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A compound fuzzy disturbance observer based on sliding modes is developed, and its application on flight simulator is presented. Fuzzy disturbance observer (FDO) is an effective method in nonlinear control. However, traditional FDO is confined to monitor dynamic disturbance, and the frequency bandwidth of the system is restricted. Sliding mode control (SMC) compensates the high-frequency component of disturbance while it is limited by the chattering phenomenon. The proposed method uses the sliding mode technique to deal with the uncompensated dynamic equivalent disturbance. The switching gain of sliding mode control designed according to the error of disturbance estimation is a small value. Therefore, the proposal also helps to decrease the chattering. The validity of the proposal method is confirmed by experiments on flight simulator.

Flight simulator simulates the attitude of aircraft and helps the ground experiments. High precision motion control is the key of a flight simulator, which influences the accuracy of simulation experiments. As a typical kind of servomotor system, the robustness against external nonlinear disturbances, time-varied characters, and modeling uncertainties is urgently required [

Fuzzy method, as a nonlinear method, has been studied with the basic idea that a fuzzy logic system can well approximate arbitrary highly nonlinear system [

Sliding mode control (SMC) can inhibit high-frequency disturbance by switching control value, which also causes chattering phenomenon. SMC is an effective approach to deal with nonlinear systems [

In this paper, a compound fuzzy disturbance observer (CFDO) based on sliding modes is proposed, and the task of disturbance compensation is divided into two parts. Low-frequency disturbance is compensated by FDO while high-frequency disturbance is treated by SMC. As low-frequency component is the main part of equivalent disturbance, SMC deals with only the secondary part of the disturbance. Consequently, the switching gain of SMC may be designed as a relative small value, and the chattering alleviation is achieved. The proposed method comprehended the advantages of both FDO and SMC. By using this method, the equivalent disturbance can be compensated more accurately, and the resonance caused by traditional methods in controlling elastic electromechanical systems can be avoided. Compared with the traditional proposed DOB and FDO schemes, CFDO has better robustness when there exists large nonlinear factors, decreases the modeling mismatch, and extends the frequency bandwidth of the systems. The model of disturbance is not required when the CFDO is designed. As a typical kind of servo motor system, the theoretic results in flight simulator can be used in other servo motion control systems.

The brief outline of the paper is as follows. In Section

Consider a system described as

Figure

Structure of the control system with fuzzy disturbance observer.

In order to achieve the compensation, the estimated value can be obtained by fuzzy logic system, which is described briefly here. The fuzzy inference engine uses the fuzzy IF-THEN rules to perform a mapping from an input compact set

The disturbance observation error

The FDO makes system response the same as the nominal model. Compared with DOB, FDO-based control has advantages on the robust stability and static performance when the system lacks mechanical stiffness. Unfortunately, some flight simulator systems are elastic electromechanical systems, and the use of DOB is restricted. Therefore, the FDO helps to improve the static performance and robustness of these flight simulators.

However, the nonlinear disturbance, such as friction, is composed of the components of many frequencies. The high-frequency components limit the system performance and the effect of FDO is limited in practice [

Consider the flight simulator system (

If

Structure of the control system with compound fuzzy disturbance observer.

In order to test the effect of the proposed method, an experiment is implemented by using a three-axis flight simulator shown in Figure

The three-axis flight simulator.

As in the previous discussion, FDO monitors both the internal and the external disturbance so that each axis of the flight simulator can be designed independently. Therefore, the pitch axis is chosen herein to verify the method. The controller design is based on the parameters which are acquired by identifying the flight simulator. The parameters of the nominal model are identified as

The fitting curves for frequency characteristics of actual plant and nominal model.

Gaussian membership functions.

Figure

The curves of the steady-state speed under DOB, FDO, and CFDO schemes.

Figure

The comparison of error curves and control value in the case of sin input (

Figure

The comparison of error curves and control value in the case of sin input (

Neither the steady-state error of FDO nor the error of CFDO is influenced by the extra constant disturbance, as FDO compensates the constant disturbance over time. However, under the condition of small time-varying disturbance like Figure

The part of sliding mode controller compensates the high-frequency component of disturbance and improves not only the robustness but also the dynamic performance of the system, meanwhile, the FDO deals with the low-frequency component of disturbance and helps to weaken the chattering. In consequence, they help each other to compensate the equivalent disturbance.

To a flight simulator system, the references are often slow-varying signals, which can be seen as static signals, in most part of an aircraft trajectory. In the last part of the trajectory, there will be fast-varying signals. CFDO meets the demand of these systems perfectly: FDO guarantees the accuracy, chattering is limited in most part of time, and SMC helps the system to respond fast while facing enormous variations.

This paper proposes a compound fuzzy disturbance observer based on sliding modes. The equivalent disturbance is sufficiently compensated by using the proposed CFDO when there exists huge modeling mismatch, and the disadvantages of FDO and SMC are avoided. The performance, especially the accuracy, of the system is improved. The switching gain of sliding mode controller is designed by disturbance estimation error, and the reduction of switching gain helps to weaken the chattering.

The method has been validated by experiments. By using the proposed method, the maximum tracking error decreases from 0.037 deg to 0.028 deg in low-frequency condition with the reference of

However, the coefficient about the fuzzy disturbance observer error can only be decided by trying in practice and an unsuitable parameter may lead to performance degradation or make the system unstable. In future work, better ways to decide switching gain will be studied and the fuzzy adjustable method will be optimized.

This work was supported by the National Natural Science Foundation of China (Grant no. 91216304).