Have you tried the trial and error method. It seems best solution for your case. But remember to use the proper PID controller combination. I mean speed control goes withPI type controller. Position control requires a PI or a PD type controller.

Hope it works.

Best luck

By using genetic algorithm or particle swarm

Great, but what does an offline search algorithm (genetic or particle swarm) do, if the underwater robotic system runs with time.

Best regards

If you use MATLAB, there's a very good PID tuning functionality embedded: http://nl.mathworks.com/help/slcontrol/gs/automated-tuning-of-simulink-pid-controller-block.html

@Pedro Unfortunately, I don't have mathematical or function model of the robot. Do you have Idea how to use this tool without function model?

I guess it's just an optimiser running on top of your system.

If you are restricted to use a combination of PID controller thus trial and error method is best for your case, otherwise I would use Intelligent controller instead.

If you want to tune it by trial and error a method is the following:

a) Set integral and derivative gains to zero (work only with the P part).

b) Vary this proportional gain until you obtain the best possible performance.

c) Keeping this prop. gain, now vary the integral gain. This fact will reduce the steady state error but (as expected) it may introduce some oscillations and overshoot. Select the best one like this.

d) You should have obtained a fast response system but with (possibly) high overshot and oscillations. Now, keeping fixed the above mentioned gains, vary the derivative gain. This will damp your system reducing oscillations and overshoot. Naturally, this new variation may affect the general performance but try to select the best deriv. gain.

e) Return to step (a) in order to improve your closed loop performance as best as possible. However, recall that, in general, PID controllers can not deal well with highly nonlinear plants. If this process does not work you may a very different control law (a nonlinear one, fuzzy logic or so). If you do not have a lot of experience in control sysrems you may try fuzzy logic controllers (actually they are static nonlinear PIDs).

I suggest, model the whole underwater vehicle as a simple first order system where the input is the motor speed and the output is the water depth, which should normally be a first order case.  Experimentally, you can do this step.  You can get a 2D plot here of points. you can use Matlab's Curve fitting toolbox to determine the equation that best fits your data, I think an exponential can do this.  Now, you can get G(s) = Depth(s)/MotorSpeed(s) by using Laplace transforms.  

you may now use Matlab's control toolbox to design your PID parameters.  

Let me know if you made this work. :)

If you are professional in fuzzy systems, you will use it in order to tuning of PID parameters. Of course, you have to know the related-systems completely and determination of fuzzy mamdani's rules.

@Ricardo Zavala-Yoe thank you for the clarify the steps of the trial and error a method. Indeed, I have tested the the following methods: 

First one

{

1-Set all gains to zero.

2-Increase the P gain until the response to a disturbance is steady oscillation.

3-Increase the D gain until the the oscillations go away (i.e. it's critically damped).

4-Repeat steps 2 and 3 until increasing the D gain does not stop the oscillations.

5-Set P and D to the last stable values.

6-Increase the I gain until it brings you to the setpoint with the number of oscillations desired (normally zero but a quicker response can be had if you don't mind a couple oscillations of overshoot)

}

Second one (Sounds like Ziegler-Nichols)

{

1-Set all gains to 0.

2-Increase Kd until the system oscillates.

3-Reduce Kd by a factor of 2-4.

4-Set Kp to about 1% of Kd.

5-Increase Kp until oscillations start.

6-Decrease Kp by a factor of 2-4.

7-Set Ki to about 1% of Kp.

8-Increase Ki until oscillations start.

9-Decrease Ki by a factor of 2-4.

}

but I have not fully success or maybe I need some patience to make it better, I would like to ask you, what is your assessment of this steps of the methods if you are comparing with your steps of trial and error method?

Yes, I think the best practical method is that of Ziegler-Nichols that you can find every where.

@Elmer Magsino thank you for your suggestion. I'm very interesting to get G(s) of my robot. But before starting to execute the testing I have some questions:

1- The experiment have to apply on a closed loop or open loop system?

2- What is the type of the input on motors, Is it impulse or step response? 

3-I don't have directly the speed of the motors, but I have PWM  signals that send to motors to change the speed. Is it possible  (or correct) to calculate the speed of the robot in the water using the depth data (distance) and the time?

Regards

For the nonlinear and complicated systems, there is no specific way to get the optimal gain tuning. But, if you are familiar with optimization algorithms, you can easily use genetic algorithm or other similar methods to tune the PID gains based on your desires. You can find some examples in my researchgate papers.

Hello Ammar,

1- The experiment have to apply on a closed loop or open loop system? --> OPEN LOOP

2- What is the type of the input on motors, Is it impulse or step response?  --> STEP RESPONSE, get the final depth for each PWM value

3-I don't have directly the speed of the motors, but I have PWM  signals that send to motors to change the speed. Is it possible  (or correct) to calculate the speed of the robot in the water using the depth data (distance) and the time?  --> USE PWM VALUE vs DEPTH as your open loop system.

Recall that  the system you are dealing with (from the most general viewpoint) as a nonlinear multivariable system (the real, the actual underwater vehicle). So, as I mentioned, a PID -most likely- will not work. However, the trial and error method I suggested may deal with this but it may take a longer time to tune it because the little increments you do on any gain (say Kp=Prop. gain) will not respond neither linearly nor as small as you would expect (of course, in contrast to a linear plant). I do not think that Ziegler-Nichols can help. I would rather work with the trial and error method but proceeding slower than before. Increase a bit Kp and so on. Fix it. Increase a bit Ki (integrsl gain) and so on. Now, how much is a bit...? It is not known for sure. You may try increments of 0.1 or even 0.01. This may take some time, In addition, write down a nonlinear model (single input,single output) for your system (just to start with) and introduce it to SIMULINK. Add a PID block and select the "Autotuning" button. Repeat this for a linearized version of your system. Recall that your underwwater vehicle is a multi input/multioutput structure with very highly coupled output variables (if you vary a bit output 1 by action of input 1, output2, ..., output n, may vary a lot). Try all of this. Best regards.

Practical method for tuning is Ziegler-Nichols (two methods). Also there is the root-locus which is accurate.

I think that my paper "Practical Implementation of GA-Based PID Controller for Brushless DC Motor " can answer your question.

The best way is numerical optimization. You can use Matlab, or VisSim https://en.wikipedia.org/wiki/VisSim

The best method for tuning PID controller parameters is depend of your system Regards

Dear Ammar Amory

You can use fuzzy logic based online tuning of PID controller

Regards

Two basic methods:

1. Ziegler-Nichols (very crude)

2. CHT graphical and fine PID tunning books such as Astrom & Whitenmark.