Study On Prescribed Performance Control Method In Nonlinear Mechanical Systems

With comprehensive consideration of the modelling errors,parameter uncertainties,actuator faults and external disturbance,it shows great importance both in theory and application to achieve an autonomously reliable control protocol with guaranteed transient and steady-state performance for the nonlinear systems.This dissertation aims at solving the control problems existed in a class of single input single output(SISO)or multiple input multiple output(MIMO)mechanical systems.Faced with the unknown system dynamics,actuator faults and multiple disturbances,this dissertation investigates the prescribed performance control(PPC)method for some typical mechanical systems with the purpose of improving the transient and steady-state performance via a low-complexity control effort.The main innovative research work and results are listed as follows:(1)Research on the neural state observer-based PPC method for a class of mechanical systems subject to unknown nonlinearities for the SISO.First,a radial basis neural network(RBFNN)is applied to approximate the unknown nonlinearities existed in the mechanical model.And based on the approximated results,a state observer is designed to estimate the unknown system states.Then,via applying the backstepping and dynamic surface control techniques,an adaptive prescribed performance controller is devised along with a detailed stability analysis based on the Lyapunov theory.The adaptive preset performance control method proposed in this paper does not use the complex error conversion process and does not need continuous high-order derivation of the virtual controller under the premise of ensuring the transient and steady-state performance of the tracking error system.Therefore,the complexity of the controller is low and it is easier to obtain on-line.Finally,two groups of numerical simulations for a single robotic manipulator are organized to validate the effectiveness of the proposed control methods.The simulation results demonstrate the transient and steady-state performance is achieved with the estimated states under the proposed control methods.(2)Research on the fault-tolerant PPC method for a class of MIMO mechanical systems subject to actuator faults.First,a Euler-Lagrange model is used to described the MIMO mechanical systems with actuator faults.Then,a barrier Lyapunov function is used to handle the performance constraints imposed on the state variables.And an adaptive fault-tolerant controller is designed via exploring the backstepping technique.In the meanwhile,the Lyapunov theory is applied to analyze the stability of the developed controller and adaptive scheme.The advantages of the proposed one are twofold: the transient and steady-state performance of the controlled systems can be preassigned a priori.Moreover,no extra estimations for the actuator fault types and parameters are required,which great lowers the complexity of the relevant control systems.Finally,three groups of illustrative examples for the second-order robotic manipulators are organized to verify the effectiveness of the proposed control methods.Based on the simulation results,it shows that the proposed fault-tolerant PPC control method has prominent superiorities in terms of robustness and tracking accuracy in the presence of unknown actuator faults and disturbances.(3)Research on the Extended State Observer-based(ESO)-based PPC method for a class of MIMO mechanical systems subject to multiple-source disturbances.First,an extended state observer(ESO)is devised to estimate the lumped uncertainties and multiple-source disturbances.Then,based on the estimated results,the backstepping technique is applied to develop a robust prescribed performance compensation controller with a detailed stability analysis.The proposed one integrates the advantages of the ESO and PPC to preassign the tracking performance and disturbance suppression simultaneously.Finally,simulations on the robotic joint angle systems are organized to validate the effectiveness of the proposed control methods with respect to the lower complexity and disturbance rejection.In the meanwhile,compared with the traditional PD control method,the proposed one is superior in terms of guaranteed the transient and steady-state performance under the similar computational complexity and control input.(4)Research on the low-complexity distributed PPC method for multiple MIMO mechanical systems.First,some basic preliminary knowledge on the graph theory is introduced along with a brief description of the distributed leader-following systems.Meanwhile,the performance envelope is designed for the leader-following position tracking errors.Then,by applying norm bounding technique and Lyapunov theory,a low-complexity model-free distributed PPC controller is developed along with a sound stability analysis.The unknown nonlinear dynamic model is not required to estimate online.This decreases the complexity of the relevant controller while the tracking performance is guaranteed a priori.Finally,three groups of numerical examples are organized to validate the effectiveness of the proposed control methods in terms of guarantee the leader-following tracking errors.Compared with the traditional distributed PD control methods,a faster convergence rate and higher tracking accuracy are achieved with similar computational complexity and control input under the proposed one.68 figures and 154 references are included in this paper.