hi there i'm working on quadrotor path tracking in matlab's simulink . there is an inner loop which is responsible for tracking the desired euler angles generated by the outer loop . feedback linearization is applied to a kinematic inversion block to generate reference euler angles . and a three separate sliding mode controllers are devoted for each three euler angles(fi , teta , sai).and i should mention that the kinematic inversion block's calculations are only valid under the condition that sai is held zero. so the corresponding sliding mode control should hold the sai zero . the problem is that for appropriate values for eta and landa(eta is the velocity of reaching the sliding surface and landa is the velocity of sliding toward zero when our variable is on the sliding surface) and feedback linearization parameters(alpha and beta), x and y track their reference values with the least possible error and so do the euler angles. but z does not at all track its reference value and starts to unboundedly diverge. what do you think i should do ? where do you think the problem may come from ? any advices or answers will be greatly appreciated.
At first when you are applying Slinding Mode controller then there is no need to linearize the quadrotor dynamics. Yes to gerenerate desired trajectory for Phi and Theta you need a inner loop control but it doesn't mean that Psi should always be zero it can have be of any degree depending upon the described path.
Hi.
From what I know, to generate the desired euler angles trajectory from the cartesian information, you need to linearize around hovering condition, i.e. fi, theta approximately 0 (assuming fi is the rotation around axis x and theta around axis y), while sai can be any desired angle. Moreover, quadrotors are underactuated system, meaning you can independently control only a partial pose of the system. From your question I see that you're controlling the euler angles, then you have convergence for sai while convergence for x and y depends on fi and theta. Are you employing also an altitude controller? If your outer loop generates a cartesian acceleration, you can simply take the z component of such acceleration, and a control law for the thrust force could be
fz = m(acc_z + g)/(cos(fi)cos(theta))
where m is the quadrotor mass and g the gravity acceleration
Yes the outer loop controls the altitude, phi, theta and psi . the acceleration equation for altitude is right and after double integration you caan get the zth position.
you are right quadrotor is an underactuated system, mean you have 4 states and to control them you need to have four controllers. forget about you path or helical trajectory, and just provide a step ref for all the 4 states and check your control design .
Marcello Sorge
thank you for answering this question. i can say that i tried two different ways for controlling the altitude. none of which lead to expected results. in the first method , right side of position dynamic equations are taken a feedback linearization part and with this assumption, the reference values for fi,teta and u1(equivalent to thrust input) are obtained. for instance in this method u1 is equal to :m*sqrt(ux^2+uy^2+uz^2)
m is the mass of the quadrotor and ux , uy , uz are refered to as feedback linearization parts.
but in the second method, first of all i design a controller for altitude dynamics(i mean z dynamics).so u1 should be designed in such a way that make the z track a reference zd . and then with having u1, i achieve reference values for fi and teta. in the second method z tracks zd successfully but x and y start to diverge and they don't track their reference values. but in the first method everything is reverse. z starts to diverge but with tunning the controllers parameters appropriately , x and y track their reference values. i attached two photos for better understanding
Like that from U1 you can't get the refrnc for phi and theta . for Phi and theta you have assigne separate refrnc. To better understant how sliding mode works you can follow my confer paper "https://ieeexplore.ieee.org/document/10404859/references#references" mentioned in my profile and also 10.1109/APCASE.2015.62 "https://ieeexplore.ieee.org/document/7287038".
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