Made state variable from Uin

Model/boost_model.tex

@@ -69,7 +69,8 @@ U_{in} &= (R_{62} + R_{Q25} + R_{L3})i_l + L_3\derivative{i_l}{t} + R_{Q24}i_l \
 
 \begin{align}
 \derivative{i_l}{t} &= \frac{1}{L_3}U_{in}-\frac{R_{62}+R_{Q25}+R_{L3}+R_{Q24}}{L_3}i_l \\
-\derivative{u_c}{t} &= -\frac{1}{C_{out}(R_{63}+R_{load})}u_c
+\derivative{u_c}{t} &= -\frac{1}{C_{out}(R_{63}+R_{load})}u_c \\
+\derivative{U_{in}}{t} &= 0
 \end{align}
 
 \vspace{1em}
@@ -77,16 +78,14 @@ U_{in} &= (R_{62} + R_{Q25} + R_{L3})i_l + L_3\derivative{i_l}{t} + R_{Q24}i_l \
 
 \begin{align}
 \derivative{}{t}
-\begin{bNiceMatrix} i_l \\ u_c \end{bNiceMatrix}
+\begin{bNiceMatrix} i_l \\ u_c \\ U_{in} \end{bNiceMatrix}
 &=
 \begin{bNiceMatrix}
--\frac{R_{62}+R_{Q25}+R_{L3}+R_{Q24}}{L_3} & 0 \\
-0 & -\frac{1}{C_{out}(R_{63}+R_{load})}
+-\frac{R_{62}+R_{Q25}+R_{L3}+R_{Q24}}{L_3} & 0 & \frac{1}{L_3} \\
+0 & -\frac{1}{C_{out}(R_{63}+R_{load})} & 0 \\
+0 & 0 & 0
 \end{bNiceMatrix}
-\begin{bNiceMatrix}i_l \\ u_c \end{bNiceMatrix}
-+
-\begin{bmatrix} \frac{1}{L_3} \\ 0 \end{bmatrix}
-U_{in}
+\begin{bNiceMatrix}i_l \\ u_c \\ U_{in}\end{bNiceMatrix}
 \end{align}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -107,7 +106,8 @@ C_{out}\derivative{u_c}{t} &= i_l - \frac{u_c}{R_{63}+R_{load}}
 
 \begin{align}
 \derivative{i_l}{t} &= \frac{1}{L_3}(U_{in}-u_c)-\frac{R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}}}{L_3}i_l \\
-\derivative{u_c}{t} &= \frac{1}{C_{out}}i_l-\frac{1}{C_{out}(R_{63}+R_{load})}u_c
+\derivative{u_c}{t} &= \frac{1}{C_{out}}i_l-\frac{1}{C_{out}(R_{63}+R_{load})}u_c \\
+\derivative{U_{in}}{t} &= 0
 \end{align}
 
 \vspace{1em}
@@ -115,16 +115,14 @@ C_{out}\derivative{u_c}{t} &= i_l - \frac{u_c}{R_{63}+R_{load}}
 
 \begin{align}
 \derivative{}{t}
-\begin{bmatrix} i_l \\ u_c \end{bmatrix}
+\begin{bmatrix} i_l \\ u_c \\ U_{in} \end{bmatrix}
 =
 \begin{bmatrix}
--\frac{R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}}}{L_3} & -\frac{1}{L_3} \\
-\frac{1}{C_{out}} & -\frac{1}{C_{out}(R_{63}+R_{load})}
+-\frac{R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}}}{L_3} & -\frac{1}{L_3} & \frac{1}{L_3} \\
+\frac{1}{C_{out}} & -\frac{1}{C_{out}(R_{63}+R_{load})} & 0 \\
+0 & 0 & 0
 \end{bmatrix}
-\begin{bmatrix}i_l \\ u_c \end{bmatrix}
-+
-\begin{bmatrix} \frac{1}{L_3} \\ 0 \end{bmatrix}
-U_{in}
+\begin{bmatrix}i_l \\ u_c \\ U_{in} \end{bmatrix}
 \end{align}
 
