Design & Optimization Fuzzy Logic Controller for General Helicopter Model

Transcription

1 Design & Optimization Fuzzy Logic Controller for General Helicopter Model Hasan A. AbuMeteir Graduated Student of Control Engineering IUG Gaza-Palestine Abstract Helicopter aviation is a difficult task that requires simultaneous manipulation of several controls in order to achieve a desired movement. Development of knowledge and skills are required for a person to be able to safely and efficiently navigate a helicopter. Therefore, the question was raised on whether there is a possibility to develop a robust agent that will act as an intermediate between the user and the helicopter conventional controls, which will enable even inexperienced users to fly a helicopter. Fuzzy Logic control is found suitable for this application, as it provides possibility to model human experience and skills. The helicopter fuzzy logic controller that was developed is capable to control the vertical displacement and orientation of a developed mathematical helicopter model. A Graphic User s Interface (GUI) has also been implemented to provide ability to the user to interactively change the parameters of the simulation, and perform different experiments and simulations. The GUI is also used to convey information back to the user by graphical representations or numerical displays. The whole system, mathematical helicopter model, fuzzy logic controller and GUI were developed using Matlab and its tools (Simulink, Fuzzy Logic Toolbox, and GUI Toolbox). The performance of the controller was found satisfactory as both the desired altitude and the heading are achieved and maintained. This first step has set the basis for further study and development of a fully autonomous aerial vehicle. The purpose of this paper design and optimization fuzzy logic control for general helicopter model. Keyword: Helicopter Model, Fuzzy Logic Control, PID Controller I. Introduction THE helicopter is specific in regards to other transportation means, not just by its structure but also by its motion possibilities. The helicopter can move vertically, float in the air, turn in place, move forward and lateral, and can perform these movements in combinations. Because of this, helicopter dynamics modeling is a very complex problem. In the present, problems in helicopter flight dynamics are mostly solved in aid of modern computers and software. In many complex problems, computers do not make it possible to understand the physical nature of the problem. Fortunately, many problems considering helicopters can be analyzed without overly complex calculus and with the use of simple formulas. Certain assumptions are taken into consideration in order to simplify the modeling procedure, such as that atmospheric and other disturbances are ignored. II. Problem Description and formulation A helicopter is generally and mainly controlled by three operating controls. Those controls are throttle, the collective pitch controller and the cyclic pitch controller. The collective pitch angle of a rotor blade is the angle between the chord line and a reference plane determined by the rotor 1

2 hub or the plane of rotation (Figure 1). The cyclic pitch angle is between the rotor disk and the air speed caused by tilting the rotor disk either up (positive) or down (negative) (Figure 2). The throttle main purpose is to control the angular speed of the main rotor. In this helicopter model, we are going to assume constant angular speed in order to focus more on the effect of the other controllers. The collective pitch control angles all blades equally and simultaneously and allows the aircraft to rise vertically (Figure3). The cyclic pitch control allows each blade to be angled individually and allows the aircraft to move forward or backward, nose upward or downward, and roll from side to side (Figure 4). A tail rotor is used to maintain yaw control and counteract the torque effect. By changing the pitch of the tail rotor's blades, this rotor will produce a side force that turns the helicopter nose left or right (Figure 5). There is also a coupling effect when using the cyclic pitch due to the angled lift that consists of vertical and horizontal force components. In this model, the helicopter will be controlled by entering four inputs: main rotor collective pitch angle, tail rotor collective pitch angle, longitudinal cyclic pitch angle and lateral cyclic pitch angle. The purpose of this paper is to design a controller able to stabilize the nonlinear helicopter model. Intelligent Autonomous Systems., two possible choices of control-strategies are available: Robust control and optimal control. As the use of robust control gives system-stability guarantees within defined boundaries, this choice of control would probably be suitable for autonomous helicopter applications because of the critical stability demands to these systems. However, robust control is likely to give a controller-performance reduction, compared to what is possible with optimal control. Because of the magnitude of the above-mentioned modelling task, the somewhat more challenging task of designing a robust controller for the helicopter system is considered to be beyond the scope of this project. Thus, fuzzy logic control is applied to the non-linear helicopter model. The two main purposes of the paper are summarized here: Development of a minimum-complexity helicopter simulation math model and implementation of this in the simulation environment SIMULINK. Design of a controller, using fuzzy logic control, to stabilize the model in a hover man oeuvre. To solve the above-mentioned tasks, several objectives need to be achieved: 2

