New Approach to a Hybrid Fuzzy-Sliding Mode Control to a Brushless AC Motor Scheme

— This paper deals with fuzzy-sliding mode control strategies of a Brushless AC Motor. The system combines the performance of fuzzy logic control and sliding mode control. Sliding mode control scheme, fuzzy logic controller strategies and the hybrid fuzzy-sliding mode controller were simulated with Matlab/ Simulink for comparison. Behind this strategy, the main objective is to improve the performance of the fuzzy-sliding mode control scheme. An experimentation, where all the command were implemented to an MSK23335 Board with a PM50 module and a 90W BLAC Motor is used to validate all the result.

So, in this paper, an attempt is made to develop a methodology using a Sliding Mode Controller combined with a Fuzzy Logic Controller applied to control a Brushless AC Motor drive. This hybrid controller is developed [9], [10].
After the introduction about the paper, the structure of the proposed system is given. The Brushless AC modeling is shown before applying all the controller. These controllers are: vector control, SMC and FLC. An approach of the hybrid fuzzy-siding mode controller is developed in the next section. The SMC strategy is applied to the BLAC motor for more comprehension of the system. The next one deals with the simulation and experimentation of the proposed methodology through respectively the Matlab and Simulink environment and an MSK development kit [11]. Results and discussions gives more details of the objectives of this study. This report is closed by conclusions.

II. PROPOSED SYSTEM
The system, showed by figure Fig. 1, is composed of a DC Sources or an AC/DC converter, the three phase PWM Inverter, the controller and the Brushless Motor. Closed loop control of the brushless motor is used to minimize the presence of parameter variation and load disturbance [3].

C. Motion equation
The electromagnetic torque is expressed as according to currents and flux by: where, m J the total inertia, f the viscous friction coefficient.

D. Park d-q model for a BLAC Motor
Then, in the static d-q presentation, a brushless dc motor can be presented by:  The inverter is modeled by: 2 1 1 V. CONTROL STRATEGY In this part, vector control, sliding mode control, fuzzy logic control and the hybrid controller combined by sliding mode control and fuzzy logic control are presented for more comprehension of control scheme.

A. Vector control
The more often strategy used consists to maintain the induced reaction flux in quadrature with the rotor flux or replace the magnets by a spool crossed by a current constant If which produces a flux equivalent to the one of the magnets. 0 The evolution of the couple follows the one of Iq because the flux and the current remained in quadrature. Then, the electromechanical torque is defined by: In this paper, direct vector control of a brushless ac is adopted. A classical PI controller is given by,

B. Sliding Mode Control
The basic idea of SMC is to bring a system in an area properly selected and then, design a control law to maintain the system in this area [5]. Usually, the SMC goes through three stages as follows: The general form of the switching surface is given by the equation below [ (9) With e : the error (Xd -X), λ : the measured signals and n the order of the system.
The convergence condition is defined by the Lyapunov equation [5]; it is the condition to ensure the area to be attractive and invariant.
Where the control signal is u, the equivalent control signal given by ueq and the switching control term un.
The equivalent control signal is calculated with the conditions: In the general cases, relation (13) gives the function for the switching control term, . .
In relation (14), a proportional term is added with the first expression of the relation (13). It is made to increase the attraction. .
Where k and k 1 are constant positive.

C. Fuzzy Logic Control
This method avoids modelling the process but having knowledge of its behaviour is required. The reasoning is close to human perception.
Nowadays, the fuzzy controller begins to take an important place in electrical applications. It can be used for optimization and command, [7], [8]. The common scheme for a Fuzzy controller is given in Fig. 3. With, e: error, de: error variation, di: controller output. The fuzzification consists in projecting a real physical variable distributed on the domains variable characterizing this variable: linguistic variable is so obtained and then the fuzzification makes it possible to have a precise measurement of the membership degree of the real variable to each fuzzy subset.

International Journal of Engineering
Generally, the inference method is a logical operation by which one admits a proposal under the terms of its relation with other proposals held for true. At this stage, rules are established by the knowledge of the desired behavior of the system. They are often as: Here, x1 and x2 are the inputs and sk the output which is also a linguistic variable. Membership function may be also defined for the output variable. There are several inference methods, which may be applied.
The results of the aggregation of the inference rules still give fuzzy variables. To be used in a real control, these fuzzy variables must be translated into real or numerical variables: it is the function of the defuzzification block. Here, there are also some methods for the defuzzification.
In this paper, the Sugeno's methods are chosen: for the fuzzy inference, a singleton is used as the membership function of the rule consequent combined by the (max-min) method for the rule evaluation. Thus in relation (15), C is a constant. The Sugeno defuzzification is then a weighted average method.
For the two inputs (e, de), the triangular and trapezoidal forms are used.
The number of the membership functions of membership N=5 is adopted. For the output, the function of membership of the output is as singleton. Table 1 gives the inference matrix. The

D. Fuzzy Sliding Mode Control
This new hybrid controller is a derivative of the scheme proposed in [9], [10]. Here, the switching control term is replaced by a command resulting from fuzzy logic controller (FLC). It is showed by the relation (18)

A. Simulation model
Matlab Environment is used for the implementation of the brushless dc motor modelling.  Fig. 6, Fig. 7, Fig. 8 and Fig. 9 show the results of the simulation with all the controllers in Matlab environment. The system combined the robustness of the SM controller with the performance of the FL Controller.

A. Experimental platform
The platform [8] is composed by a MSK23335 board. This MSK is used for the implementation which all the parts are: 1, is the DSP controller and the power supply, 2, is the BLDC motor, 3, is an intelligent controller for commanding the load effect in a specified time, 4, is the load (another BLDC motor).  Fig. 12, Fig. 13 and Fig. 14 Fig. 15 shows more details about the confirmation below. As shown in (a), all the results are presented. In (b), at the start time, the application of the SMC controller presents more oscillation into the speed results.

Experimental results
And the use of fuzzy-sliding mode control to the system rejects the perturbation and reduces the overshoot into 0%. In All the experimental results are resumed in Fig. 16 (a). The configuration used here is look like the simulation consign. In (b), the use of a fuzzy-sliding mode control (SMCFLC) gives a conclude result for controlling the system. All the simulation and the experiment results show that the proposed hybrid controllers based on SMC-FLC are realizable and give good performances as disturbance rejection, good behavior in respect of variation parameter.

X. CONCLUSION
Vector control, Sliding Mode Control, Fuzzy Logic Control and Fuzzy-sliding mode control are used to control a Brushless AC Motor.
The method based on the hybrid controller is proposed and applied. The result shows the effectiveness and performance of this method. In this paper, it is highlighted that the SMC-FLC is the best controller.