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Section 5. Electroenergetics
Monjengue David, Independent Researcher Obtained a BTech degree in Digital electronic at TUT South Africa, in 2011.
Since then he has been conducting personal researches on model-free controllers
E-mail:
SIMPLE AND EFFICIENT MODEL-FREE CONTROLLER FOR AUTONOMOUS UNDERWATER VEHICLE DEPTH CONTROL
Abstract. In this study, we intended to design an efficient model-free controller for AUV depth control, which can overcome the difficulties of derive the mathematical models coming from the versatile environment where operate the AUVs. The model-free controller proposed here shows the ability to tract accurately a reference input signal and has good performances compare to H-infinity controller for AUV. It is also simple to design and implement, with few parameters to tune, when needed to refine the system performances.
Keywords: Autonomous underwater Vehicle (AUV), Remote Operating Vehicle (ROV), H-infinity controller, Model-free controller, Fuzzy logic controller (FLC), Sliding mode controller (SMC).
I. Introduction
Remotely operated vehicles (ROVs) and Autonomous Underwater Vehicles (AUV) are important tool for marine development and exploitation of resources located at deep oceanic environment [1] and are also used in risky and hazardous operations such as ocean rescue, underwater detection and observation, ocean floor analysis, and inspections or maintenance of underwater facilities.
AUV response depends heavily on its particular design and configuration, operating conditions, and environmental forces. Any automatic controller design for an AUV must satisfy two conflicting requirements: First, it has to be sophisticated enough to perform its mission in the realm of complicated and
ever-changing vehicle/environment interactions; secondly, it has to be simple enough so that on-line implementation is possible by the onboard vehicle computer at a sufficiently high sample rate [2].
Inherently, nonlinear dynamics ofAUVs make it more difficult to exert commonly used linear control. The dynamic characteristics of an AUV are quite complex due to its high nonlinearity, time-varying dynamic behavior, uncertainties in hydrodynamic coefficients, and disturbances caused by sea currents and waves [3].
Various control techniques have been proposed for AUVs. This includes linear controllers [4; 5], sliding Mode Controller (SMC) [6], Fuzzy Logic Control (FLC) [7], adapt ive control [8], which have
performed satisfactorily and have shown good robustness and tuning ability.
The objective of this paper is to develop a model free controller for attitude control system of AUV, that is simple, easy to use and efficient compare to advanced controllers. The goals are to:
- Achieve a suitable and simple controller to control depth of an AUV;
- Simulate the AUV's system and analyze the performances of the controller against the H-infinity Controller.
II. Problem statement
The problem that we want to solve here can be define as follow:
How can we design a controller that will be able to control the depth of an AUV, without relying on AUV system parameters?
Such controller should be model-free and its parameters should be easy to tune to improve the system performances (settling time, overshoot, error). III. Model-free controller design The idea is to supply the system with the right input signal, which derived from the closed-loop system output, plus the error signal. The error is passed through a compensator, which conditions it and makes it suitable to compensate the deficit that may occur in the first stage closed-loop. The following figure describe the model-free controller structure.
Figure 1. System with Model-free controller Block diagram
With, G(s): AUV transfer function With: Z (s): AUV depth,
Suppose the AUV is represented by the following ^ / ): a uv pitchangle
transfer function:
Z (s) n N ,lvl2: AUV parameters
From fig.1 we can obtain the overall system transfer function as:
6(s) s3 + lls2 + l2s Z (s)_
(1)
KNs + (a + b )KN
e(s) s3 + (( + a )s2 + (( + al, + 2KN) s + a (( + KN) + (a + b )KN
(2)
Hypothesis This means, the system is stable; therefore, we
Our hypothesis is as follow: The System in (1) can apply the final value theorem on it.
does not have any pole in the right half side of the Final value theorem complex plane nor in the imaginary axis, except at s=0.
Vf = lim sZ (s) = lim s
J s ^0 v '
KNs + (a + b )KN
s ^0
s3 +(( + a )s2 +((2 + al, + 2KN )s + a ((2 + KN ) + (a + b )KN's
(3)
1
V,
(a + b )KN
f = a ((2 + KN ) + (a + b )KN if we make a ©0,
v,bKN = i
f bKN
(4)
(5)
The more the controller parameter "a" is near to zero the more the system is accurate. We are left with two parameters "b" and "K" that will be used to drive system to the desired performances.
