A practical method for the design of sliding mode controllers using linear matrix inequalities

Automatica ◽  
2004 ◽  
Vol 40 (10) ◽  
pp. 1761-1769 ◽  
Author(s):  
Christopher Edwards
Keyword(s):  
Linear Matrix Inequalities ◽  
Sliding Mode ◽  
Practical Method ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Sliding Mode Controllers

Observer-based sliding mode control for piezoelectric wing bending-torsion coupling flutter involving delayed output

2020 ◽  
pp. 107754632094912
Author(s):  
Da Li ◽  
Hui Yang ◽  
Na Qi ◽  
Jiaxin Yuan
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Linear Matrix Inequalities ◽  
Closed Loop ◽  
Sliding Mode ◽  
Loop System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Piezoelectric Patch

An observer-based sliding mode control scheme is proposed for suppressing bending-torsion coupling flutter motions of a wing aeroelastic system with delayed output by using the piezoelectric patch actuators. The wing structure is modeled as a thin-walled beam, and the aerodynamics on the wing are computed by the strip theory. For the implementation of the control algorithm, the piezoelectric patch is bonded on the top surface of the beam to act as the actuator. Ignoring the effect of piezoelectric actuators on structural dynamics, only considering the bending moments induced by piezoelectric effects, the corresponding dynamic motion equation is established by using the Lagrange method with the assumed mode method. The flutter speed and frequency of the closed-loop system with time delay are obtained by solving a polynomial eigenvalue problem. An observer-based controller that does not dependent on time delay is developed for suppressing the flutter, and the corresponding gain matrices are obtained by solving linear matrix inequalities. The sufficient condition for the asymptotic stability of the closed-loop system is derived in terms of linear matrix inequalities. The simulation results demonstrate that the proposed control strategy based on the piezoelectric actuator is effective in wing bending-torsion coupling flutter system with a delayed output.

Linear Matrix Inequalities in Robust Unified Smooth Sliding Mode Controller Design

2012 ◽  
Author(s):  
Siew Min See ◽  
Johari Halim Shah Osman
Keyword(s):  
Sliding Mode Control ◽  
Linear Matrix Inequalities ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
H Infinity ◽  
Mode Control ◽  
Mismatched Uncertainties ◽  
Guaranteed Cost ◽  
Mismatched Disturbances

Sebahagian besar masalah yang dihadapi dalam teori kawalan sistem boleh dikurangkan kepada beberapa masalah pengoptimuman cembung atau kuasi–cembung piawai yang melibatkan ketaksamaan matriks lelurus (LMI). Dengan perkembangan terbaru tentang cara titik dalaman, masalah pengoptimuman tersebut dapat diselesaikan secara efisien dengan kaedah berangka. Satu daripada aplikasi LMI boleh dilihat dalam penyelesaian masalah kawalan ragam gelincir. Sistem kawalan ragam gelincir berkemampuan supaya tidak terpengaruh secara keseluruhan oleh ketidakpastian padanan apabila berada dalam ragam gelincir. Akan tetapi, sistem masih menghadapi gangguan yang tidak diingini apabila diusik oleh ketidakpastian tidak terpadan, serta masalah gelugutan. Dalam kertas kerja ini, permukaan gelincir direka bentuk dengan integrasi suatu kriteria H infiniti terjamin kos optimum untuk mengurangkan gangguan tidak terpadan. Permukaan kos terjamin tersebut diterbitkan daripada prosedur pengoptimuman cembung yang diformulasikan sebagai masalah LMI. Satu kawalan licin seragam diaplikasikan untuk menyelesaikan masalah gelugutan. Keputusan menunjukkan bahawa pengawal tersebut dapat memperbaiki prestasi dari segi penyingkiran gelugutan secara keseluruhan dan penyisihan gangguan tidak terpadan Kata kunci: Ketaksamaan matriks lelurus (LMI), kawalan ragam gelincir, gangguan tidak terpadan, bebas gelugutan, kriteria H infiniti terjamin kos optimum A wide range of problems encountered in system control theory can be reduced to a few standard convex or quasiconvex optimisation problems involving linear matrix inequalities (LMI). With recent developed of interior point methods, the optimisation problems can be solved numerically very efficiently. One of the applications of the LMI may be seen in solving the sliding mode control problems. The sliding mode control system is capable of total invariance to the matched uncertainties while remain in the sliding mode. But the system may still face the undesirable distractions cause by the mismatched uncertainties, and chattering problem. In this paper, the sliding surface is designed with integration of an optimal guaranteed cost H infinity criterion to attenuate the mismatched disturbances. The guaranteed cost surface is derived from a convex optimisation procedure formulated as an LMI problem. A unified smooth control law is applied to solve the chattering problem. The results showed that the controller may improve the performance with total chattering elimination and mismatched disturbances rejection. Key words: Linear matrix inequalities (LMI), sliding mode control, mismatched uncertainties, chattering free, optimal guaranteed cost H infinity criterion

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
Sign in / Sign up

Export Citation Format

Share Document