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cs:control:start [2016/11/24 08:27] Ryan Summers [Control Command] |
cs:control:start [2017/05/30 10:01] James Irwin [Control System Notes] |
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| ===== 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 |
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| - | 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 |
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| - | 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 $C$ | ||
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| ====== Control System Notes====== | ====== Control System Notes====== | ||
| - | 1. When tuning pitch and roll tune PID params while the sub is moving. This is because we only currently care about keeping the sub level while moving. | + | 1. When tuning pitch and roll PID params, tune them just to keep the sub stable when moving forward/strafing. This is because we only currently care about keeping the sub level while moving, don't really care as much about overshoot when moving between different pitch/roll angles. |
