Multi-objective PID control for non-Gaussian stochastic distribution system based on two-step intelligent models

Abstract

A new method for controlling the shape of the conditional output probability density function (PDF) for general nonlinear dynamic stochastic systems is proposed based on B-spline neural network (NN) model and T-S fuzzy model. Applying NN approximation to the measured PDFs, we transform the concerned problem into the tracking of given weights. Meanwhile, the complex multi-delay T-S fuzzy model with exogenous disturbances, parametric uncertainties and state constraints is used to represent the nonlinear weight dynamics. Moreover, instead of the non-convex design algorithms and PI control, the improved convex linear matrix inequality (LMI) algorithms and the generalized PID controller are proposed such that the multiple control objectives including stability, robustness, tracking performance and state constraint can be guaranteed simultaneously. Simulations are performed to demonstrate the efficiency of the proposed approach.probability density function, non-Gaussian stochastic systems, PID controller, B-spline NN, L 1 performance index, T-S fuzzy model

Robust PI speed tracking control for PMSM system based on convex optimization algorithm

“…By solving a series of LMIs (9), (19), (20), the new PI control gains K P 1 , K P 2 and K I can be computed as K P 1 = −0.9459, K P 2 = −1.0523, K I = 56.1426…”

“…However, in these results a nonsingular constraint related to well-posedness should be guaranteed, which might result in non-convex algorithms and conservative outcomes. For the shape control of the output stochastic distribution, the improved PI controller design based on a series of convex LMI optimization algorithms was developed in [19], [20].…”

Disturbance observer-based L1 robust tracking control for hypersonic vehicles with T-S disturbance modeling

“…On the other hand, in order to optimize the dynamical tracking performance for the interference term " d 2 ðtÞ, the peak-to-peak control gain is used (see Scherer and Weiland 21 and Yi et al 39 ), which is defined as follows…”

Disturbance rejection control of yaw channel of a small-scale unmanned helicopter via Takagi–Sugeno disturbance modeling approach

“…Then, by smoothly blending those local linear models together with designed membership functions, the overall T-S models of nonlinear dynamics can be successfully obtained. It has been shown that many physical nonlinear control systems can be modeled and analyzed using T-S fuzzy models, such as networked control systems, 33 chaotic systems, 34 descriptor systems, 35 stochastic systems, 36 time-delay systems, 37 and so on. Inspired by the above observations, this article aims to investigate the disturbance estimation and rejection problem for yaw channel model of a small-scale UAV helicopter with unknown mismatched disturbances.…”