 
@@ -143,16 +141,14 @@ $A_1$, $B_1$ - Q24 v uzavřeném stavu, $A_2$, $B_2$ - Q24 v otevřeném stavu.
 
 \begin{align}
 \derivative{}{t}
-\begin{bmatrix} i_l \\ u_c \end{bmatrix}
+\begin{bmatrix} i_l \\ u_c \\ U_{in} \end{bmatrix}
 =
 \begin{bmatrix}
--\frac{R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}}}{L_3} & -\frac{1-d}{L_3} \\
-\frac{1-d}{C_{out}} & -\frac{1}{C_{out}(R_{63}+R_{load})}
+-\frac{R_{62}+R_{Q25}+R_{L3}+R_{s_{D6}}}{L_3} & -\frac{1}{L_3}(1-d) & \frac{1}{L_3} \\
+\frac{1}{C_{out}}(1-d) & -\frac{1}{C_{out}(R_{63}+R_{load})} & 0 \\
+0 & 0 & 0
 \end{bmatrix}
-\begin{bmatrix}i_l \\ u_c \end{bmatrix}
-+
-\begin{bmatrix} \frac{1}{L_3} \\ 0 \end{bmatrix}
-U_{in}
+\begin{bmatrix}i_l \\ u_c \\ U_{in} \end{bmatrix}
 \end{align}
 
 \subsection{Odezva otevřené smyčky pro různé hodnoty střídy}
@@ -172,43 +168,42 @@ U_{in}
 
 \begin{align}
     \derivative{}{t}
-    \begin{bmatrix} i_l \\ u_c \end{bmatrix}
+    \begin{bmatrix} i_l \\ u_c \\ U_{in} \end{bmatrix}
     =
     \begin{bmatrix}
-        -\frac{R_{in}}{L_3} & 0 \\
-        0 & -\frac{1}{C_{out}R_{out}}
+        -\frac{R_{in}}{L_3} & 0 & \frac{1}{L_3} \\
+        0 & -\frac{1}{C_{out}R_{out}} & 0 \\
+        0 & 0 & 0
     \end{bmatrix}
-    \begin{bmatrix}i_l \\ u_c \end{bmatrix}
+    \begin{bmatrix}i_l \\ u_c \\ U_{in}\end{bmatrix}
     +
     \begin{bmatrix}
         -\frac{\overline{u_c}}{L_3} \\
-        \frac{\overline{i_L}}{C_{out}}
+        \frac{\overline{i_L}}{C_{out}} \\
+        0
     \end{bmatrix}
     D
-    +
-    \begin{bmatrix} \frac{1}{L_3} \\ 0 \end{bmatrix}
-    U_{in}
 \end{align}
 
 
 \section{Diskretizace}
 \begin{align}
     \derivative{}{t}
-    \begin{bmatrix} i_l \\ u_c \end{bmatrix}
+    \begin{bmatrix} i_l \\ u_c \\ U_{in} \end{bmatrix}
     =
     \begin{bmatrix}
-        -\frac{R_{in}}{L_3} & 0 \\
-        0 & -\frac{1}{C_{out}R_{out}}
+        -\frac{R_{in}}{L_3} & 0 & \frac{1}{L_3} \\
+        0 & -\frac{1}{C_{out}R_{out}} & 0 \\
+        0 & 0 & 0
     \end{bmatrix}
-    \begin{bmatrix}i_l \\ u_c \end{bmatrix}
+    \begin{bmatrix}i_l \\ u_c \\ U_{in}\end{bmatrix}
     +
     \begin{bmatrix}
-        -\frac{\overline{u_c}}{L_3} & \frac{1}{L_3} \\
-        \frac{\overline{i_L}}{C_{out}} & 0
-    \end{bmatrix}
-    \begin{bmatrix}
-        D \\ U_{in}
+        -\frac{\overline{u_c}}{L_3} \\
+        \frac{\overline{i_L}}{C_{out}} \\
+        0
     \end{bmatrix}
+    D
 \end{align}
 