3 1- Design of non-linear helicopter model: The first part which needs to be devised is a nonlinear model of the helicopter system. This model must approximate the behavior of the actual helicopter system as closely as possible. 2- Implementation of non-linear model: The non-linear model needs to be implemented in SIMULINK, for testing of the devised controller. 3- Design of linear helicopter-model: To design a linear controller, a linearized model is required. This model will be linearized using small-angle approximations and operating point linearization. 4- Design of fuzzy controller: Given the linear model, a fuzzy controller is designed. This controller must be able to stabilize the helicopter model in hover. 5- Test of fuzzy controller: Lastly the fuzzy controller needs to be tested to examine whether or not it is able to stabilize the model, and to determine the robustness of the controller. III. System Molding Considering the helicopter equations of motion in nonlinear form given by:,, In 6 degree of freedom form, the motion states and controls are:,,,,,,,,,, Starting from the following non-linearized form of equations of motion: By using the small perturbation theory in the form and by writing all forces in the following approximate form: Then the linearized equations of motion for the full six degrees of freedom can be written as: In fully expanded form, the system and control matrices can be written as: 3

4 The final model of the helicopter will be performed using SIMULINK. The entire model consists of three boxes in which the equations used in the model are derived and represented, this is sketched in Figure.6 Figure 6 (helicopter model with input output). IV. Fuzzy Controller The task of modeling and simulating human knowledge and intelligence has occupied a great part of the research world in the last decades. There are various examples of procedures were the knowledge for a formulated relation between the inputs and the outputs is unknown and therefore control cannot be achieved with conventional methods. Still, experienced users manage to efficiently control such processes without having absolute knowledge of the physics or mechanics behind them. In practice, the user consciously or subconsciously, uses rules that he has learned and which he constantly updates. These rules are the result of experience acquired out of continuous exposure and practice of the user to the certain process. The sum of all these rules that describe how a process should be controlled result to an intuitive model. Intelligent fuzzy controllers make use of these experience models and the description of the control rules is not analytic, but it is expressed in linguistic rules. The basic problems in the design of such a fuzzy controller are the representation of such an experienced model and knowledge in a concise and computational treatable way. To be able to succeed in such an attempt it is necessary to distinguish the different parts of our experience model. The basic parts of every fuzzy (experienced) model are displayed in the following Figure 7. For the development and implementation of a fuzzy controller, the required inputs and outputs must be determined first. The next step is to determine (approximately) the number, shape and width of the membership functions of the fuzzy inputs and outputs. 4

5 Figure7: Basic parts of a Fuzzy Controller. Then, the fuzzy rules must be set in a linguistic form that will describe the relation between the inputs and the outputs. An example of such a linguistic rule is the following where there are two inputs (speed, acceleration) and one output (action). If speed is reached and acceleration is increasing then action is brake When a values appear in the inputs of the fuzzy controller, certain fuzzy membership functions are enabled, each with a certain contribution rate (μj). Then, the rule base is determined which outputs membership functions are enabled from the inputs and what values should be applied to them. And according of the defuzzyfication method that was chosen, a unique discrete value is computed for each output. V. Design Fuzzy Controller Fuzzy Controller for longitude (X_Direction): The longitude (main rotor) control system consists of one fuzzy logic controller figure 8 which controls the main rotor collective command according to the required vertical displacement. Figure 8 Fuzzy Controller for longitude (X_Direction) As it can be view in the above figure the output of the S- function HeadingFuzzy (Heightpositional controller) is connected with and integrating scheme. There are also several of saturators before and after the controllers. The first fuzzy logic control consist of two input (Error, ErrorRate), and one output (LongConX). The inputs of the controller are the Error, which represents the difference between the current and the requested altitude of the helicopter model, and the ErrorRate, which is the rate that this error changes. The input Error consists of the following seven membership functions as displayed in Figure 9 5