IV. Simulation
For the simulations we uesed, the AUV system described by [9], with AUV transfer function given by:
2 (s 4'16 (6)
e(s)
s3 + 0.82s2 + 0.69s
The controller parameters are as follow: K = -1,fl = 0.1, b = 1
Figure 2. Step response simulation with K= -1, a=0.1, b=1
The system performances are resumed in the below table:
Table 1. - System Performances form the 1st simulation
Param. Ts (s) OS (%) Error (%)
Model-free controller 14.94 18.87 9.60
In order to improve the system performances, to reach the performance of the H-infinity controller [9], we choose the following values for our controller:
N
1
0.9 0.8
,0J -0.6-_ 0.5
<U"0 4 Q
0.3 0.20.1 0
K = -100,fl = 0.1,fc = 7_ Input 9=1 m
0.5
1.5
2.5
3.5
4.5
Time (sec)
Figure 3. Step response simulation with K= -100, a=0.1, b=5
The Model-free controller performances are resumed and compared to H-Infinity controller performances [9], for the same system in the below table:
Table 2. - System Performances compared form the 2nd simulation
Ts (s) OS Error
Param. (%) (%)
H-Infinity controller 1 4 2
Model-free controller 1.36 NO 1.90
The model-free controller was able to control the system and drive system to performances similar to the one obtained with an advanced controller (H-in-finity), without the need to know system parameters. Conclusion
This study showed that a simple model-free controller can control AUV attitude efficiently, without the need to know neither system model nor system dynamics. The simulations confirmed that the proposed model-free controller also has good performances and is easy to tune. The simple structure of the model-free controller proposed here make it suitable for both hardware and software implementation. The controller performances are very closed to those obtained with H-Infinity controller.
References:
1. Kim Y. S., Lee J., Park S. K., Jeon B. H., Lee P. M. Path tracking control for under actuated AUVs based on resolved motion acceleration control. In Proceedings of the 4th International Conference on Autonomous Robots and Agents, IEEE, Wellington, New Zealand, 2009.- P. 342-346.
2. Cristi R., Papoulias F. A. and Healey A. J. "Adaptive Sliding Mode Control of Autonomous Underwater Vehicles in the Dive Plane". IEEE Journal of oceanic engineering,- Vol. 15.- No. 3.- July 1990.
3. Vahid S., Javanmard K. "Modeling and Control ofAutonomous Underwater Vehicle (AUV). In Heading and Depth Attitude via PPD Controller with State Feedback", International Journal of coastal & offshore engineering, IJCOE No. 4 / Autumn 2016 (11-18).
4. Yildiz O., Gokalp R. B., Yilmaz A. E. A review on motion control of the Underwater Vehicles. In: Proceedings of electrical and electronics engineering, 2009. ELECO 2009, Bursa, 2009.- P. 337-341.
5. Wadoo S., Kachroo. "Autonomous underwater vehicles: modeling, control design and simulation." CRC Press, edn 1, 2010.
6. Buckham B.J., Podhorodeski R. P., Soylu S. "A chattering-free sliding-mode controller for underwater vehicles with fault tolerant infinity-norm thrust allocation." J Ocean Eng, 35(16): 2008; 1647-1659.
7. Jun S. W., Kim D. W., Lee H. J. "Design of T-S fuzzy model based controller for depth control of autonomous underwater vehicles with parametric uncertainties." In: 11th international conference on control, automation and systems, ICCAS2011, Gyeonggi-do, Korea, Republic of, 2011.- P. 1682-1684.
8. Qi X. Adaptive coordinated tracking control of multiple autonomous underwater vehicles. Ocean Eng 91:2014.- P. 84-90.
9. Nag A., Patel S. S., Kishore K. and Akbar S. A. "A robust H-infinity based depth control of an autonomous underwater vehicle" 2013. International Conference on Advanced Electronic Systems (ICAES), Pilani, 2013.- P. 68-73. doi: 10.1109/ICAES.2013.6659363.
