的执行时间为[0 0.1 0.25 0.5 0.75 1.0 1.1…]。
如果用户想继承被连接模块的采样时间，ts只要设置为[-1 0]。
子函数的作用
(1).mdlInitializeSizes函数-初始化函数
function[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes sizes = simsizes; sizes.NumContStates = 0; %连续状态个数 sizes.NumDiscStates = 0; %离散状态个数 sizes.NumOutputs = 0; %输出个数 sizes.NumInputs = 0; %输入个数 sizes.DirFeedthrough = 1; %是否直接馈通 sizes.NumSampleTimes = 1; %采样时间个数，至少一个 sys = simsizes(sizes); %将size结构传到sys中 x0 = []; %初始状态向量，由传入的参数决定，没有为空 str = []; ts = [0 0]; %设置采样时间，这里是连续采样，偏移量为0 % Specify the blocksimStateCompliance. The allowed values are: % 'UnknownSimState', < The defaultsetting; warn and assume DefaultSimState % 'DefaultSimState', < Same sim state as abuilt-in block % 'HasNoSimState', < No sim state % 'DisallowSimState' < Error out whensaving or restoring the model sim state simStateCompliance = 'UnknownSimState';
(2).mdlGetTimeOfNextVarHit(t,x,u)函数-计算下一个采样时间
functionsys=mdlGetTimeOfNextVarHit(t,x,u) sampleTime = 1; % Example, set the next hit to be one secondlater. sys = t + sampleTime;
(3).mdlOutputs函数-计算S函数输出
functionsys=mdlOutputs(t,x,u) sys = [];
(4).mdlUpdate函数-更新 function sys=mdlUpdate(t,x,u) sys = [];
(5).mdlDerivatives函数-微分函数（计算连续状态导数）
functionsys=mdlDerivatives(t,x,u) sys = [];
(6).mdlTerminate函数-终止仿真 functionsys=mdlTerminate(t,x,u) sys = [];
function [sys,x0,str,ts,simStateCompliance] = sfuntmpl_c(t,x,u,flag) %%%%Simulink中s函数模板的翻译版 %[sys,x0,str,ts,simStateCompliance] = sfuntmpl(t,x,u,flag，p1,…pn) % flag result 描述 % —– —— ——————————————– % 0 [sizes,x0,str,Ts] 初始化，返回SYS的大小，初始状态x0,str,采样时间Ts % 1 DX 返回连续状态微分SYS. % 2 DS 更新离散状态 SYS = X(n+1) % 3 Y 返回输出SYS. % 4 TNEXT Return next time hit for variable step sample time in SYS. % 5 Reserved for future (root finding). % 9 [] 结束 perform any cleanup SYS=[]. % 当flag=0时，以下信息必须赋值回传 % SYS(1) = 连续状态个数 % SYS(2) = 离散状态个数 % SYS(3) = 输出量个数 % SYS(4) = 输入量个数 注：上述4个变量可以赋值为-1，表示其值可变 % SYS(5) = 保留值。为0. % SYS(6) = 直接馈通标志(1=yes, 0=no).如果u在flag=3时被使用，说明S函数是直接馈通，赋值为1. 否则为0. % SYS(7) = 采样时间个数，Ts的行数 % % X0 = 初始状态。没有则赋值为[].除flag=0外，被忽略。 % STR = 系统保留，设为[]. % TS = m*2 矩阵。（采样周期，偏移量） % TS = [0 0, : 连续采样 % 0 1, : 在1个Ts后连续采样 % PERIOD OFFSET, : Discrete sample time where % PERIOD > 0 & OFFSET < PERIOD. % -2 0]; : 变步长离散采样， % flag=4用于决定下一个采样时刻 % 注： % 若希望每个时间步都运行，则设Ts=[0,0] % 若希望继承采样时间运行，则设Ts=[-1,0] % 若希望继承采样时间运行，且希望在微步内不变化，应该设Ts=[-1,1] % 若希望仿真开始0.1s后每隔0.25秒运行，则设Ts=[0.25,0.1] % 若希望按照不同速率执行不同任务，则Ts应按照升序排列。 % 即：每隔0.25秒执行一个任务，同时在开始0.1秒后，每隔1秒执行另一个任务 % Ts=[0.25,0; 1.0,0.1],则simulink将在下列时刻执行s函数[0,0.1,0.25,0.5,0.75,1,1.1,…] % 以下是S函数的主函数 switch flag, case 0, % 初始化 [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes; case 1, % 连续时间导数 sys=mdlDerivatives(t,x,u); case 2, % 更新离散状态量 sys=mdlUpdate(t,x,u); case 3, % 计算输出 sys=mdlOutputs(t,x,u); case 4, % 计算下一步采样时刻 sys=mdlGetTimeOfNextVarHit(t,x,u); case 9, % 结束仿真 sys=mdlTerminate(t,x,u); otherwise % 未知flag值 DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag)); end % S函数主程序结束 %============================================================================= % mdlInitializeSizes % 返回s函数的sizes、初始条件、采样时刻 %============================================================================= function [sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes % 调用simsizes函数为sizes结构赋值 % simsizes函数是S函数模块特有的。它的结构和代码是固定的。 sizes = simsizes; sizes.NumContStates = 0; %连续状态个数 sizes.NumDiscStates = 0; %离散状态个数 sizes.NumOutputs = 0; %输出量个数 sizes.NumInputs = 0; %输入量个数 sizes.DirFeedthrough = 1; %直接馈通标志 sizes.NumSampleTimes = 1; % 至少有一个采样时刻 sys = simsizes(sizes); x0 = 0; % 状态初始化 str = []; % str 始终为空 ts = [0 0];% 初始化采样时间 % 指定simStateCompliance的值. % ‘UnknownSimState’, < 默认值; 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'; % 子函数mdlInitializeSizes 结束 %============================================================================= % mdlDerivatives % 返回连续状态量的导数 %============================================================================= function sys=mdlDerivatives(t,x,u) sys = []; % 子函数mdlDerivatives结束 %============================================================================= % mdlUpdate %更新离散时间状态，采样时刻和主时间步的要求。 %============================================================================= function sys=mdlUpdate(t,x,u) sys = []; % 子函数 mdlUpdate 结束 %============================================================================= % mdlOutputs % 计算并返回模块输出量 %============================================================================= function sys=mdlOutputs(t,x,u) sys = []; % 子函数 mdlOutputs 结束 %============================================================================= % mdlGetTimeOfNextVarHit % 返回下一个采样时刻。注意返回结果是一个绝对时间，只在Ts=[-2,0]时使用。 %============================================================================= function sys=mdlGetTimeOfNextVarHit(t,x,u) sampleTime = 1; % 例子。设置下一个采样时刻为1s后。 sys = t + sampleTime; % 子函数 mdlGetTimeOfNextVarHit 结束 %============================================================================= % mdlTerminate % 仿真结束 %============================================================================= % function sys=mdlTerminate(t,x,u) sys = []; % 子函数 mdlTerminate结束
function [sys,x0,str,ts,simStateCompliance]=limintm(t,x,u,flag,lb,ub,xi）
%传入的三个参数放在后面lb,ub,xi的位置 %LIMINTM Limited integrator implementation. % Example MATLAB file S-function implementing a continuous limited integrator % where the output is bounded by lower bound (LB) and upper bound (UB) % with initial conditions (XI). % % See sfuntmpl.m for a general S-function template. % % See also SFUNTMPL. % Copyright 1990-2009 The MathWorks, Inc. % $Revision: 1.1.6.2 $ switch flag %%%%%%%%%%%%%%%%%% % Initialization % %%%%%%%%%%%%%%%%%% case 0 [sys,x0,str,ts,simStateCompliance] = mdlInitializeSizes(lb,ub,xi); %%%%%%%%%%%%%%% % Derivatives % %%%%%%%%%%%%%%% case 1 sys = mdlDerivatives(t,x,u,lb,ub); %%%%%%%%%%%%%%%%%%%%%%%% % Update and Terminate % %%%%%%%%%%%%%%%%%%%%%%%% case {2,9} sys = []; % do nothing %%%%%%%%%% % Output % %%%%%%%%%% case 3 sys = mdlOutputs(t,x,u); otherwise DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag)); end % end limintm % %============================================================================= % mdlInitializeSizes % Return the sizes, initial conditions, and sample times for the S-function. %============================================================================= % function [sys,x0,str,ts,simStateCompliance] = mdlInitializeSizes(lb,ub,xi) sizes = simsizes; sizes.NumContStates = 1;%1个连续状态，即积分状态 sizes.NumDiscStates = 0; sizes.NumOutputs = 1; sizes.NumInputs = 1; sizes.DirFeedthrough = 0; sizes.NumSampleTimes = 1; sys = simsizes(sizes); str = []; x0 = xi; %积分状态初始条件‘ ts = [0 0]; % sample time: [period, offset] % speicfy that the simState for this s-function is same as the default simStateCompliance = 'DefaultSimState'; % end mdlInitializeSizes % %============================================================================= % mdlDerivatives % Compute derivatives for continuous states. %============================================================================= % function sys = mdlDerivatives(t,x,u,lb,ub) if (x <= lb & u < 0) | (x>= ub & u>0 ) sys = 0; else sys = u; end % end mdlDerivatives % %============================================================================= % mdlOutputs % Return the output vector for the S-function %============================================================================= % function sys = mdlOutputs(t,x,u) sys = x; % end mdlOutputs
