function [t,y,u,t_e,y_e,e_e] = ppp_lin_run (Name,Simulate,ControlType,w,x_0,p_c,p_o) ## usage: [t,y,u,t_e,y_e,e_e] = ppp_lin_run (Name,Simulate,ControlType,w,x_0,p_c,p_o) ## ## ## Linear closed-loop PPP of lego system (and simulation) ## ## Name: Name of system (in mtt terms) ## Simulate = 0: real thing ## Simulate = 1: simulate ## Control = 0: step test ## Control = 1: PPP open-loop ## Control = 2: PPP closed-loop ## w is the (constant) setpoint ## par_control and par_observer are structures containing parameters ## for the observer and controller ##Defaults if nargin<1 # Default name to dir name names = split(pwd,"/"); [n_name,m_name] = size(names); Name = deblank(names(n_name,:)); endif ## System sys = mtt2sys(Name); # Create system [A,B,C,D] = sys2ss(sys); # SS form [n_x, n_u, n_y] = abcddim(A,B,C,D); # Dimensions if nargin<2 Simulate = 1; endif if nargin<3 ControlType = 2; endif if nargin<4 w = ones(n_y,1);; endif if nargin<5 x_0 = zeros(n_x,1); endif if nargin<6 p_c.N = 50; endif if nargin<7 p_o.sigma = 1e-1; endif if !struct_contains(p_c,"delta_ol") p_c.delta_ol = 0.5; # OL sample interval endif if !struct_contains(p_c,"T") p_c.T = 10; # Last time point. endif if !struct_contains(p_c,"augment") p_c.augment = 0; # Augment basis funs with constant endif if !struct_contains(p_c,"integrate") p_c.integrate = 0; # Augment basis funs with constant endif if !struct_contains(p_c,"Tau_u") p_c.Tau_u = []; p_c.Min_u = []; p_c.Max_u = []; endif if !struct_contains(p_c,"Tau_y") p_c.Tau_y = []; p_c.Min_y = []; p_c.Max_y = []; endif if !struct_contains(p_c,"Method") p_c.Method = "lq"; endif if struct_contains(p_c,"Method") if strcmp(p_c.Method,"lq") p_c.Q = eye(n_y); p_c.R = (0.1^2)*eye(n_u); p_c.n_U = n_x; elseif strcmp(p_c.Method,"original"); if !struct_contains(p_c,"A_w") p_c.A_w = 0; endif if !struct_contains(p_c,"A_u") p_c.n_U = n_x; a_u = 2.0; p_c.A_u = laguerre_matrix(p_c.n_U,a_u); if p_c.augment # Put in constant term p_c.A_u = ppp_aug(0,p_c.A_u); endif endif else error(sprintf("Method %s not recognised", p_c.Method)); endif endif if !struct_contains(p_c,"tau") # Time horizon if strcmp(p_c.Method,"lq") p_c.tau = [0:0.1:1]*2; elseif strcmp(p_c.Method,"original"); p_c.tau = [10:0.1:11]; else error(sprintf("Method %s not recognised", p_c.Method)); endif endif if !struct_contains(p_o,"x_0") p_o.x_0 = zeros(n_x,1); endif if !struct_contains(p_o,"method") ##p_o.method = "continuous"; p_o.method = "intermittent"; endif ## Check w. [n_w,m_w] = size(w); if ( (n_w!=n_y) || (m_w!=1) ) error(sprintf("ppp_lin_run: w must a column vector with %i elements",n_y)); endif ## Initialise x_est = p_o.x_0; ## Initialise simulation state x = x_0; if ControlType==0 # Step input I = 1; # 1 large sample p_c.delta_ol = p_c.T # I K_w = zeros(p_c.n_U,n_y); K_w(1,1) = 1; K_w(2,1) = -1; K_x = zeros(p_c.n_U,n_x); else I = ceil(p_c.T/p_c.delta_ol) # Number of large samples if strcmp(p_c.Method, "original") ## tau = [10:0.1:11]*(2/a_u); # Time horizons [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww] =\ ppp_lin(A,B,C,D,p_c.A_u,p_c.A_w,p_c.tau); # Design elseif strcmp(p_c.Method, "lq") # LQ design ## tau = [0:0.001:1]*2; # Time horizons [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] \ = ppp_lin_quad (A,B,C,D,p_c.tau,p_c.Q,p_c.R); p_c.A_u = A_u; else error(sprintf("Control method %s not recognised", p_c.Method)); endif ##Sanity check A_u [p_c.n_U,M_u] = size(p_c.A_u); if (p_c.n_U!