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{"@context":"https://schema.org","@type":"QAPage","mainEntity":{"@type":"Question","name":"Issue following find_eqpt documentation","text":"
I'm trying to use find_eqpt in order to trim an aircraft. I need to solve for the trim throttle input and the angle of attack.
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There are a couple of ways that I can't figure out how to use find_eqpt, commented below. How do I specify that d/dt of only some of the states (u, w, theta, and q) matters in this calculation, given that other states are specified as fixed?
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Also, it doesn't seem like find_eqpt handles bounds or constraints, such that you can constrain a quaternion to norm 1 (this example just uses Euler angles).
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# Fix output at:\nVinf = 30\nbeta = 0\ngamma = 0\n\n# Find this output:\nalpha = 0 # guess\n\n# Find this input:\nthrottle = 0.5 # guess\n\n# State guess\nx = 0\ny = 0\nz = 0\nu = Vinf\nv = 0\nw = 0\nphi = 0    # Roll angle\ntheta = 0\npsi = 0    # Yaw angle\np = 0\nq = 0\nr = 0\n\nx0 = np.array([x, y, z, u, v, w, phi, theta, psi, p, q, r])\nu0 = np.array([throttle])\n\ntrim_state, trim_input, yeq, result = ct.find_eqpt(\n  aircraft_6dof_model, \n   x0, \n   u0=u0, \n   y0=[Vinf, alpha, beta, gamma],\n   iy=[0, 2, 3],           \t\t\t# Constrain Vinf, beta, gamma\n   ix=[4, 6, 8, 9, 10, 11],   \t\t\t# Constrain v, phi, psi, p, q, r\n   # dx0=[0,0,0,0,0,0,0,0,0,0,0,0],\t# How to specify that xdot, ydot, and zdot don't matter?\n   idx=[3, 5, 7, 10], \t\t\t        # Only care about d/dt of u, w, theta, and q\t\n   return_y = True,\n   return_result = True\n)
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Depending on how I formulate the arguments, I get an input/output mismatch error, or the find_eqpt function runs infinitely.
","upvoteCount":1,"answerCount":2,"acceptedAnswer":{"@type":"Answer","text":"
The issue is that the problem I desire to solve is over-constrained. I get the intended result if I change the line in find_eqpt that calls root to result = root(rootfun, z0, method='lm'), adding the \"least squares method\" designator to the args.
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Does it make sense for find_eqpt to do this if num_constraints > num_freedoms?
","upvoteCount":0,"url":"https://github.com/python-control/python-control/discussions/1053#discussioncomment-11137221"}}}