6 -Big Negative Error (BNE): When the helicopter s altitude is a lot bigger than the controller s height set point value. Represents values of [-inf 1] m. - Negative Error(NEG): When the helicopter s altitude is a little bigger than the controller s height set point value. Represents values of [-5 1] m. -Small Negative Error (SNE): When the helicopter s altitude is a little bigger than the controller s height set point value. Represents values of [-1 0.1] m. - Zero (Zero): When the helicopter s altitude angle is the same as the controller s height set point value. Represents values of [ ] m. - Small Positive Error (SPE): When the helicopter s altitude is a little smaller than the controller s height set point value. Represents values of [0 1] m. -Positive Error (POS):When the helicopter s altitude is a little bigger than the controller s height set point value. Represents values of [.1 5 ] - Big Positive Error (BPE): ): When the helicopter s altitude is a lot smaller than the controller s height set point value. Represents values of [1 +inf] m. Figure 9 Error Input of X_Direction position Fuzzy Controller. The ErrorRate input, which represents the rate of the error input, also consists of seven membership functions as displayed in Figure 10 - Big NegativeErrorRate (BNER): When the error in altitude is decreasing very fast. Represents the values of [-inf 1] m/sec. - NegativeErrorRate(NEGR): When the error in altitude is decreasing fast. Represents the values of [-5.1] m/sec. - Small NegativeErrorRate (SNER): When the error in altitude is decreasing. Represents the error values of [-1 0 ] m/sec. - Zero Acceleration (Zero): When the error of the heading angle is not increasing or decreasing. Represents values of [ ] m/sec. - Small PositiveErrorRatre (SPER): When the error of in altitude is increasing. Represents values of [0.1] m/sec. - PositiveErrorRate (PER): When the error of in altitude is increasing. Represents values of [.1 5] m/sec. 6

7 - Big PositiveErrorRate (BPER): When the error of in altitude is increasing very fast. Represents values of [1 +inf] m/sec. Figure 10 ErrorRate The LongConX output of the main rotor collective fuzzy controller consists of seven membership functions as displayed in Figure 11 - Big Negative longitude (BNL): Big reduction of the main rotor s angle. Represents the angle values of [-inf 3.34] degrees. - Medium Negative longitude (EMNL): Normal reduction of the main rotor s angle. Represents values of [-5 1] degrees. - Small Negative longitude (SNL): Small reduction of the main rotor s angle. Represents the angle values of [-3 -.1] degrees. - Zero(Zero): No change of the main rotor s angle. Represents the values of [ ]. - SmallPositive longitude (SPL): Small increase of the main rotor s angle. Represents the angle values of [1 3] degrees. - Medium Positive longitude (PMNL): Normal increase of the main rotor s angle. Represents the angle values of [1 5] degrees. - Big Positive longitude (BPL): Big increase of the main rotor s angle. Represents the angle values of [3.34 +inf] degrees. Figure 11: Longitude Control X_ Direction Output The rules to for the Longitude control are simple. The helicopter pilot increases the collective angle when there is need to gain Longitude, and decreases it when there is need to lose Longitude. The collective command is kept in a certain angle when the pilot wants to hover. Each altitude has a different hovering angle as air density and temperature contribute greatly to the thrust of the helicopter s main rotor blades. 7

8 VI. Results After simulate helicopter model in GUI Matla we can see if we introduce a desired input to the stabilized system the response is unstable like: After designing a PD controller of block diagram like: atitude Y D_Y D_X set piont Out1 feedback PD Distance y set point Out1 feedback PD Distance X u_lat u_long position Y B_1c Z X altitude Z B_1c To Workspace3 Flapping 1c Helicopter_translation Helicopter_rotation flapping s 1 flapping c 1 VR system1 D_altitude set point Out1 feedback PD altitude u_col velocity position1 X speed 9 speed 8 speed 7 angular velocity B_1s u_pedal u_ped Subsystem atitude1 B_1s To Workspace4 Flapping 1s speed 12 speed 11 speed 10 PD Control signal _XDirection PD Control signal _ZDirection PD Control signal _YDirection cntx To Workspace cnty To Workspace1 cntz To Workspace2 Translatory velocities Rotary velocities Attitude 8

9 The system still unstable: The problem of the complex system was not solved so we are going to design a fuzzy controller The problem of the complex system was not solved so we are going to design a fuzzy controller of 4 rule base sets and compare results 9

10 VII. Conclusion As we see, we apply different approach in the helicopter model (open loop, open PID,and fuzzy controller ). In open loop the response in not staple, and open PID. In fuzzy controller, we apply different rules bases and getting result better than from the first and second approach VIII. References [1] Fahad A Al Mahmood, Constructing & Simulating a Mathematical Model of Longitudinal Helicopter Flight Dynamics. [2] H. AbuMeteir & M.deep, Design Fuzzy Controller for Helicopter Model,2009 [3] Dimitrios Iakovou, Fuzzy Control for Helicopter Aviation,