مجله کنترل
سال شانزدهم شماره 2 (تابستان 1401)

Nonlinearity is one of the main behaviors of systems in the real world. Therefore, it seems necessary to introduce a method to determine the stability margin of these systems. Although the gain and phase margins are established criteria for the analysis of linear systems, finding a specific way to determine the true value of these margins in nonlinear systems in general is an ongoing research in the literature. The main goal of this paper is to introduce a new method to determine these margins more precisely for particular type of nonlinearities. Based on Lyapunov theorem, stability conditions are obtained and the stability margins of Lur'e systems are determined by applying the extended circle criterion. By providing numerical examples, the correctness of the obtained results is checked and by comparing them with other methods, the accuracy of the obtained results is evaluated.

In this article, a new approach is proposed to design robust switching gain-scheduled dynamic output feedback control for switched uncertain continuous-time linear parameter varying (LPV) systems. The proposed robust switching gain-scheduled controllers are robustly designed so that the stability and H2-gain performance of the switched closed-loop uncertain LPV system can be guaranteed even under controller switching determined by scheduling parameters. Hysteresis switching law is exploited for the switching controller synthesis. The system matrices are supposed to depend polynomially on both the scheduling and uncertain parameters which are assumed to belong to intervals with a priori known bounds. The proposed approach is formulated in terms of solutions to a set of parameter-dependent LMIs using parameter searches for two scalar values. Finally, the method is applied to electromagnetic suspension system to verify the applicability of the presented approach.

In this paper, the blood glucose control for type 1 diabetic patients in the presence of model uncertainties and uncertain meals is considered. In order to present an efficient control approach, it is assumed that the dynamics describe the mechanism of the blood glucose regulation in type 1 diabetic patients are completely unknown. Hence, based on the universal approximation property of the radial basis neural network equipped with an adaptive algorithm, as well as using the minimal learning parameter approach, unknown model dynamics are approximated. Then, based on the feedback-linearization approach and robust adaptive compensation scheme, an appropriate control method is designed to regulate blood glucose in type 1 diabetic patients in the presence of a meal. By a Lyapunov based analysis, it is shown that the closed-loop system of blood glucose control is uniformly ultimately bounded and that the blood glucose of diabetic patients converges to a desired level. Finally, simulation results are shown to demonstrate the efficiency of the designed controller.

In the recent decades, metrics have been introduced as mathematical tools to determine the robust stability of the closed loop control systems. However, the metrics drawback is their limited applications in the closed loop control systems with nonlinear dynamics. As a solution in the literature, applying the metric theories to the linearized models is suggested. In this paper, we show that using the linear model is not adequate to analyze the robust stability. To this end, the definition of general operator space is proposed as the important novelty to determine the weakest topology between two nonlinear dynamic systems. In this space, all nonlinear operators (nonlinear dynamic systems) with differentiable manifold topology can be considered as isometric isomorphism. The result of this definition is possibility of the nonlinear gap metric solution which leads to definition of the s-gap metric. In fact, we show that the calculation of the nonlinear gap metric leads to the most conservative tangent spaces in the defined space. Also, based on the new results, the gain bound of the closed-loop system is determined, which together with the s-gap offers a new theory for robust stability analysis. Advanced operator theory and simulation results confirm the correctness of the claims.

The line of sight (LOS) rate is a parameter that is needed to calculate the acceleration applied to missiles by the proportional guidance laws in order to hit the target. This rate is usually measured using gimbaled seekers. However, if the type of missile seeker be strap down, the LOS rate must be calculated from deriving the missile's seeker output angles or estimation methodes. The derivation method is not desirable due to the noisy output of the seekers and low pass filters are needed to achieve an acceptable output, which will cause a lag in the guidance loop. In this paper, a discrete time extended state observers will be designed to estimate the LOS rate. The advantage of the time discontinuity of the observer is that issues related to the implementation of the observer on the processors, such as the choice of sampling time, considered from the design level and examined in computer simulation.

In this paper, statistical modeling of online advertising systems is addressed. The proposed model relies on the highest bidding price estimation in an auction network and the click-through rate estimation of the ad campaign. The estimation problem is faced with serious challenges due to the extremely time-varying and nonlinear behavior of users, the competitive behavior of the ad campaigns, and the variety of strategies incorporated by the demand-side platforms. Accordingly, estimation algorithms based on Kalman filtering may fail to provide reliable solutions in a real-time setting. In this paper, particle filtering is utilized to estimate the probability distribution of the highest bidding price. Advertisers observe the highest bidding price only if they win the auction. Otherwise, they do not have access to the highest bidding price. Thus, a biconditional update rule is proposed for the particles. The weighting scheme modifies the posterior distribution in case of winning or losing the auction. Next, the click-through rate of the ad campaign is introduced based on the Bayesian estimation. Since the user response is extremely variable over time, an adaptation rule is proposed to update the forgetting factor and the level of emphasis on the recent observations. Finally, by estimation of the highest bidding price and the click-through rate distributions, the input-output model of the ad campaign is developed. The input is the bidding signal or the control signal and the output is the total number of winning impressions for the campaign. The results are reported for a campaign with four individual segments and confirm that the proposed statistical approach can provide a reliable model for ad campaigns.

A new method based on piecewise affine approximation is proposed to model a distillation column and a novel robust MPC is addressed for PWA systems considering multiple prediction trajectories. Distillation columns have highly nonlinear and complex behavior. However, even in a rigorous dynamical model a number of model simplifications are included. Piecewise affine maps have universal approximation properties which are useful for modeling of nonlinear systems in a wide range of operation. Model predictive control for PWA systems faces multiple prediction trajectories at each sample time due to different system dynamics over prediction horizon. Thus, the computational burden increases exponentially with the prediction horizon length. In order to decrease the computational burden, a suboptimal method is used to solve MIQP problems in MPC for PWA systems in presents of model uncertainty and disturbances. A real distillation column of a debutanizer unit in South Pars Gas refineries is modeled with PWA method and validated using the appropriate nonlinear model. A tube-based model predictive control proposed in such a way that the optimization problem can be solved considering multiple prediction trajectories at each sample time. In the proposed method, the computational burden is increased linearly by the prediction horizon length.