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Keywords = the polyhedral model control theory

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19 pages, 3066 KB  
Article
A Convex Constraint Approach for High-Type Control Loop Design
by Chao Liu, Xiaoxia Qiu and Yao Mao
Electronics 2025, 14(12), 2491; https://doi.org/10.3390/electronics14122491 - 19 Jun 2025
Viewed by 312
Abstract
This paper proposes a high-type control loop design method for LQR-LMI based on Lyapunov and polyhedral model theory. The high-type control loop design problem is simplified into a convex constraint problem, which achieves superior tracking performance. In this framework, the input amplitude of [...] Read more.
This paper proposes a high-type control loop design method for LQR-LMI based on Lyapunov and polyhedral model theory. The high-type control loop design problem is simplified into a convex constraint problem, which achieves superior tracking performance. In this framework, the input amplitude of the control signal, the poles of the closed-loop system, the suppression of external interference and the perturbation of internal parameters are considered, and the linear matrix inequality (LMI) method is effectively used to solve the problems. In this paper, the polyhedral model control theory is introduced to characterize the uncertainty of the system for the change of model parameters of the controlled plant. Aiming at the problem of external disturbance suppression, the H2/H control method is introduced into the system. These control methods provide the basis for the design of the high-type control loop. Compared with the simulation results of other optimization algorithms, the effectiveness and superiority of the controller parameter tuning rules in the proposed high-type control loop are verified. Full article
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18 pages, 355 KB  
Article
Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems
by Hongli Yang, Xindong Si and Ivan G. Ivanov
Fractal Fract. 2024, 8(5), 255; https://doi.org/10.3390/fractalfract8050255 - 25 Apr 2024
Cited by 3 | Viewed by 1254
Abstract
This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints [...] Read more.
This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on the decomposition and separation method and coordinate transformation, the DFOLCS can be transformed into an equivalent fractional-order reduced system; hence, the CSRP of the DFOLCS is equivalent to the CSRP of the reduced system. By means of positive invariant sets theory, Lyapunov stability theory, and some mathematical techniques, necessary and sufficient conditions for the polyhedral positive invariant set of the equivalent reduced system are presented. Models and corresponding algorithms for solving the CSRP of a linear feedback controller are also presented by the obtained conditions. Under the condition that the resulting closed system is positive, the given model of the CSRP in this paper for the DFOLCS is formulated as nonlinear programming with a linear objective function and quadratic mixed constraints. Two numerical examples illustrate the proposed method. Full article
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18 pages, 688 KB  
Article
Robust PD-Type Iterative Learning Control of Discrete Linear Repetitive Processes in the Finite Frequency Domain
by Lei Wang, Mu Li and Huizhong Yang
Mathematics 2020, 8(6), 1004; https://doi.org/10.3390/math8061004 - 18 Jun 2020
Cited by 2 | Viewed by 2117
Abstract
This paper studies a robust iterative learning control design for discrete linear repetitive processes in the finite frequency domain. Firstly, the state-space model of the iterative learning process is deduced. Then the dynamic performance condition of the control system in the finite frequency [...] Read more.
This paper studies a robust iterative learning control design for discrete linear repetitive processes in the finite frequency domain. Firstly, the state-space model of the iterative learning process is deduced. Then the dynamic performance condition of the control system in the finite frequency domain is derived by combining it with the stability theory of discrete linear repetitive processes. The system performances in the finite frequency domain are then transformed into the corresponding solutions of the linear matrix inequality by using the generalised KYP lemma. Finally, an integrated state feedback PD-type iterative learning control strategy is proposed. The robust control problem with norm-bounded uncertainty and convex polyhedral uncertainty are also considered in this paper. The simulation of the injection velocity in injection molding verified that the proposed methods in this paper are more effective than the P-type state feedback iterative learning control algorithm. Full article
(This article belongs to the Section E: Applied Mathematics)
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