=M_u) error("A_u must be square"); endif ## Checks [ol_zeros, ol_poles] = sys2zp(sys) cl_poles = eig(A - B*k_x) t_max = 1/min(abs(cl_poles)) t_min = 1/max(abs(cl_poles)) endif ## Initial control U U = zeros(p_c.n_U,1); ## Short sample interval dt = p_c.delta_ol/p_c.N; ## Observer design G = eye(n_x); # State noise gain sigma_x = eye(n_x); # State noise variance Sigma = p_o.sigma*eye(n_y); # Measurement noise variance if strcmp(p_o.method, "intermittent") Ad = expm(A*p_c.delta_ol); # Discrete-time transition matrix if (ControlType==2) # [L, M, P, obs_poles] = dlqe(Ad,G,C,sigma_x,Sigma); else L = zeros(n_x,n_y); obs_poles = eig(Ad); endif elseif strcmp(p_o.method, "continuous") Ad = expm(A*dt); # Discrete-time transition matrix A_ud = expm(p_c.A_u*dt); # Discrete-time input transition if (ControlType==2) # [L, M, P, obs_poles] = dlqe(Ad,G,C,sigma_x,Sigma); else L = zeros(n_x,n_y); obs_poles = eig(Ad); endif else error(sprintf("Observer method ""%s"" unknown", p_o.method)); endif ## Display the poles obs_poles ## Write the include file for the real-time function ## Use double length to allow for overuns overrun = 2; Ustar = ppp_ustar (p_c.A_u, n_u, [0:dt:overrun*p_c.delta_ol], 0,0); if p_c.integrate # Integrate Ustar disp("Integrating Ustar"); Ustar = cumsum(Ustar)*dt; endif disp("Writing Ustar.h"); ppp_ustar2h(Ustar); ## Control loop y = []; u = []; t = []; y_e = []; t_e = []; e_e = []; tick = time; i=0; for j=1:4 for k=1:I tim=time; # Timing i++; if Simulate # Exact simulation t_sim = [1:p_c.N]*dt; # Simulation time points [yi,ui,xsi] = ppp_ystar(A,B,C,D,x,p_c.A_u,U,t_sim); # Simulate x = xsi(:,p_c.N); # Current state (for next time) ti = [(i-1)*p_c.N:i*p_c.N-1]*dt; y_i = yi(1); # Current output t_i = ti(1); else # The real thing [t_i,y_i,u_i] = ppp_put_get(U); # Generic interface to real-time endif ## Observer if strcmp(p_o.method, "intermittent") [x_est y_est y_new, e_est] = ppp_int_obs \ (x_est,y_i,U,A,B,C,D,p_c.A_u,p_c.delta_ol,L); elseif strcmp(p_o.method, "continuous") Ui = U; # U at sub intervals for k = 1:p_c.N [x_est y_est y_new e_est] = ppp_int_obs \ (x_est,yi(:,k),Ui,A,B,C,D,p_c.A_u,dt,L); Ui = A_ud'*Ui; y_e = [y_e; y_new']; e_e = [e_e; e_est']; endfor endif ##Control if ( (p_c.Tau_u==[])&&(p_c.Tau_y==[]) ) U = K_w*w - K_x*x_est; else ## Input constraints [Gamma_u, gamma_u] = \ ppp_input_constraints(p_c.A_u,p_c.Tau_u,p_c.Min_u,p_c.Max_u); ## Output constraints [Gamma_y,gamma_y] = \ ppp_output_constraints(A,B,C,D,x_est,p_c.A_u,\ p_c.Tau_y,p_c.Min_y,p_c.Max_y); ## Composite constraints - t=0 Gamma = [Gamma_u; Gamma_y]; gamma = [gamma_u; gamma_y]; [u_qp,U] = ppp_qp (x_est,w,J_uu,J_ux,J_uw,Us0,Gamma,gamma,1e-6,1); endif ## Save data if Simulate t = [t;ti']; y = [y;yi']; u = [u;ui']; else t = [t;t_i]; y = [y;y_i']; u = [u;u_i']; endif if strcmp(p_o.method, "intermittent") y_e = [y_e; y_new']; e_e = [e_e; e_est']; t_e = [t_e; t_i]; endif if !Simulate delta_comp = time-tim; usleep(floor(1e6*(p_c.delta_ol-delta_comp-0.01))); endif endfor # Main loop w = -w; endfor # Outer loop if !Simulate ppp_put_get(0*U); # Reset to zero endif if strcmp(p_o.method, "continuous") t_e = t; endif sample_interval = (time-tick)/i ## Put data on file (so can use for identification) filename = sprintf("%s_ident_data.dat",Name); eval(sprintf("save -ascii %s t y u",filename)); endfunction