Applying Popov's theory to the stability analysis of predictive control with input nonlinearity

2005 ◽  
Author(s):  
Baocang Ding ◽  
Shaoyuan Li
Keyword(s):  
Stability Analysis ◽  
Predictive Control ◽  
Input Nonlinearity ◽  
The Stability

scholarly journals Practical Computational Approach for the Stability Analysis of Fuzzy Model-Based Predictive Control of Substrate and Biomass in Activated Sludge Processes

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 531
Author(s):  
Pedro M. Vallejo LLamas ◽  
Pastora Vega
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Activated Sludge ◽  
Predictive Control ◽  
Closed Loop ◽  
Complex Dynamics ◽  
Linear Time ◽  
Fuzzy Model ◽  
The Stability ◽  
The Mathematical Model

This paper presents a procedure for the closed-loop stability analysis of a certain variant of the strategy called Fuzzy Model-Based Predictive Control (FMBPC), with a model of the Takagi-Sugeno type, applied to the wastewater treatment process known as the Activated Sludge Process (ASP), with the aim of simultaneously controlling the substrate concentration in the effluent (one of the main variables that should be limited according to environmental legislations) and the biomass concentration in the reactor. This case study was chosen both for its environmental relevance and for special process characteristics that are of great interest in the field of nonlinear control, such as strong nonlinearity, multivariable nature, and its complex dynamics, a consequence of its biological nature. The stability analysis, both of fuzzy systems (FS) and the very diverse existing strategies of nonlinear predictive control (NLMPC), is in general a mathematically laborious task and difficult to generalize, especially for processes with complex dynamics. To try to minimize these difficulties, in this article, the focus was placed on the mathematical simplification of the problem, both with regard to the mathematical model of the process and the stability analysis procedures. Regarding the mathematical model, a state-space model of discrete linear time-varying (DLTV), equivalent to the starting fuzzy model (previously identified), was chosen as the base model. Furthermore, in a later step, the DLTV model was approximated to a local model of type discrete linear time-invariant (DLTI). As regards the stability analysis itself, a computational method was developed that greatly simplified this difficult task (in a local environment of an operating point), compared to other existing methods in the literature. The use of the proposed method provides useful conclusions for the closed-loop stability analysis of the considered FMBPC strategy, applied to an ASP process; at the same time, the possibility that the method may be useful in a more general way, for similar fuzzy and predictive strategies, and for other complex processes, was observed.

scholarly journals Design and Stability Analysis of Uncertain Networked Predictive Control Systems with Multiple Forward Channels

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hongbo Song
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Predictive Control ◽  
Uncertain Systems ◽  
Closed Loop ◽  
Control Performance ◽  
Selection Scheme ◽  
Signal Selection ◽  
Networked Predictive Control ◽  
The Stability

This paper is concerned with the design and stability of networked predictive control for uncertain systems with multiple forward channels. The delays and packet dropouts are distributed such that the classic networked predictive control (NPC) needs modifications to be implemented. An improved control signal selection scheme with distributed prediction length is proposed to increase the prediction accuracy and hence achieve better control performance. Moreover, stability analysis results are obtained for both constant and random cases. Interestingly, it is shown that the stability of the closed-loop NPC system is not related to the distributed delays when they are constant and the system model is accurate. Finally, a two-axis milling machine example is given to illustrate the effectiveness of the proposed method.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

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