 \vspace{1em}
@@ -216,34 +211,13 @@ U_{in}
 
 \begin{align}
     \begin{bmatrix}
-        i_{l,t+1} \\ u_{c,t+1}
+        i_{l,t+1} \\ u_{c,t+1} \\ U_{in,t+1}
     \end{bmatrix}
     =
     \boldsymbol{A}
-    \begin{bmatrix}i_l \\ u_c \end{bmatrix}
+    \begin{bmatrix}i_{l,t} \\ u_{c,t} \\ U_{in,t}\end{bmatrix}
     +
-    \boldsymbol{B}
-    \begin{bmatrix}
-        D \\ U_{in}
-    \end{bmatrix}
-\end{align}
-
-\begin{align}
-    \begin{bmatrix}
-        i_{l,t+1} \\ u_{c,t+1}
-    \end{bmatrix}
-    =
-    \boldsymbol{A}
-    \begin{bmatrix}i_l \\ u_c \end{bmatrix}
-    +
-    \begin{bmatrix}
-        \boldsymbol{B}_{1,1} \\ \boldsymbol{B}_{2,1}
-    \end{bmatrix}
-    D +
-    \begin{bmatrix}
-        \boldsymbol{B}_{1,2} \\ \boldsymbol{B}_{2,2}
-    \end{bmatrix}
-    U_{in}
+    \boldsymbol{B}D
 \end{align}
 
 
@@ -256,78 +230,74 @@ U_{in}
 
 \begin{align}
     \begin{bmatrix}
-        i_{l,t+1} \\ u_{c,t+1} \\ \Delta_{t+1}
+        i_{l,t+1} \\ u_{c,t+1} \\ U_{in,t+1} \\ \Delta_{t+1}
     \end{bmatrix}
     &=
     \begin{bmatrix}
-        \boldsymbol{A}_{1,1} & \boldsymbol{A}_{1,2} & 0 \\
-        \boldsymbol{A}_{2,1} & \boldsymbol{A}_{2,2} & 0 \\
-        0 & \mathrm{d}t & 1 \\
+        \boldsymbol{A}_{1,1} & \boldsymbol{A}_{1,2} & \boldsymbol{A}_{1,3} & 0 \\
+        \boldsymbol{A}_{2,1} & \boldsymbol{A}_{2,2} & \boldsymbol{A}_{2,3} & 0 \\
+        \boldsymbol{A}_{3,1} & \boldsymbol{A}_{3,2} & \boldsymbol{A}_{3,3} & 0 \\
+        0 & \mathrm{d}t & 0 & 1 \\
     \end{bmatrix}
     \begin{bmatrix}
-        i_{l,t} \\ u_{c,t} \\ \Delta_t
+        i_{l,t} \\ u_{c,t} \\ U_{in,t} \\ \Delta_t
     \end{bmatrix}
     +
     \begin{bmatrix}
         \boldsymbol{B}_{1,1} \\
         \boldsymbol{B}_{2,1} \\
+        \boldsymbol{B}_{3,1} \\
         0
     \end{bmatrix}
     D +
     \begin{bmatrix}
-        \boldsymbol{B}_{1,2} \\
-        \boldsymbol{B}_{2,2} \\
-        0 \\
-    \end{bmatrix}
-    U_{in} +
-    \begin{bmatrix}
-        0 \\ 0 \\ -\mathrm{d}t
+        0 \\ 0 \\ 0 \\ -\mathrm{d}t
     \end{bmatrix}
     u_{c,t}^*
 \end{align}
 
