scholarly journals Design of PI Controllers for Irrigation Canals Based on Linear Matrix Inequalities

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 855 ◽  
Author(s):  
Teresa Arauz ◽  
José M. Maestre ◽  
Xin Tian ◽  
Guanghua Guan
Keyword(s):  
Linear Matrix Inequalities ◽  
Pi Controller ◽  
Water Levels ◽  
Linear Matrix ◽  
Irrigation Canal ◽  
Matrix Inequalities ◽  
Tuning Method ◽  
Satisfactory Performance ◽  
Pi Controllers

A new Proportional-Integral (PI) tuning method based on Linear Matrix Inequalities (LMIs) is presented. In particular, an LMI-based optimal control problem is solved to obtain a sparse feedback that provides the PI tuning. The ASCE Test Canal 1 is used as a case study. Using a linearised model of the canal, different tunings for the design of the PI controller are developed and tested using the software Sobek. Furthermore, the proposed method is also compared with other tunings proposed for the same canal available in the literature. Our results show that the proposed method reduces by half the maximum errors with respect to other assessed alternatives and minimizes undesired mutual interactions between canal pools. Also, our method improves the optimality degree of the PI tuning by 30%. Therefore, it is concluded that the LMI based PI controllers lead to satisfactory performance in regulating water levels and canal flows/structure outflows, outperforming other tested alternatives, thus becoming a useful tool for irrigation canal control.

Linear Matrix Inequalities for Digital Redesign Under Delay Suitable for PI Controllers with Application to PMSMs

2019 ◽  
Vol 30 (4) ◽  
pp. 479-489
Author(s):  
Thieli S. Gabbi ◽  
Gustavo G. Koch ◽  
Rodrigo P. Vieira ◽  
Vinícius F. Montagner ◽  
Eduardo S. Tognetti ◽  
...  
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Digital Redesign ◽  
Pi Controllers

scholarly journals Robust Model Predictive Control Using Linear Matrix Inequalities for the Treatment of Asymmetric Output Constraints

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Mariana Santos Matos Cavalca ◽  
Roberto Kawakami Harrop Galvão ◽  
Takashi Yoneyama
Keyword(s):  
Model Predictive Control ◽  
Linear Matrix Inequalities ◽  
Predictive Control ◽  
Constraint Satisfaction ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Model Predictive Control ◽  
Robust Model ◽  
Output Constraints

One of the main advantages of predictive control approaches is the capability of dealing explicitly with constraints on the manipulated and output variables. However, if the predictive control formulation does not consider model uncertainties, then the constraint satisfaction may be compromised. A solution for this inconvenience is to use robust model predictive control (RMPC) strategies based on linear matrix inequalities (LMIs). However, LMI-based RMPC formulations typically consider only symmetric constraints. This paper proposes a method based on pseudoreferences to treat asymmetric output constraints in integrating SISO systems. Such technique guarantees robust constraint satisfaction and convergence of the state to the desired equilibrium point. A case study using numerical simulation indicates that satisfactory results can be achieved.

Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

2018 ◽  
Vol 10 (10) ◽  
pp. 4-19
Author(s):  
Magomed G. GADZHIYEV ◽  
◽  
Misrikhan Sh. MISRIKHANOV ◽  
Vladimir N. RYABCHENKO ◽  
◽  
...  
Keyword(s):  
Power System ◽  
Electric Power ◽  
Linear Matrix Inequalities ◽  
Electric Power System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Power System Controllers

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Contractors and Linear Matrix Inequalities

2015 ◽  
Vol 1 (3) ◽  
Author(s):  
Jeremy Nicola ◽  
Luc Jaulin
Keyword(s):  
Fixed Point ◽  
Large Class ◽  
Linear Matrix Inequalities ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Constraints ◽  
Linear Matrix ◽  
Nonlinear Constraints ◽  
Matrix Inequalities ◽  
Convex Constraints

Linear matrix inequalities (LMIs) comprise a large class of convex constraints. Boxes, ellipsoids, and linear constraints can be represented by LMIs. The intersection of LMIs are also classified as LMIs. Interior-point methods are able to minimize or maximize any linear criterion of LMIs with complexity, which is polynomial regarding to the number of variables. As a consequence, as shown in this paper, it is possible to build optimal contractors for sets represented by LMIs. When solving a set of nonlinear constraints, one may extract from all constraints that are LMIs in order to build a single optimal LMI contractor. A combination of all contractors obtained for other non-LMI constraints can thus be performed up to the fixed point. The resulting propogation is shown to be more efficient than other conventional contractor-based approaches.

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