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Tracking Antenna Elevation Control: Equation to Block Diagram
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[QUOTE="super sky, post: 2675817, member: 244625"] I'm having a little trouble using the Latex thing so I've only used it for some of the equations. [h2]Homework Statement [/h2] Elevation control of a tracking antenna. Equation of motion for the system J[tex]\theta[/tex][tex]^{..}[/tex]+B[tex]\theta[/tex][tex]^{.}[/tex] = T[SUB]c[/SUB]+w ... [B]Equation 1[/B] (those dots are meant to be above the thetas, but I don't know how to do that... see attachment q1 for the equation) Antenna and drive mechanism have J = moment of inertia, B is the damping coefficient, T[SUB]c[/SUB] is the torque from the drive motor, w is a disturbance torque, and [tex]\theta[/tex] is elevation angle of the dish. Model the dish as a thin disc with diameter 2m, mass 40kg and rotates about central axis (J=MR[SUP]2[/SUP]/4) Damping coefficient = 20Nmsec Torque exerted by DC motor: T[SUB]m[/SUB]=K[SUB]T[/SUB]/R[SUB]a[/SUB]Va-K[SUB]T[/SUB]K[SUB]B[/SUB]/R[SUB]a[/SUB][tex]\theta[/tex][SUB]m[/SUB][tex]^{.}[/tex] ... [B]equation 2[/B] where [tex]\theta[/tex][SUB]m[/SUB] is the angular position of the motor shaft which is connected to the load, via a 50:1 gearbox. Motor parameters J[SUB]m[/SUB]=0.01kgm[SUP]2[/SUP], R[SUB]a[/SUB]=5ohms, K[SUB]T[/SUB]=0.2Nm/A, K[SUB]B[/SUB]=2Vsec a) Draw a block diagram of the motor itself(i.e. showing the relationship between the applied voltave V[SUB]a[/SUB], the load torque T[SUB]c[/SUB] and motor speed [tex]\theta[/tex][SUB]m[/SUB][tex]^{.}[/tex] and position [tex]\theta[/tex][SUB]m[/SUB]) b) Find the transfer function between the applied voltage V[SUB]a[/SUB] and the antenna angle theta assuming zero disturbance torque. c) Suppose the applied voltage is computed so that theta tracks a reference command theta[SUB]r[/SUB] according to the feedback law V[SUB]A[/SUB]=K(theta[SUB]r[/SUB]-theta) where K is the feedback gain. Draw a block diagram of the resulting feedback system showing both theta, the reference position theta[SUB]r[/SUB] and disturbance torque w. Find the transfer function between theta[SUB]r[/SUB] and theta assuming zero disturbance torque. There are a few other parts to the question, but they need to be worked through sequentially and I'm a little more hopeful about having an idea of them once I know what to do here. [h2]Homework Equations[/h2] Laplace Transforms... The derivative one: Laplace{\ddot{f}}=s[SUP]2[/SUP]F(s)-sf(0)-s\dot{f}(0) Transfer function of a closed loop system T(s) = G(s)/(1+G(s)H(s)) [h2]The Attempt at a Solution[/h2] Taking [B]equation 1[/B] and laplace transforming, assuming zero initial conditions: Js[SUP]2[/SUP]theta(s) + Bstheta(s) = T[SUB]c[/SUB](s) +w Rearrange: theta(s) = 1/(Js[SUP]2[/SUP]+Bs) * (T[SUB]c[/SUB](s) +w) See attachment 1, after where I've written equations 1 and 2... I think I'm going ok up to where I try to draw the block diagram with T[SUB]m[/SUB] in attachment 2. Then I'm not sure what to do with the equation to make it into a block diagram. I don't think it's a closed loop (because that comes later in part c with the reference..?) but I seem to have two inputs, V[SUB]a[/SUB] and theta[SUB]m[/SUB]... And so I'm not sure how to go about putting it in a block diagram other than what I've done. Any help would be super. Thanks. [/QUOTE]
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Tracking Antenna Elevation Control: Equation to Block Diagram
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