二阶阻尼弹簧系统的simulink仿真（s函数）

function [sys,x0,str,ts,simStateCompliance] = controller(t,x,u,flag, pa) %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,pa); %%%%%%%%%%%%%%%%%%%%%%% % 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; %控制器中一般没有状态变量，而状态变量一般都在被控对象中。这也就导致了没有连续状态变量的定义，也就没有了连续状态更新的函数定义（状态方程） sizes.NumDiscStates = 0; sizes.NumOutputs = 1; %输出的就是u，注意是控制器的u，不是输入的u，这里可以换个符号uc sizes.NumInputs = 5; %输入有x1、x2、x1d、dx1d、ddx1d sizes.DirFeedthrough = 1; %有u就有直接馈入 sizes.NumSampleTimes = 1; % at least one sample time is needed sys = simsizes(sizes); % % initialize the initial conditions % x0 = []; %x0不需要定义值，因为本来就没有状态变量 % % 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) % 没有状态变