Elsevier

Applied Soft Computing

Volume 65, April 2018, Pages 184-195
Applied Soft Computing

PSO tuned FLC for full autopilot control of quadrotor to tackle wind disturbance using bond graph approach

https://doi.org/10.1016/j.asoc.2018.01.015Get rights and content

Highlights

  • Quadrotor model in bond graph approach is considered.

  • An FLC-PID controller is proposed for full controlling the quadrotor.

  • Fuzzy rules are obtained via Particles Swarm Optimization (PSO).

  • Gimbal lock problem is eliminated by quaternion equations.

  • Robustness of the controller against wind disturbance is simulated.

Abstract

The ability of Bond Graph (BG) in modeling multi-domain structures results in a more precise and expansive interface. Hence, this paper develops the model of a quadrotor using BG approach. Then, the paper introduces and optimizes a Fuzzy Logic Controller (FLC) with the aim of making intelligent decisions close to human decisions. Additionally, a Particle Swarm Optimization (PSO) algorithm is utilized to have minimum 4 rules for FLC, which leads the controller to be quick. It is because a fast FLC is necessary in the next part to convert the controller to a full one (considering all main states). Furthermore, two Proportional-Integral-Derivative (PID) controllers have helped the FLC to bring all the main states of quadrotor under control. In addition, the set points for the angles, which cause higher nonlinearity behavior, could now be set close to π/2. Furthermore, multi-domain model of the system has helped in modeling of constant and random variable wind disturbances for which a logical solution is suggested.

Introduction

Nowadays, Unmanned Arial Vehicles (UAVs) have important roles in human life, and their application is expanding. Aside hobby applications, many new missions are defined for them. For instance, posting by quadrotors have been taken into account in modern life due to the fact that in some areas, there is still no posting coverage because of climate or far distances from urban centers. In addition, quadrotor s can be employed for high quality imaging purposes. As a result, it is obvious that quadrotors propose better solutions for these situations, and it seems that new applications will be defined by development of quadrotors.

To respond to the demand, quadrotors need more accurate positioning and a reliable platform. Moreover, these developments will improve the old applications such as inspection, data-logging, rescuing, and military purposes. Nevertheless, for utilizing the advantages of a quadrotor, it is unavoidable to overcome its under-actuated structure. That is, for controlling six Degrees of Freedom (DOF), there are only four motor speeds available to be controlled. Scientists have shown the possibility of controlling quadrotors, and several practical projects have been designed which accomplish the applications in real life. However, as a current issue, it seems there is still a gap between qualified full control of quadrotors and related works in literature.

In order to overcome the challenges posed by quadrotors, it is fundamental to have an accurate model. In 1961, Henry Paynter [1] introduced a new way of modeling for mechanical systems called Bond Graph. It is a powerful tool for demonstration of the system equations via a graphical approach. The advantage of using BG is its independent elements from different energy domains such as electrical, mechanical, thermal, and chemical. Two main concepts in this modeling approach are Effort and Flow. By this modeling, Effort is given to have Flow in the system, and their multiplication is Power. Considering these concepts, the causality in real life is taken into account in modeling part, which can help us solve many after-construction problems. The principles of BG including bonds, R-L-C elements, 0-junction and 1-junction, causality and its assignment, transformer and gyrator, and rules of modeling are illustrated in [[2], [3]]. As mentioned earlier, BG has same elements for different energy domains, and many specialists with different expertise have published many papers based on BG.

Another advantage of using BG is the capability to utilize the result of researches on other energy domains in modeling different parts. Therefore, the tolerance synthesis discussed in [4] could be used on quadrotors through this paper. The linear time varying in [5] could be applied to model the aging problem of the parameters. The model of photovoltaic cells in [6] is beneficial to consider the power source from the sunlight. The representation of BLDC motors in [7] is also suitable to integrate the accurate model of commonly used motors in quadrotors. Moreover, the research over non-circular body rolling in [8] could be considered for analysis of accident of quadrotor with soft surfaces.

As the contributions of the paper, the comprehensive BG modeling, full control over all main states, tracking trajectories for angles and position, using PSO-tuned FLC and Ziegler-Nichols (ZN)-tuned PID in series to have a controller with capabilities of aggressive control, solved gimbal lock through quaternions, and impressively overcoming the wind disturbance, altogether make the paper to call an adroit autopilot of the quadrotors.

The BG approach for quadrotors is very strange in the literature. Thus, the BG utilized in [9], [10] have not supported well in results. In [11], also the controller is just simple PID, which is not suggested for such a nonlinear system.

