User Tools
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
|
cs:control:start [2016/11/24 08:20] Ryan Summers |
cs:control:start [2016/11/24 08:49] Ryan Summers |
||
|---|---|---|---|
| Line 63: | Line 63: | ||
| $$ | $$ | ||
| - | where $C_{x}$ represents the scale factor for thruster x. Take note that conceptually, it is easy to differentiate translational and rotational goals | + | where $C_{x}$ represents the scale factor for thruster x. Take note that conceptually, it is easy to separate translational from rotational goals |
| $$ | $$ | ||
| Line 75: | Line 75: | ||
| ===== Total Force ===== | ===== Total Force ===== | ||
| - | By substituting ($\ref{eq:control:M}$) and ($\ref{eq:control:C}$) into ($\ref{eq:control}$), it can be seen that | + | $F$ in ($\ref{eq:control}$) is the necessary force to apply to the submarine to cause a transition from the current state to a desired state. By substituting ($\ref{eq:control:M}$) and ($\ref{eq:control:C}$) into ($\ref{eq:control}$), it can be seen that the dimensions of F are also known |
| $$ | $$ | ||
| Line 98: | Line 98: | ||
| $$ | $$ | ||
| - | Therefore, $F$ is also a vector with 6 elements in it. Each element of $F$ is the summation of each of the rows of $M$ multiplied by the weights in $C$. | + | Therefore, $F$ is also a vector with 6 elements in it. Each element of $F$ is the summation of each of the rows of $M$ multiplied by the weights in $C$. Because the mass and inertial moments of the submarine are also known, $F$ can also be calculated utilizing the current and desired state. |
| ===== Solving the Equation ===== | ===== Solving the Equation ===== | ||
| - | Now that all of the parameters of ($\ref{eq:control}$) have been defined, we can use it to find our control. Notice that there are two knowns within the system, both $M$ and $F$ can be analytically determined. $M$ can be found by measuring the position and orientation of each thruster. $F$ results from the desired position of the sub. To determine $F$, P, I, D, W, H, and Error need to be known. Let | + | Now that all of the parameters of ($\ref{eq:control}$) have been defined, we can use it to find our control. Notice that there are two knowns within the system, both $M$ and $F$. $M$ can be found by measuring the position and orientation of each thruster. $F$ results from the desired position of the sub. To determine $F$, P, I, D, W, H, and Error need to be known. Let |
| $$ | $$ | ||
| Line 126: | Line 126: | ||
| $$ | $$ | ||
| - | after both windup and hysteresis are applied to Error. Note that $E'$ is the derivative of $E$ over time, $I$ is the integral state for the accumulated error for each of the states within $E$, and $K_x$ are the respective P, I, and D weights. | + | after both windup and hysteresis are applied to $E$. Note that $E'$ is the derivative of $E$ over time, $I$ is the integral state for the accumulated error for each of the states within $E$, and $K_x$ are the respective P, I, and D weights. |
| Because both $F$ and $M$ are known, ($\ref{eq:control}$) can be solved for $C$ | Because both $F$ and $M$ are known, ($\ref{eq:control}$) can be solved for $C$ | ||
