1)Change the structure of the control system.  Apply the supervisory fuzzy SMC .

However, we need to remember that this approach usually decreases the controller

performance to some degree.

2) in fuzzy set we also check the rule table. but which parameter is more important in rule table????

Originally you use a sliding mode control, why you have integrate a fuzzy logic control with your SMC. I think that SMC alone is enough to get good performances for your system. because in your case, while your control scheme become more complicated, you will get the same responses as without fuzzy logic.

It is my view, maybe i am wrong.

I think as Nadir Kabache about SMC, however, I think that the combination with fuzzy logic could have some advantage, which?. Also, I think that if we use linear Takagi-Sugeno fuzzy models as an approximation of the non-linear model, this approximation can be very close to the non-linear system and the controllers designed for this set of linear models can guarantee stability and performance (so I disagree with Monica Patrascu). Any linear control technique can be applied, including SMC for linear systems.

In such cases Robust Control  Methods may be tried. Please see whether the Following Articles will be useful.

Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design. Robust control methods are designed to function properly so long as uncertain parameters or disturbances are within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modeling errors.

Link:   http://en.wikipedia.org/wiki/Robust_control

1.  Journal of Control Engineering and Technology JCET

Robust Adaptive Type-2 Fuzzy Sliding Mode Control for Non-Linear uncertain SISO systems

Ayman Al-Khazraji, Karim M Aljebory

Abstract-

This paper deals with the synthesis of adaptive type-2 fuzzy logic controller for a class of single-input single-output system. Due to its ability in serving in universal approximation, the type-2 fuzzy logic system is used to approximate the unknown system dynamics, which will be adjusted according to the on-line adaptation laws deduced from the stability analysis. To ensure the closed loop system robustness, a modified sliding mode control signal is used. In this work, variable sliding surface is replaced by type-2 fuzzy logic system in order to reduce the starting energy without deteriorating the tracking performances. Furthermore, the knowledge of the upper bounds of the external disturbances and also the approximation errors is not needed. The global stability of the closed loop system is guaranteed in the sense of Lyapunov. As well, all signals involved are uniformly bounded. Finally, experiment results are presented to show the performance of the developed approach.

Keywords

- Adaptive control; Type-2 fuzzy logic system; sliding mode control; nonlinear system control

Link:   http://www.vkingpub.com/UploadFiles/2014-08/372/201408221648583343.pdf

2.  Type-2 fuzzy sliding mode control without reaching phase for nonlinear system

Ayman Al-khazraji, Najib Essounbouli , Abdelaziz Hamzaoui ,Frédéric Nollet ,

Janan Zaytoon

Abstract

A new sliding mode control (SMC) algorithm for the nth order nonlinear system suffering from parameters uncertainty and subjected to an external perturbation is proposed. The algorithm employs a time-varying switching plane. At the initial time t=t0, the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the plane moves to the origin of the state space. Since the nonlinear system is sensible to the perturbations and uncertainties during the reaching phase, the elimination of such phase yields in a considerable amelioration of system robustness. Switching plane is chosen such that: (1) the reaching phase is eliminated, (2) the nonlinear system is insensitive to the external disturbance and the model uncertainty from the initial time (3) the convergence of the tracking error to zero. Furthermore, a Type-2 fuzzy system is used to approximate system dynamics (assumed to be unknown) and to construct the equivalent controller such that: (1) all signals of closed-loop system are uniformly ultimately bounded, (2) the problems related to adaptive fuzzy controllers like singularity and constraints on the control gain are resolved. To ensure the robustness of the overall closed-loop system, analytical demonstration using Lyapunov theorem is considered. Finally, a robot manipulator is considered as a real time system in order to confirm the efficiency of the proposed approach. The experimentation is done for both regulation and tracking control problems.

Keywords

Sliding mode control;Type-2 fuzzy systems;Robustness;Tracking control; Non-linear systems

Link:   http://www.sciencedirect.com/science/article/pii/S0952197610001752

3.  Iranian Journal of Fuzzy Systems Vol. 3, No. 2, (2006) pp. 33-51

Received: August 2005; Accepted: June 2006

Key words and phrases: Nonlinear control, Fuzzy logic, Sliding mode control, Uncertainty, External

disturbances, Duffing forced-oscillation, Adaptive PI control.

DIRECT ADAPTIVE FUZZY PI SLIDING MODE CONTROL OF SYSTEMS

WITH UNKNOWN BUT BOUNDED DISTURBANCES

M. -R. AKBARZADEH -T. AND R. SHAHNAZI

ABSTRACT. An asymptotically stable direct adaptive fuzzy PI sliding mode

controller is proposed for a class of nonlinear uncertain systems. In contrast to

other existing approaches of handling disturbances, the proposed approach

does not require this bound to be known, only requiring that it exists.

Moreover, a PI control structure is used to attenuate chattering. The approach

is applied to stabilize an open-loop unstable nonlinear system as well as

the Duffing forced-oscillation chaotic nonlinear system amid significant

disturbances. Analysis of simulations reveals the effectiveness of the proposed

method in terms of a significant reduction in chattering while maintaining

asymptotic convergence.

Link:   journals.usb.ac.ir/Fuzzy/en-us/Articles/Article_68

P.S.

I think the same things that Nadege Kabache

I definitely disagree with the statement of Monica Patrascu "fuzzy never guarantees stability". A countless number of  papers has been published especially on "Sliding mode fuzzy control" or "Fuzzy sliding mode control" (see Palm 1992,1994) and on TS-fuzzy control systems (see K.Tanaka, 1992). The reason for instability of a fuzzy SMC can be manifold as it also could be for a classical one. Sources of instability could be a wrong choice of the output scaling factor or the neglection of  the finite sample time of the system.

Another thing is when the fuzzy controller is a little expert system  describing indirectly  the system to be controlled (e.g. a chemical process) and the operator's expert knowledge at the same time. In this case a stability analysis is quite difficult to accomplish and an according guarantee for stability is hard to be given.