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POCross characteristics of a non-linear equation in Matlab
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copied!<p>I'd like to create a Matlab plot of propeller angular velocity in terms of applied current. The point is, this requires combining two interdependent sets of data. </p> <p>Firstly, drag coefficient <code>c_d</code> depends on angular velocity <code>omega</code> (I have no formula, just data) as seen on the plot below - the characteristics <code>c_d(omega)</code> could be easily linearised as <code>c_d(omega) = p*omega + p_0</code>.</p> <p>Secondly, <code>omega</code> depends not only on applied current <code>i</code>, but also on the drag coefficient <code>c_d(omega)</code>.</p> <p>A script that solves the case, where <code>c_d</code> is constant below. It must be somehow possible to join those two using Matlab commands. Thanks for any help.</p> <pre><code>%%Lookup table for drag coefficient c_d c_d_lookup = [248.9188579 0.036688351; %[\omega c_d] 280.2300647 0.037199094; 308.6091183 0.037199094; 338.6636881 0.03779496; 365.8908244 0.038305703; 393.9557188 0.039156941; 421.9158934 0.039667683; 452.2846224 0.040348674; 480.663676 0.041199911; 511.032405 0.042051149; 538.9925796 0.042561892; 567.2669135 0.043242882; 598.4734005 0.043668501; 624.1297405 0.044264368; 651.9851954 0.044604863; 683.6105614 0.045200729]; subplot(2,1,1) plot(c_d_lookup(:,1), c_d_lookup(:,2)) title('This is how c_d depends on \omega') ylabel('c_d') xlabel('\omega [rad/s]') %%Calculate propeller angular speed in terms of applied current. omega %%depends on c_d, which in turn depends on omega. The formula is: % omega(i) = sqrt(a*i / (b * c_d(omega))) % Where: % i - applied current % omega - propeller angular velocity % a,b - coefficients i = [1:15]; a = 0.0718; b = 3.8589e-005; %If c_d was constant, I'd do: omega_i = sqrt(a .* i / (b * 0.042)); subplot(2,1,2) plot(i, omega_i) ylabel({'Propeller ang. vel.', '\omega [rad/s]'}) xlabel('Applied current i[A]') title('Propeller angular velocity in terms of applied current') </code></pre> <p><img src="https://i.stack.imgur.com/7oB7B.png" alt="enter image description here"></p> <p><strong>EDIT:</strong></p> <p>Trying to follow <strong>bdecaf's</strong> solution. So I created a function <code>c_d_find</code>, like so:</p> <pre><code>function c_d = c_d_find(omega, c_d_lookup) c_d = interp1(c_d_lookup(:,1), c_d_lookup(:,2), omega, 'linear', 'extrap'); end </code></pre> <p>I don't know anything about Matlab function handles, but seem to understand the idea... In Matlab command window I typed:</p> <pre><code>f = @(omega) omega - sqrt(a .* i / (b * c_d_find(omega, c_d_lookup))) </code></pre> <p>which I hope created the correct function handle. What do I do next? Executing the below doesn't work:</p> <pre><code>>> omega_consistent = fzero(f,0) ??? Operands to the || and && operators must be convertible to logical scalar values. Error in ==> fzero at 333 elseif ~isfinite(fx) || ~isreal(fx) </code></pre>

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