 \begin{align}
     \begin{bmatrix}
-        i_{l,t+1} \\ u_{c,t+1} \\ \Delta_{t+1}
+        i_{l,t+1} \\ u_{c,t+1} \\ U_{in,t+1} \\ \Delta_{t+1}
     \end{bmatrix}
     &=
     \begin{bmatrix}
-        \boldsymbol{A}_{1,1} & \boldsymbol{A}_{1,2} & 0 \\
-        \boldsymbol{A}_{2,1} & \boldsymbol{A}_{2,2} & 0 \\
-        0 & \mathrm{d}t & 1 \\
+        \boldsymbol{A}_{1,1} & \boldsymbol{A}_{1,2} & \boldsymbol{A}_{1,3} & 0 \\
+        \boldsymbol{A}_{2,1} & \boldsymbol{A}_{2,2} & \boldsymbol{A}_{2,3} & 0 \\
+        \boldsymbol{A}_{3,1} & \boldsymbol{A}_{3,2} & \boldsymbol{A}_{3,3} & 0 \\
+        0 & \mathrm{d}t & 0 & 1 \\
     \end{bmatrix}
     \begin{bmatrix}
-        i_{l,t} \\ u_{c,t} \\ \Delta_t
+        i_{l,t} \\ u_{c,t} \\ U_{in,t} \\ \Delta_t
     \end{bmatrix}
     +
     \begin{bmatrix}
-        \boldsymbol{B}_{1,1} & \boldsymbol{B}_{1,2} & 0 \\
-        \boldsymbol{B}_{2,1} & \boldsymbol{B}_{2,2} & 0 \\
-        0 & 0 & -\mathrm{d}t
+        \boldsymbol{B}_{1,1} & 0 & 0 & 0 \\
+        \boldsymbol{B}_{2,1} & 0 & 0 & 0 \\
+        \boldsymbol{B}_{3,1} & 0 & 0 & 0 \\
+        0 & 0 & 0 & -\mathrm{d}t
     \end{bmatrix}
     \begin{bmatrix}
-        D \\ U_{in} \\ u_{c,t}^*
+        D \\ 0 \\ 0 \\ u_{c,t}^*
     \end{bmatrix}
 \end{align}
 
 
 \section{Regulátor}
 \begin{align}
-    d &= -\boldsymbol{L}x_t - \boldsymbol{K}w \\
-    d &= -\boldsymbol{L}
+    D &= -\boldsymbol{L}x_t - \boldsymbol{K}w \\
+    D &= -\boldsymbol{L}
     \begin{bmatrix}
-        i_{l,t} \\ u_{c,t} \\ \Delta_{t}
+        i_{l,t} \\ u_{c,t} \\ U_{in,t} \\ \Delta_{t}
     \end{bmatrix}
-    - \boldsymbol{K}
-    \begin{bmatrix}
-        D \\ U_{in} \\ u_{c,t}^*
-    \end{bmatrix} \\
+    - \boldsymbol{K}u_{c,t}^* \\
     \boldsymbol{L} &= dlqr(\boldsymbol{A}, \boldsymbol{B}, \boldsymbol{Q}, \boldsymbol{N}, \boldsymbol{R}) \\
     \boldsymbol{K} &= \{-\boldsymbol{C_w}[\boldsymbol{I}-(\boldsymbol{A}-\boldsymbol{BL})]^{-1}\boldsymbol{B}\}^{-1} \\
     \boldsymbol{C}_w &= \begin{bmatrix}
-        1 & 0 & 0 \\
-        0 & 1 & 0 \\
-        0 & 0 & 1
+        1 & 0 & 0 & 0 \\
+        0 & 1 & 0 & 0 \\
+        0 & 0 & 1 & 0 \\
+        0 & 0 & 0 & 1
     \end{bmatrix}
 \end{align}
 

Model/model_sim.m

@@ -30,13 +30,15 @@ il_lin = 0.83;
 
 
 % Continuous time matrixes
-cssm.A = [-par.Rin/par.L3, 0;
-          0, -1/(par.Cout*par.Rout)];
+cssm.A = [-par.Rin/par.L3, 0, 1/par.L3;
+          0, -1/(par.Cout*par.Rout), 0;
+          0, 0, 0];
 
-cssm.B = [-uc_lin/par.L3, 1/par.L3;
-          il_lin/par.Cout, 0];
+cssm.B = [-uc_lin/par.L3;
+          il_lin/par.Cout;
+          0];
 
