چكيده به لاتين
Sliding Mode Control (SMC) is a robust control scheme that has a good performance to overcome nonlinearities, time varying parameters, disturbances and plant uncertainties. This method is effective when the bound of the uncertainties are known. A conventional sliding mode controller is designed using a presumed upper bound of uncertainties, as a control parameter, which may generate excessively large amplitude chatters in the control input. The recently introduced Adaptive Fuzzy Sliding Mode Control (AFSMC) and Adaptive Sliding Mode Observer (AFSMO) methodology have the advantage that the upper bound of the uncertainty can be estimated on line, even when the exact knowledge of the plant nonlinear dynamics is not available. The AFSMC method can be either in direct or indirect forms. In the direct approach, the ideal controller is designed exactly as in the SMC scheme, where the nonlinear equations of the system are employed, except that an adaptively-tuned fuzzy inference system is employed to estimate the model-based part of the conventional SMC method. Furthermore, the upper bound of the plant uncertainty is adaptively estimated.
In this research, the application of the AFSMC and AFSMO to the complicated and industrial problems of flight simulator and task-space hybrid position/force control of Stewart Manipulator (SM) is proposed for the first time. The first contribution of this thesis is extending and mixing the conventional AFSMC method with AFSMO for state-dependent, non-diagonal and non-positive definite input gain matrix. The second contribution of this thesis is extending the conventional AFSMC method for nonlinear continuous time systems with state-dependent upper bound of the uncertainties.
To validate the feasibility of the proposed method, simulations and experimental results are presented for position control of SM. SM is a parallel robot with 6 degrees of freedom (DOF). It consists of two plates named Moving Platform (MP) and Bottom Platform (BP) that are connected to each other with six arms. The actuators are located on prismatic joints, i.e., the arms can be extended or shortened. The SM has impressive features, including high load carrying capacity, low inertia, high stiffness, very good repeatability and positioning accuracy. Important applications of the SM include flight moving simulators and machining tools.
For hybrid position/force control of the SM, a complete dynamic model of the system is obtained, and then reduced into a simpler dynamic system, by neglecting the very complex terms related to the inertial, centrifugal and gravitational effects of the legs. The remaining terms which are associated with the dynamics of the MP are much simpler and more manageable from the control strategy point of view. The neglected terms are considered as un-modeled dynamics, for which an extended form of the adaptive fuzzy sliding mode controller and observer (E-AFSMCO) is employed. The reduced dynamic model of the SM is converted to affine form, with an input gain matrix which is neither diagonal nor positive definite and state-dependent. This peculiarity prevents the application of conventional AFSMC methodology for control of such a manipulator. In this research, the mentioned limitations of the conventional AFSMC method are relaxed by employing a particular decomposition of the gain matrix. In the conventional SMC control method, the ideal controller is constructed as a model-based sliding mode scheme. In the E-AFSMCO approach, a simple Takagi-Sugeno (TS) fuzzy system is used as a replacement for the ideal controller. An adaptation law and a robust switching strategy compensate the differences between the fuzzy controller and the unknown ideal controller. Unlike the conventional sliding mode method, the upper bound of the plant lumped uncertainty is estimated using an adaptive scheme, which prevents the excessive switching of the robust part of the controller. Robot’s environment is considered as an elastic and deformable material, which is described by Hunt-Crossley nonlinear dynamic model. These parameters are estimated using Modified Extended Kalman Filter (MEKF) for the first time, which is effective for nonlinear recursive problems. The second Lyapunov theorem is used to prove the closed-loop asymptotic stability. Numerical simulations and experimental implementation depict the effectiveness of the proposed controller and observer in comparison with the conventional sliding mode control method with nonlinear observer.