To discuss the other merits, the paper is compared with non-BG methods in results and the quality of the controller. Thus, the sliding mode controller in [12] with promising results do not cover φ and θ angles for higher values, as the same drawback in [13]. Due to high nonlinearity and under actuated dynamics, the investigations are mostly stabilizing [[14], [15], [16]], which needs a higher endeavor to have the capability of tracking trajectory [17]. The proposed paper not only tracks a trajectory for position but also the trajectory is a permanently changing sinusoidal track with a better profile than [18]. On the other hand, tracking sinusoidal trajectory for angles not only have been accomplished but also its amplitude (80°) makes the classification in the aggressive control, as the boundaries of the researches about UAVs. Hence to get this capability, the gimbal lock problem is eliminated using quaternions and completed by adequate controller. The controller has two complementary parts. An FLC, which a PSO algorithm is utilized to find least possible four rules. Whereas, the [16] with 49 rules has handled only stabilization and step changes for quadrotor. The other part of the controller is the PID which is tuned with well-known ZN method. The whole plan results in a full control of all (six) main states despite under actuated dynamics of the quadrotor, unlike [19] which has agreed to height and attitude control (4 states of 6). In spite of simple structure of the PID-FLC, there is a great background to choose MFs and rules to have as possibly quick as human decisions. Therefore, the PSO searches for the suitable least rules. Then, the methodology of choosing the MFs completes the process. Thus, the type of MFs are known for natural behavior. Additionally, The MFs have minimum overlap determinately to separate the numbers to negative, zero and positive. Whereas, the four rules in [15] have not promising results without these considerations.

As the interesting part, the wind disturbance is handled in this paper as real-time forces, unlike [20] which has done extra effort to estimate the wind. The lookup table in [21], as the pre known information of the wind has values with maximum of 0.4 [N] less than our simulations. The experimental two scenarios in [22] and considering wind disturbance as uncertainty in [18], generally could not be compared with this paper. Except in the proposed paper, the approach enables the UAVs to discuss about whirlwind and pursue the aerodynamics-depended wind disturbances in the later works.

Section snippets

Model of the quadrotor in BG

The Euler angles, Roll, Pitch, and Yaw, are defined by assigning North-East-Up coordinates to the body of a quadrotor as in Fig. 1. From then on, they would be called Euler angles by symbols φ, θ, and ψ corresponding to turning the body frame around X, Y, and Z-axes respectively.

The typical equations of dynamics of quadrotor is illustrated in [[23], [24]], which are conclusions of Newton’s second law, and they are the same with Eqs. (1) and (2) from [25].Fx,ext=mv˙xmvyωz+mvzωyFy,ext=mv˙ymvzωx+

Design of the controller

A controlling method is proposed which consists of two supplementary controllers as shown in Fig. 4. An FLC controller in low level interacts directly with speeds of the motors. The FLC has a high duty in controlling three angles (φ, θ, and ψ) and the altitude (the Z position). After handling the control of these delicate states, the PID controllers complete the full control by sending suitable commands to θ and φ in the higher level to control horizontal positions. A scheme is proposed to

Proposed model for wind disturbance

As a natural and more possible event, the wind could affect the quadrotor, which needs to be addressed properly. To study wind disturbances, the structure in Fig. 12 is proposed. That is, the wind is considered as external forces along three axes. Therefore, its effect on the quadrotor is like gravitational force. Therefore, these forces are added to gravitational force (effort). That is, the wind forces could be measured and sent to the controller via nozzles and strain gauges. The discussion

Simulation and results

For simulating the model and validity of equations and proposed solution, the structural parameters of a real quadrotor are used from [24]. These parameters are listed in Table 3.

The structure of the set points for simulations in the rest of the paper is [x y z φ θ ψ]. The units for position variables (x, y, z) and angles (φ, θ, ψ) are meters and degrees, respectively. The simulations for position set points are reflected in Fig. 13, Fig. 14, Fig. 15, Fig. 16.

In comparison with Fig. 14, Fig. 15

Conclusion

An FLC-PID controller was designed and utilized to handle full control on nonlinear and under-actuated structure of quadrotors. The model of quadrotor was considered in BG representation, which lacked a suitable and intelligent controller. It is also noteworthy that even the classic controllers for quadrotors modeled in BG were a few in number, and they did not present impressive results. Our results showed that lateral angles could be set near π/2, by which going far from the equilibrium point

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