This paper considers the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls. To stabilize the system, the authors propose the torque and nonlinear distributed...This paper considers the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls. To stabilize the system, the authors propose the torque and nonlinear distributed controls applied on the disk and flexible beam respectively. As long as the angular velocity of the disk does not exceed the square root of the first eigenvalue of the related self-adjoint positive definite operator, the authors show that the torque and nonlinear distributed control laws suppress the system vibrations, in the sense that the beam vibrations are forced to decay exponentially to zero and the body rotates with a desired angular velocity.展开更多
We propose a novel kind of termination criteria, reduced precision solution (RPS) criteria, for solving optimal control problems (OCPs) in nonlinear model predictive control (NMPC), which should be solved quickly for ...We propose a novel kind of termination criteria, reduced precision solution (RPS) criteria, for solving optimal control problems (OCPs) in nonlinear model predictive control (NMPC), which should be solved quickly for new inputs to be applied in time. Computational delay, which may destroy the closed-loop stability, usually arises while non-convex and nonlinear OCPs are solved with differential equations as the constraints. Traditional termination criteria of optimization algorithms usually involve slow convergence in the solution procedure and waste computing resources. Considering the practical demand of solution precision, RPS criteria are developed to obtain good approximate solutions with less computational cost. These include some indices to judge the degree of convergence during the optimization procedure and can stop iterating in a timely way when there is no apparent improvement of the solution. To guarantee the feasibility of iterate for the solution procedure to be terminated early, the feasibility- perturbed sequential quadratic programming (FP-SQP) algorithm is used. Simulations on the reference tracking performance of a continuously stirred tank reactor (CSTR) show that the RPS criteria efficiently reduce computation time and the adverse effect of computational delay on closed-loop stability.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61273130 and 61673061
文摘This paper considers the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls. To stabilize the system, the authors propose the torque and nonlinear distributed controls applied on the disk and flexible beam respectively. As long as the angular velocity of the disk does not exceed the square root of the first eigenvalue of the related self-adjoint positive definite operator, the authors show that the torque and nonlinear distributed control laws suppress the system vibrations, in the sense that the beam vibrations are forced to decay exponentially to zero and the body rotates with a desired angular velocity.
基金supported by the National Natural Science Foundation of China (Nos. 60934007 and 60974007)the National Basic Research Program (973) of China (No. 2009CB320603)
文摘We propose a novel kind of termination criteria, reduced precision solution (RPS) criteria, for solving optimal control problems (OCPs) in nonlinear model predictive control (NMPC), which should be solved quickly for new inputs to be applied in time. Computational delay, which may destroy the closed-loop stability, usually arises while non-convex and nonlinear OCPs are solved with differential equations as the constraints. Traditional termination criteria of optimization algorithms usually involve slow convergence in the solution procedure and waste computing resources. Considering the practical demand of solution precision, RPS criteria are developed to obtain good approximate solutions with less computational cost. These include some indices to judge the degree of convergence during the optimization procedure and can stop iterating in a timely way when there is no apparent improvement of the solution. To guarantee the feasibility of iterate for the solution procedure to be terminated early, the feasibility- perturbed sequential quadratic programming (FP-SQP) algorithm is used. Simulations on the reference tracking performance of a continuously stirred tank reactor (CSTR) show that the RPS criteria efficiently reduce computation time and the adverse effect of computational delay on closed-loop stability.
