Research On Robust Control For Fuzzy Uncertain Mechanical Systems With Parameters Optimization Based On Game Theories

Mechanical systems need to improve performance and reduce control cost to satisfy complicated requirements with the development of the industry,placing higher demands on control design and parameter optimization,etc.Among many factors that limit control affects,uncertainty has a significant impact on system performance and control cost,which has drawn extensive attention recently.Various related approaches and theories are proposed accordingly.However,the following key issues still need to be explored in-depth:(1)Due to the existence of uncertainty,the system occurs with overshoot or jitter resulting in excessive system output and control input.Therefore,the boundary problem of uncertain systems should be considered to limit the output and input values.(2)Traditional mathematical or physical models cannot reflect unknown uncertainties,resulting in controllers that cannot accurately compensate.Finding a method that can correctly describe the uncertainty is a key issue in improving the system performance.(3)Facing the complex working environment,the variable uncertainties constantly change the control requirements.Therefore,the controller of a mechanical system should be able to trade off system performance and control cost with robustness and practicality.To address the above difficulties,the control method must compensate for the uncertainty while efficiently seeking optimal values of control parameters.The dissertation explored the influence of uncertainty on mechanical systems through simulations and experiments and gave a complete control method based on theoretical derivations and mathematical proofs concerning the process of setting system output and control input boundaries,design the high precision controller,and optimizing control parameters,respectively.The main research contents include:(1)To set the boundary range based on the diffeomorphism principle for the phenomenon that uncertainty leads to excessive system output and control input.(2)To establish an accurate fuzzy dynamical model of the mechanical system based on fuzzy theory to address the limitations of traditional uncertainty description approaches.(3)To design a novel robust control based on Lyapunov theory to solve the problem of unsatisfactory control cost and effect.(4)To propose a classification and solution method for control parameters optimization based on game theory for the disadvantage of low solving efficiency in complex optimization problems.(5)To conduct experimental validations based on different complex mechanical systems for control requirements under different practical situations.The specific research results of this dissertation are as follows.(1)To reduce the influence of uncertainty,the boundary setting of the mechanical system is used by imposing and dealing with inequality constraints.Firstly,a control input diffeomorphism approach(CIDA)is proposed to solve the input boundary problem by constructing auxiliary functions,with the input values limited by upper and lower bounds.Secondly,a state transformation approach(STA)is proposed to convert the constrained system output to an unconstrained form.Then,the maximum value of the system output is limited to the desired range.Finally,the effectiveness of the approach is verified by simulations.(2)To study the uncertain mechanical system,the analysis focuses on the uncertainty and its effects.Firstly,an approach to describe time-varying but bounded uncertainty is proposed based on fuzzy set theory,employing the concept of occurrence degree to characterize the degree of influence of uncertainty.Combining this approach with the matching condition,the uncertainty in the dynamical model of the mechanical system can be separated.As a result,the uncertain portions and the nominal portions without uncertainty are obtained.The uncertain portions are within the prescribed fuzzy set;the bounds are the fuzzy numbers.This gives a new description for characterizing the nature of uncertainty.(3)To improve the control effect and practicality of the control algorithm,a high-order robust control(HORC)is designed for fuzzy dynamical models.Based on the Lyapunov approach,it is demonstrated that the controller can accurately compensate for the uncertainty described by the fuzzy-based approach and guarantee uniform boundedness and uniform ultimate boundedness.The control design has three main advantages over classical robust controllers.All matrices and parameters in this control are deterministic,improving calculation efficiency.The high-order term quickly stabilizes the system,improving convergence speed.The flexibility of choosing the tunable parameters balances the system performance and control cost.The results of the theoretical analysis are verified by simulation,clarifying how the controller affects the system performance and control cost and laying the foundation for the formulation of the optimization problem.(4)To balance the performance and control cost of the uncertain mechanical system,the relationships among the control parameters in HORC,control cost,and system performance are studied.A game theory-based optimization approach(GTOA)for classifying and solving the optimization problem is proposed.Firstly,the players and decision sets in the game are defined and two cost functions are presented.Secondly,the mathematical expressions of game logic and steps to solve the Pareto-optimality,Nash equilibrium,and sequential optimal point are given.Finally,the accumulative errors and accumulative control inputs under different optimal values are obtained by simulation and compared with the results under LQR control.The results show that the optimal control parameters solved based on the Stackelberg game maximize the system performance while reducing the control cost,proving the classification and solution approach effectiveness.(5)To verify the control method,the experiment platforms of a permanent magnet synchronous rotary motor(PMSM)and a collaborative robot are established,with corresponding sets of comparison experiments designed and conducted.The experimental results show that the control method based on optimal control parameters can solve the boundary problem of the uncertain mechanical system and improve the system performance with a small control cost,meeting the expected control requirements and research targets.In conclusion,this study proposes a complete control method based on strict mathematical derivations and proofs for the performance and control cost of uncertain mechanical systems.The above theoretical method is verified to be able to satisfy the control requirements in complex environments and solve practical engineering problems through multiple sets of simulations and experiments.This dissertation provides a complete and universal control method for uncertain mechanical systems with theoretical support.