• Journal of the Korean Society for Precision Engineering
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• v.27 no.12
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• pp.59-66
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• 2010

We developed a model-based controller for 6-DOF micropositioning of a precision stage using $H_{\infty}$ norm, For the design, a state-space system of the mathematical model of the stage is derived In developing the controller, weighting functions are effectively designed in consideration of upper bounds of the sensitivity of the control loop and control input. Step responses in open and closed loop control are provided to verify the micropositioning performance of the stage. By applying the developed controller we prove that the inverse of the weighting function forms the upper bound of the control loop. It is also found that the controller makes the same sensitivity shape with all the DOFs due to the use of $H_{\infty}$ norm. The developed controller is expected to be applied successfully for industrial use.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.2
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• pp.95-103
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• 2002

This paper deals with the H$_{\infty}$ control problems for discrete-time linear systems with time-varying delays in states. The existence condition and the design method of the H$_{\infty}$ state feedback controller are given. In this paper, the H$_{\infty}$ control law is assumed to be a memoryless state feedback, and the upper-bound of time-varying delay and S-procedure are used. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.11
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• pp.896-903
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• 2001

This study investigates the use of mixed $H_2/H_{$\infty}$ and $\mu$-synthesis to construct a robust controller for the benchmark problem. The model treated in the problem is a coupled three-inertial system that reflects the dynamics of mechanical vibrations. This kind of problem requires to be satisfied the robust performance (both in the time and frequency-domain specifications). We, first, adopt the mixed $H_2/H_{$\infty}$ theory to design a feedback controller K(s). Next, $\mu$-synthesis method is applied to the overall system to make use of structured parametric uncertainty. This process permits higher levels of controller authority and reduces the conservativeness of the controller. Finally, the feedforward controller is also used to improve the transient response of the output. We confirm that all design specifications except a complementary sensitivity condition can be achieved.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.9
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• pp.747-756
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• 2002

The automatic steering system for unmanned vehicle was developed. The magnet and MR (Magnetoresistive) sensors are used for the tue detecting system. The lateral distance between sensor and the center line of the road is determined by the linearization of the distance according to the output. The PD control theory is used for the design of the controller to compare with $H_\infty$ control theory. The $H_\infty$ control theory is used for the design of the controller to reduce the disturbance. The performance of the PD controller and $H_\infty$ controller is compared in simulations and tests. The PD controller is easy to tune in the test site. The $H_\infty$ controller is robust far the disturbances in the test results.

• Journal of Mechanical Science and Technology
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• v.16 no.12
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• pp.1613-1626
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• 2002

This paper presents hybrid control of an active suspension system with a full-car model by using H$\sub$$\infty$/ and nonlinear adaptive control methods. The full-car model has seven degrees of freedom including heaving, pitching and rolling motions. In the active suspension system, the controller shows good performance: small gains from the road disturbances to the heaving, pitching and rolling accelerations of the car body. Also the controlled system must be robust to system parameter variations. As the control method, H$\sub$$\infty$/ controller is designed so as to guarantee the robustness of a closed-loop system in the presence of uncertainties and disturbances. The system parameter variations are taken into account by multiplicative uncertainty model and the system robustness is guaranteed by small gain theorem. The active system with H$\sub$$\infty$/ controller can reduce the accelerations of the car body in the heaving, pitching and rolling directions. The nonlinearity of a hydraulic actuator is handled by nonlinear adaptive control based on the back-stepping method. The effectiveness of the controllers is verified through simulation results in both frequency and time domains.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.287-290
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• 1995

Recently H$_{\infty}$ control theory for nonlinear systems based on the Hamilton-Jacobi inequality has been developed. In this paper, we apply the state feedback controller solved via Riccati equation to a semi-active suspension model, two degree of freedom vehicle model, and show that it is effective for vibration control..

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.2
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• pp.109-114
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• 1997

In this paper, we present an output feedback $H^\infty$controller design method and derive the sufficient condition of the bounded real lemma for linear systems with multiple delays in states. For state delayed systems, sufficient conditions for the existence $\kappa$-th order $H^\infty$controllers are given in terms of three linear matrix inequalities(LMIs). Furthermore, we show how to construct such controllers from the positive definite solutions of their LMIs and given an example to illustrate the validitiy of the proosed design procedure.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.562-565
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• 1993

It is well known that H$_{\infty}$ control problem involves solving an algebraic Riccati equation which includes a pair of parameters (.gamma., .epsilon.). Focusing on .epsilon. the maximum of .epsilon.. We discuss in this paper about the properties between the H$_{\infty}$ norm of a trnsfer function matrix and the parameters(.gamma., .epsilon.). We can change the algebraic relattion between .gamma. and .epsilon. by the similarity transformation of a considered system and we can find a proper transformation to get a simple quadratic algebraic equation between .gamma. and .epsilon.. This relation provide the H$_{\infty}$ norm of a transfer function.on.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.81-84
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• 1996

We propose the robust nonlinear controller design methodology, the $H_{\infty}$ constrained quasi - linear quadratic Gaussian control (QLQG/ $H_{\infty}$), for the statistically-linearized multivariable system with hard nonlinearties such as Coulomb friction, deadzone, etc. The $H_{\infty}$ performance constraint is involved in the optimization process by replacing the covariance Lyapunov equation with the Riccati equation whose solution leads to an upper bound of the QLQG performance. Because of the system's nonlinearity, however, one equation among three Riccati equations contain the nonlinear correction terms that are very difficult to solve numerically. To treat this problem, we use simple algebraic techniques. With some analytic transformation for Riccati equations, the nonlinear correction terms can be so eliminated that the set of a linear controller to the different operating points are designed. Synthesizing these via inverse random input describing function (IRIDF) technique, the final nonlinear controller can be designed.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.475-484
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• 2004

In this paper, we present a dynamic output-feedback receding horizon $H_{\infty}$controller for linear discrete-time systems with disturbance. The controller is obtained numerically from the finite horizon output-feedback $H_{\infty}$optimization problem, which is, in fact, hardly solved analytically. Under a matrix inequality condition on the terminal weighting matrix, the monotonic decreasing property of the cost is shown. This property guarantees both the closed-loop stability and the $H_{\infty}$norm bound. Then, we extend the proposed design method to a reference tracking problem and a problem for time-varying systems. Numerical examples are given to illustrate the performance of the proposed controller.