8 votes

What is $\alpha \sin(\theta) + \beta \frac{d \theta}{d t}$ in the inverted pendulum problem?

The function $f$ comes from the equation of motion for the inverted pendulum problem (inverted pendulum alone, not including the motion of the wheeled platform). If you consider your figure but ignore ...
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  • 1,357
6 votes
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How to use quaternions to feed a PID quadcopter stabilization loop?

A quadcopter contains (among other things) two separate and independent algorithms: an attitude estimation algorithm, and a control algorithm. The attitude estimation algorithm computes information ...
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  • 478
6 votes
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Relation between pole placement and marginal stability?

You are most likely running into problems with the maximum time step in your simulation. This phenomenon is known as stiffness, where your equations of motion are highly sensitive to the size of the ...
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  • 1,357
5 votes
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Humanoid balancing

Keep in mind that the ZMP is a simplification. In practice with walking robots the support polygon is constantly changing so it can be tough to keep the ZMP inside. Pregenerated (offline) ...
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  • 4,205
5 votes
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Why is it so hard to walk?

I'm not sure I agree that bipedal walking is so much harder that airplane control. It depends on how you look at it. Many robots can walk (bipedal walking) and many airplanes are difficult to control ...
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  • 4,205
5 votes

For what step disturbance value the system will become unstable?

The stability is a property of the linear systems themselves, hence there is no meaning in considering stability as regarded with the input disturbance $T_d$. To verify if the closed-loop system $C/...
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4 votes
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How do I decide the size of the time steps between sensing and control actuation?

Regarding point 1, yes you are understanding the problem correctly. Regarding points 1 and 2, I believe what you are looking for is the Nyquist-Shannon sampling theory. This theory says that your ...
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4 votes
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PID Control: Integral error does not converge to zero

I don't think this is related to integral windup at all. I noticed that the I-error does not converge to zero That's a good thing, because it means your integral term is not useless. The integral ...
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4 votes

Fixed Wing UAV: Do inherently unstable systems desire to be stable for all cases when a closed loop control is implemented on them?

Not all fixed wing aircraft are inherently instable. That feature greatly depends on the center pressure and gravity center designed position. Passenger aircrafts are quite stable, and fight planes ...
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  • 440
4 votes
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Inverted pendulum controller

Without going into the details of the underlying equations of motion, I could argue that the D part is needed to damp out the oscillations of the pole while reaching for the (unstable) equilibrium ...
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3 votes

Helicopter Stabilization Algorithm

Stabilization of a helicopter and a quadrotor are similar tasks - have a reference signal, compare that to feedback, then act on the difference. A quad rotor has four motors, and the helicopter ...
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3 votes
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Deciding length of quadcopter arms

For the most part, it will increase the gain of the controller. doesn't affect lift capabilities. Adding weight to something that flies always decreases lift capabilities. However, this influence ...
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3 votes

How to use quaternions to feed a PID quadcopter stabilization loop?

This paper, Full Quaternion Based Attitude Control for a Quadrotor by Emil Fresk and George Nikolakopoulos, demonstrates what you are trying to achieve. Abstract— The aim of this article is to ...
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3 votes

How to use quaternions to feed a PID quadcopter stabilization loop?

First, I think you need to go back and look at your code. Gimbal lock is only a problem when you get very near (within a couple degrees) of 90. If you are seeing strange behavior at 45 degrees ...
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  • 2,679
2 votes

How to stabilize a quadcopter

I would suggest that you build a rig that constricts the quadcopter to rotating along just one axis. Either roll or pitch. Then you need to tune the roll/pitch controller independently. I would ...
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2 votes

Is it better to have batteries distributed at the rotors or the center of the multicopter?

Vince has it right, it is a designers choice. Depends on the application. Moving the mass away from the center point of rotation will increases the moment of inertia. Which means it will resist ...
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  • 21
2 votes

How to use quaternions to feed a PID quadcopter stabilization loop?

This MOOC free-of-charge course, Welcome to TUMx's AUTONAVx! Autonomous Navigation for Flying Robots, may help. It covers: Learning theory Exercise Quadcoptor programming that run on both stimulator ...
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  • 419
2 votes

How can I know which system is easier to control using PID controller?

Linearize the system around the operating point you're interested in. Look at the eigenvalues of the A and B matrices that represents the linearized system. Then compare the eigenvalues using from ...
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  • 1,825
2 votes

Quadcopter stability vs (PID error signal lag and sample time)

A PID can provide great control, but it's a very unsophisticated technique -- it only understands error and correction. The longer you wait between measurements, the larger your error will be each ...
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  • 10.8k
2 votes
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Fixed Wing UAV: Do inherently unstable systems desire to be stable for all cases when a closed loop control is implemented on them?

I'm going to ignore your section on aircraft and attempt to answer the (vague) question, Do inherently unstable systems desire to be stable for all cases when a closed loop control is implemented ...
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  • 14.6k
2 votes
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Quadcopter PID Tuning for Altitude Hold/Position Hold along Z axis

Currently I am performing my research on that, and in my case I decided to tune all the PIDs. Angles of the quadrotor tend to zero, while altitude controller tend to the objective height. That's ...
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  • 440
2 votes
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Quadcopter PID: Controller is Saturating

I feel like I make the same comments every time you ask a question about your controller: How are you tuning the gains? I think your slack line is interfering with your results. Your quadcopter is ...
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  • 14.6k
2 votes

Humanoid balancing

They are two main approachs for humanoid robot walking. Practically it depends on the physical capabilities of your robot and what you want to achieve. If your robot is able to sustain strong impact ...
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2 votes
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PID quaternion contoller

You are using one PID controller to try to drive a quaternion? A quaternion by definition represents three degrees of freedom, roll pitch yaw, and a PID controller is Single Input, Single Output (SISO)...
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  • 14.6k
2 votes
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Quadcopter PID Controller: Derivative on Measurement / Removing the Derivative Kick

All PID controllers act on an error signal, so you definitely should stick with your first implementation. The derivative term in the PID controller wants to "see" how the error is changing - if the ...
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  • 14.6k
2 votes
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Quadcopter PID Control: Is it possible to stabilize a quadcopter considering only angle measurements?

It is possible to stabilize a quadcopter using only angle measurements in a single loop pid. However it is easier to stabilize a quadcopter using a cascaded PID controller. Yes you are tuning more ...
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2 votes

Using Quaternions to feed a quadcopter PID stabilizing controller to avoid Gimbal lock

you should not be seeing a singularity. For the standard roll, pitch, and yaw Euler angles, which are defined by a 3-2-1 rotation from level to the vehicle attitude, there is only a singularity at ...
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  • 1,825
2 votes
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PID Gains: Drop in control loop rate, need to retune?

All three constants should be able to stay the same assuming that you calculate the derivative and integral using the actual time step size. The only effect of a lower sampling rate should be a ...
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  • 921
1 vote

PID Control: Integral error does not converge to zero

When I look at your graphs of position error and integral error, I don't see any unexpected behaviors for a system which is not quite tuned well enough. You are not showing integral windup nor ...
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