• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.595-603
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• 2009

We show that for an algebraic Riccati equation $X^*B^{-1}X-T^*X-X^*T=C$, its solutions are given by X = W + BT for some solution W of $X^*B^{-1}X$ = $C+T^*BT$. To generalize this, we give an equivalent condition for $\(\array{B&W\\W*&A}\)\;{\geq}\;0$ for given positive operators B and A, by which it can be regarded as Riccati inequality $X^*B^{-1}X{\leq}A$. As an application, the harmonic mean B ! C is explicitly written even if B and C are noninvertible.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.9
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• pp.1612-1617
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• 2008

Since most disturbance observer (DOB) approaches have been limited to minimum-phase systems (or systems having no zero dynamics), we propose a new DOB structure that can be applied to non-minimum phase systems. The new structure features an additional system, which is called as V-filter, whose role is to yield a minimum phase system when connected with the plant in parallel. In order to design the V-filter systematically we first consider a class of linear systems that can be stabilized via PID controller. By inverting the controller's transfer function, we can simply construct the filter. A convenient way of designing V-filter is presented by using an iterative linear matrix inequality (LMI) algorithm. With an illustrative example the simulation result shows that substantial improvement in the performance has been achieved compared with the control system without the DOB.

• Journal of Power Electronics
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• v.12 no.2
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• pp.294-304
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• 2012

This paper proposes a fuzzy speed tracking controller and a fuzzy rotor angular acceleration observer for a surface-mounted permanent magnet synchronous motor (SPMSM) based on the Takagi-Sugeno (T-S) fuzzy model. The proposed observer-based controller is robust to load torque variations since it utilizes rotor angular acceleration information instead of the load torque value. Linear matrix inequality (LMI) sufficient conditions are given to compute the gain matrices of the speed tracking controller and the observer. In addition, it is mathematically verified that the proposed observer-based control system is asymptotically stable. Simulation and experimental results are presented to confirm that the proposed control algorithm assures a better transient behavior and less sensitivity under model parameter variations than the conventional PI control method.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.3
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• pp.220-226
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• 2002

In this paper, we develop the intelligent digitally redesigned fuzzy controller for nonlinear systems. Takagi-Sugeno (TS) fuzzy model is used to model the nonlinear systems and a continuous-time fuzzy-model-based controller is designed based on the extended parallel-distributed-compensation(EPDC) method . The digital controllers are determined from existing analogue controllers. The proposed method provides an accurate and effective method for digital control of continuous-time nonlinear systems and enables us to efficiently implement a digital controller via the pre-determined continuous-time 75 fuzzy-model-based controller. We have applied the proposed method to the duffing forced oscillation system to show the effectiveness and feasibility of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.25-25
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• 2000

This paper presents a design method of sliding mode control (SMC) for single input linear systems with mismatched uncertainties. We define a virtual state based on the controllable canonical form of the nominal system. And we define a sliding surface for the augmented system with a virtual state. This sliding surface makes it possible to use SMC technique with various types of controllers. In this paper, we construct a controller that combines SMC with robust controller. We design a robust controller for the system with only mismatched uncertainties using a form of linear matrix inequality (LMI). We make a virtual state from this robust control input and the states of the nominal system. And we design a sliding mode controller that stabilizes the overall closed-loop system.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.4
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• pp.215-219
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• 2005

This paper aims at asymptotic stabilization for uncertain dynamic systems with state and input delays. We propose a memoryless state feedback controller which maximizes the delay bound for guaranteeing stability of the system. Using Lyapunov method and linear matrix inequality (LMI) approach, a delay-dependent stabilization criterion is devised by taking the relationship between the terms in the Leibniz-Newton formula into account. The criterion is represented in terms of LMIs, which can be solved by various efficient convex optimization algorithms. Numerical examples are given to illustrate our main method.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.163-177
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• 2012

This paper presents a LMI(linear matrix inequality)-based fuzzy approach of modeling and active vibration control of geometrically nonlinear flexible plates with piezoelectric materials as actuators and sensors. The large-amplitude vibration characteristics and dynamic partial differential equation of a piezoelectric flexible rectangular thin plate structure are obtained by using generalized Fourier series and numerical integral. Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear structural system, which combines the fuzzy inference rule with the local linear state space model. A robust fuzzy dynamic output feedback control law based on the T-S fuzzy model is designed by the parallel distributed compensation (PDC) technique, and stability analysis and disturbance rejection problems are guaranteed by LMI method. The simulation result shows that the fuzzy dynamic output feedback controller based on a two-rule T-S fuzzy model performs well, and the vibration of plate structure with geometrical nonlinearity is suppressed, which is less complex in computation and can be practically implemented.

• Journal of Electrical Engineering and information Science
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• v.3 no.2
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• pp.163-169
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• 1998

In this paper, we consider the problem of designing H$\infty$ state feedback controller for the generalized time systems with delayed states and control inputs in continuous and discrete time cases, respectively. The generalized time delay system problems are solved on the basis of LMI(linear matrix inequality) technique considering time delays. The sufficient condition for the existence of controller and H$\infty$ state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be rewritten as a LMI form in terms of transformed variables. The propose controller design method can be extended into the problem of robust H$\infty$ state feedback controller design method easily.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.3
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• pp.193-197
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• 2001

This paper presents a design method of sliding model control (SMC) for single input linear systems with mismatched uncertainties. We define a virtual state based on the controllable canonical form of the nominal system. And we defined a sliding surface for the augmented system with a virtual state. This sliding surface makes it possible to use the SMC technique with various types of controllers. In this paper, we construct a controller that combines SMC with robust controller. We design a robust controller for the system with mismatched uncertainties using a form of linear matrix inequality(LMI). We make a virtual state from this robust control input and the states of the nominal system. And we design a sliding model controller that stabilizes the overall closed-loop system.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.3
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• pp.232-235
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• 2008

This paper presents an LMI-based method to design reduced order observers by which we can substitute full order sliding mode observers for a class of uncertain time-delay systems. We show that a reduced order observer can be constructed as long as the uncertain system satisfies the previous LMI existence conditions of a full order sliding mode observer. And we give explicit formulas of the reduced order observer gain matrices. Finally, we give a simple LMI-based design algorithm, together with a numerical design example.