-cssm.C = eye(2);
+cssm.C = eye(size(cssm.B,1));
 cssm.D = zeros(size(cssm.B));
 
 
@@ -44,46 +46,48 @@ cssm.D = zeros(size(cssm.B));
 dssm = c2d(ss(cssm.A, cssm.B, cssm.C, cssm.D), Ts);
 
 % Add error integration
-dsys.A = [dssm.A(1,1), dssm.A(1,2), 0;
-          dssm.A(2,1), dssm.A(2,2), 0;
-          0, Ts, 1];
-dsys.B = [dssm.B(1,1), dssm.B(1,2), 0;
-          dssm.B(2,1), dssm.B(2,2), 0;
-          0, 0, -Ts];
-dsys.C = eye(3);
+dsys.A = [dssm.A(1,1), dssm.A(1,2), dssm.A(1,3), 0;
+          dssm.A(2,1), dssm.A(2,2), dssm.A(2,3), 0;
+          dssm.A(3,1), dssm.A(3,2), dssm.A(3,3), 0;
+          0, Ts, 0, 1];
+dsys.B = [dssm.B(1,1);
+          dssm.B(2,1);
+          dssm.B(3,1);
+          0];
+dsys.C = eye(size(dsys.B, 1));
 dsys.D = zeros(size(dsys.B));
 
 
-% Simulate system (open loop)
-% i = 1;
-% i0 = 0.75;
-% u0 = 170;
-% delta0 = 0.9;
-% tmax = 0.1;
-% 
-% sim.vars(:,1) = [i0, u0, delta0];
-% sim.t(i) = 0;
-%     
-% for t=dssm.Ts:dssm.Ts:tmax
-%     sim.vars(:, i+1) = dsys.A*sim.vars(:, i) + dsys.B*[1-d; Uin; uc_req];
-%     sim.t(i+1) = t;
-% 
-%     i = i+1;
-% end
+%Simulate system (open loop)
+i = 1;
+i0 = 0.75;
+u0 = Uin;
+delta0 = 0.9;
+tmax = 0.1;
 
-% Plot it
-%plot_sim(sim, "Open loop response", 1);
+sim.vars(:,1) = [i0, u0, Uin, delta0];
+sim.t(i) = 0;
+    
+for t=dssm.Ts:dssm.Ts:tmax
+    sim.vars(:, i+1) = dsys.A*sim.vars(:, i) + dsys.B*(1-d);
+    sim.t(i+1) = t;
+
+    i = i+1;
+end
+
+%Plot it
+plot_sim(sim, "Open loop response", 1);
 
 
 % Regulator
-Q = diag([0, 0.01, 0.5]);
+% Q = diag([0, 0.5, 0, 0.5]);
+Q = 1e-5*eye(4);
 R = 1;
-N = zeros(3);
+N = zeros(size(Q, 1),1);
 L = dlqr(dsys.A, dsys.B, Q, R, N);
 
-% Cw = eye(3);
-Cw = [1, 0, 0 ; 0, 1, 0; 0, 0, 1];
-p = inv(eye(3) - (dsys.A - dsys.B*L));
+Cw = eye(4);
+p = inv(eye(4) - (dsys.A - dsys.B*L));
 K = inv(-Cw * p * dsys.B);
 
 
@@ -148,16 +152,20 @@ title("d");
 function plot_sim(sim, what, num)
     figure(num);
     sgtitle(sprintf("%s", what));
-    subplot(1,3,1);
+    subplot(1,4,1);
     plot(sim.t, sim.vars(1,:));
     title("il");
     
-    subplot(1,3,2);
+    subplot(1,4,2);
     plot(sim.t, sim.vars(2,:));
     title("uc");
     
-    subplot(1,3,3);
+    subplot(1,4,3);
     plot(sim.t, sim.vars(3,:));
+    title("Uin");
+    
+    subplot(1,4,4);
+    plot(sim.t, sim.vars(4,:));
     title("delta");
     hold off
 end