This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation.Based on the bounds on the growth rates of the nonlinear uncertain function in the sy...This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation.Based on the bounds on the growth rates of the nonlinear uncertain function in the system model,the system is placed in a linear differential inclusion.Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation.By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law,we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system.The equilibrium point corresponds to the desired set point for the system output.Thus,the location of the equilibrium point and the size of the domain of attraction determine,respectively,the set point that the output can achieve and the range of initial conditions from which this set point can be reached.Based on these conditions,the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities(LMIs).Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.展开更多
A characteristic model based all-coefficient adaptive control law was recently implemented on an experimental test rig for high-speed energy storage flywheels suspended on magnetic bearings. Such a control law is an i...A characteristic model based all-coefficient adaptive control law was recently implemented on an experimental test rig for high-speed energy storage flywheels suspended on magnetic bearings. Such a control law is an intelligent control law, as its design does not rely on a pre-established mathematical model of a plant but identifies its characteristic model while the plant is being controlled. Extensive numerical simulations and experimental results indicated that this intelligent control law outperforms a μ-synthesis control law, originally designed when the experimental platform was built in terms of their ability to suppress vibration on the high-speed test rig. We further establish, through an extensive simulation, that this intelligent control law possesses considerable robustness with respect to plant uncertainties, external disturbances, and time delay.展开更多
基金This work was supported in part by the Fundamental Research Funds for the Central Universities,China(2662018QD031)the National Natural Science Foundation of China(51905205).
文摘This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation.Based on the bounds on the growth rates of the nonlinear uncertain function in the system model,the system is placed in a linear differential inclusion.Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation.By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law,we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system.The equilibrium point corresponds to the desired set point for the system output.Thus,the location of the equilibrium point and the size of the domain of attraction determine,respectively,the set point that the output can achieve and the range of initial conditions from which this set point can be reached.Based on these conditions,the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities(LMIs).Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.
基金Project supported by the Fundamental Research Funds for the Central Universities,China(No.2662018QD031)
文摘A characteristic model based all-coefficient adaptive control law was recently implemented on an experimental test rig for high-speed energy storage flywheels suspended on magnetic bearings. Such a control law is an intelligent control law, as its design does not rely on a pre-established mathematical model of a plant but identifies its characteristic model while the plant is being controlled. Extensive numerical simulations and experimental results indicated that this intelligent control law outperforms a μ-synthesis control law, originally designed when the experimental platform was built in terms of their ability to suppress vibration on the high-speed test rig. We further establish, through an extensive simulation, that this intelligent control law possesses considerable robustness with respect to plant uncertainties, external disturbances, and time delay.
