function [sys,x0,str,ts,simStateCompliance] = MPC_Controller(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  = 3;
sizes.NumOutputs     = 2;
sizes.NumInputs      = 3;
sizes.DirFeedthrough = 1;
sizes.NumSampleTimes = 1;   % at least one sample time is needed

sys = simsizes(sizes);

%
% initialize the initial conditions
%
x0  = [0;0;0];
global U;
U = [0;0];
%
% str is always an empty matrix
%
str = [];

%
% initialize the array of sample times
%
ts  = [0.1 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 = x;

% end mdlUpdate

%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function sys=mdlOutputs(t,x,u)
  global a b u_piao;
  global U;
  global kesi;
  tic
  Nx = 3;
  Nu = 2;
  Np = 60;
  Nc = 30;
  Row = 10;
  fprintf('Update start, t=%6.3f\n',t)
  t_d = u(3)*pi/180;
  
  r(1) = 25*sin(0.2*t);
  r(2) = 25+10-25*cos(0.2*t);
  r(3) = 0.2*t;
  vd1 = 5;
  vd2 = 0.104;
  
  kesi = zeros(Nx+Nu,1);
  kesi(1) = u(1)-r(1);%u(1)==X(1)
  kesi(2) = u(2)-r(2);%u(2)==X(2)
  kesi(3) = u(3)*pi/180-r(3);%u(3)==X(3)
  kesi(4) = U(1);
  kesi(5) = U(2);
  fprintf('Update start, u(1)=%4.2f\n',U(1))
  fprintf('Update start, u(2)=%4.2f\n',U(2))
  
  T = 0.1;
  T_all = 40;
  L = 2.6;
  
  u_piao = zeros(Nx,Nu);
  Q = 100*eye(Nx*Np,Nx*Np);
  R = 5*eye(Nu*Nc);
  a = [1 0 -vd1*sin(t_d)*T;
       0 1 vd1*cos(t_d)*T;
       0 0 1;];
  b = [ cos(t_d)*T 0;
        sin(t_d)*T 0;
        tan(vd2)*T/L vd1*T/(cos(vd2)^2);];
  A_cell = cell(2,2);
  B_cell = cell(2,1);
  A_cell{1,1} = a;
  A_cell{1,2} = b;
  A_cell{2,1} = zeros(Nu,Nx);
  A_cell{2,2} = eye(Nu);
  B_cell{1,1} = b;
  B_cell{2,1} = eye(Nu);
  A = cell2mat(A_cell);
  B = cell2mat(B_cell);
  C = [1 0 0 0 0; 0 1 0 0 0; 0 0 1 0 0;];
  PHI_cell = cell(Np,1);
  THETA_cell = cell(Np,Nc);
  for j = 1:1:Np
      PHI_cell{j,1} = C*A^j;
      for k = 1:1:Nc
          if k <= j
              THETA_cell{j,k} = C*A^(j-k)*B;
          else
              THETA_cell{j,k} = zeros(Nx,Nu);
          end
      end
  end
  PHI = cell2mat(PHI_cell);
  THETA = cell2mat(THETA_cell);
  H_cell = cell(2,2);
  H_cell{1,1} = THETA'*Q*THETA+R;
  H_cell{1,2} = zeros(Nu*Nc,1);
  H_cell{2,1} = zeros(1,Nu*Nc);
  H_cell{2,2} = Row;
  H = cell2mat(H_cell);
  
  error = PHI*kesi;
  f_cell = cell(1,2);
  f_cell{1,1} = 2*error'*Q*THETA;
  f_cell{1,2} = 0;
%  f = (cell2mat(f_cell))';
  f = cell2mat(f_cell);
  
 %%以下为约束生成区域
 %不等式约束
  A_t = zeros(Nc,Nc); %见falcone论文P181
  for p = 1:1:Nc
      for q = 1:1:Nc
          if q<=p
              A_t(p,q) = 1;
          else
              A_t(p,q) = 0;
          end
      end
  end
  A_l =kron(A_t,eye(Nu));
  Ut = kron(ones(Nc,1),U);
  umin = [-0.2; -0.54;];
  umax = [0.2; 0.332];
  delta_umin = [-0.05; -0.0082;];
  delta_umax = [0.05; 0.0082];
  Umin = kron(ones(Nc,1),umin);
  Umax = kron(ones(Nc,1),umax);
  A_cons_cell = {A_l zeros(Nu*Nc,1); -A_l zeros(Nu*Nc,1)};
  b_cons_cell = {Umax-Ut; -Umin+Ut};
  A_cons = cell2mat(A_cons_cell);
  b_cons = cell2mat(b_cons_cell);
 % 状态量约束
  M = 10;
  delta_Umin = kron(ones(Nc,1), delta_umin);
  delta_Umax = kron(ones(Nc,1), delta_umax);
  lb = [delta_Umin; 0];
  ub = [delta_Umax; M];
  
 %%开始求解过程
 % options = optimset('Algorithm','active-set');
 options = optimset('Algorithm','interior-point-convex');
 [X, fval, exitflag] = quadprog(H,f,A_cons,b_cons,[],[],lb,ub,[],options);
%%计算输出
 u_piao(1) = X(1);
 u_piao(2) = X(2);
 U(1) = kesi(4)+u_piao(1);
 U(2) = kesi(5)+u_piao(2);
 u_real(1) = U(1)+vd1;
 u_real(2) = U(2)+vd2;
 sys = u_real;
 toc   
% End of 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