Stabilization And Trajectory Tracking Of Underactuated Systems Based On T-S Fuzzy Descriptor Model

Since the underactuated system has the characteristics that the independent control input dimension is smaller than the mechanical structure's freedom of motion,such a system can effectively reduce cost,weight,volume,energy consumption,etc.A large number of underactuated robots are widely used in modern industrial,military,agricultural,and service industries.However,the underactuated system has complete constraints or non-holonomic constraints.The dynamic model also has uncertainties and external disturbances,including system parameters that are difficult to accurately estimate or experimentally measure,measure noise,and some unmodeled power.It is difficult to obtain accurate system dynamics models.The dynamic coupling between the system's actuated states and the system's underactuated states is difficult to quantify and describe nonlinear characteristics,which making it difficult to design controllers directly with traditional nonlinear control methods and linear control theory.At the same time,it is almost impossible to accurately measure the system's states in practice,and the controller is difficult to accurately use in the actual underactuated system.These factors present a significant challenge for the precise control of underactuated systems.Therefore,this paper establishes the T-S fuzzy decriptor model of underactuated system,proposes an advanced integral sliding mode control method,and studies the stabilization and tracking problem of underactuated system based on the integral sliding mode control method.The specific research contents are as follows:?1?Based on the previous research,the basic knowledge of sector nonlinear theory is used to further improve the modeling method based on TS fuzzy theory,and the inverted pendulum,overhead crane and two-wheel self-balancing trolley are constructed.The TS fuzzy singular system realizes the goal of approximating the nonlinear model of the underactuated system with a set of local linear models with arbitrary precision in the global range,and lays a foundation for the research of the sliding mode control algorithm for stabilization and tracking.Via simulation analysis,the obtained T-S fuzzy descriptor model can accurately describe the underactuated system.At the same time,the results show that the T-S fuzzy descriptor system obtained by the descriptor system representation is not artificially introduced into different input matrices,and the number of its fuzzy rules is reduced.?2?The problem of integral sliding mode control based on T-S fuzzy descriptor system is studied.Firstly,the augmented system equivalent to the original T-S fuzzy descriptor system pulse is given.The non-parallel distributed compensation method is combined with the design principle of the integral sliding mode controller to obtain the sliding modal system.By using Lyapunov stability theory,the Lyapunov function which depends on the membership function₆)????and?₄)????is designed.The sufficient condition that the system is asymptotically stable is obtained,and a general fuzzy integral sliding mode controller is proposed.The existing T-S fuzzy integral sliding mode control method has almost strict assumptions on the system matrix,such as requiring the input matrix to be equal and the parameter matrix to satisfy Hurwitz.Based on the research method of T-S fuzzy descriptor model,the strict assumptions of the system matrix are removed.Finally,a simulation example shows that the obtained theory reduces the conservativeness of the system design,expands the feasible domain,and demonstrates the effectiveness of the designed sliding mode controller.?3?Aiming at the uncertains and external disturbances of T-S fuzzy descriptor system,the dissipative integral sliding mode control strategy is proposed based on the dissipative theory,which leads to the stability of the system with strict dissipative performance.Dissipativeness can be seen as a more general performance indicator,including H?performance indicator constraints and strict passive performance indicator constraints.The dissipative performance index ensures that the closed-loop system has effective suppression of the underactuation system uncertainties and external disturbances,improves the transient performance of the unsteady system,and improves the robustness of the closed-loop system.On the basis of the existing dissipative integral sliding mode controller,an adaptive compensation controller and an adaptive parameter controller are introduced to compensate the uncertainties and external disturbances that satisfy the matching conditions.The adaptive parameter controller is used.The control gain can be automatically adjusted according to the system state,and the uncertainty can be compensated without knowing the bounds of the uncertainty in advance.Finally,through the simulation analysis of the overhead crane system,the correctness of the theoretical results and the designed dissipative sliding mode controller can effectively deal with the uncertainties and external interferences.?4?The integral sliding mode observer and control problem of T-S fuzzy descriptor systems with unpredictable antecedent variables are studied.An augmentation system equivalent to the pulse of the original system and the observer dynamics system is given.According to the constraints of the system itself,the system matrix is decoupled from the Lyapunov matrix by Finsler lemma through some equivalent linear transformations.At the same time,in order to use Finsler to remove the coupling between the observer gain matrix and the controller gain matrix and the Lyapunov matrix,the corresponding auxiliary variables are introduced into the system,and the augmentation method is adopted to increase the dimension of the system.The observer gain and the integral sliding mode controller gain are determined by a single-step algorithm.The observer-based integral sliding mode control strategy is proposed in the form of linear matrix inequalities.Finally,numerical examples are given to verify the effectiveness of the proposed method,and the results have lower design conservation.?5?The non-fragile integral sliding mode observer and controller design problem with unpredictable antecedent variable T-S fuzzy descriptor systems is studied.The designed observer and controller are assumed to have multiplier observer gain perturbation and multiply controller gain perturbation.Based on the linear matrix inequality,a series of systematic design methods based on T-S fuzzy descriptor systems for state observer design,integral sliding mode controller design,uncertainty compensation and non-fragility analysis are proposed.Finally,the inverted pendulum system is simulated and analyzed.The obtained results not only compensate the observer and controller perturbation,but also compensate the system uncertainties.?6?The self-balancing control and motion tracking control of two-wheel self-balancing trolley based on T-S fuzzy descriptor model are studied.Firstly,the difficult problems of two-wheel self-balancing trolley motion control are analyzed.The dynamic model is given and its T-S fuzzy descriptor model is established.Secondly,combined with the design results of Chapters3 and 4,the H?integral sliding mode observation and self-balancing controller of two-wheel self-balancing trolley based on T-S fuzzy descriptor model are designed.Finally,for the motion tracking control problem of two-wheel self-balancing trolley,the fuzzy position controller and fuzzy yaw angle controller are designed by Mamdani fuzzy theory.Through simulation verification,the integral sliding mode H?self-balancing controller based on T-S fuzzy generalized model designed in this chapter can balance the two-wheel self-balancing trolley,make the closed-loop fuzzy system stable,and meet a given H?performance index.