• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.9
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• pp.511-519
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• 2003

In this paper, we considered the design of gain scheduled controllers for linear systems with saturating actuators. Our basic idea is to design a control that uses higher control gain when the states are smaller, and lower gain when it is higher. By doing this, we can avoid the saturation and we can improve the performance. First, we derive a control and a reachable set expressed as LMI form, which minimizes not only the L$_2$ gain from the disturbance to the measured output but also the control is never saturated within this reachable set. Next, the reachable set is divided as nested subsets, and at each nested subset, the control gain is designed to minimize the L$_2$ gain and it is never saturated. Finally, the control gain is scheduled according to the status of states, i.e., the subset in which the states are located. A numerical example is presented to show that our gain scheduled control significantly improves the performance.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.8
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• pp.1464-1470
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• 2010

In this paper, we consider the $H_{\infty}$ control of time-delayed linear systems with saturating actuators. The considered time-delay is a time-varying one having bounds on magnitude and time-derivative, and the control permits the predetermined degree of saturation. Based on two modified Lyapunov-Krasovskii(L-K) functionals, we derive a $H_{\infty}$ control in the form of linear matrix inequalities(LMI) having three non-convex design parameters. The result is dependent on the characteristics of time-delay, predetermined degree of saturation level, and bound of disturbance. Finally, we give a comparative example to show the effectiveness and usefulness of our result.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.494-496
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• 1999

In this paper, we consider the design of a state feedback $H_{\infty}$ controller for uncertain linear systems with saturating actuators. We consider a general saturating actuator and employ the additive decomposition to deal with it effectively. And the considered uncertainty is the unstructured uncertainty which is only known its norm bound. Based on Linear Matrix Inequality(LMI) techniques, we present a condition on designing a controller that guarantees the $L_2$ gain, from the noise to the output, is not greater than a given value. A controller is obtained by checking the feasibility of three LMI's, and this can be easily done by well-known control package. Finally, we show the usefulness of our result by a numerical example.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.596-598
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• 1999

In this paper, we consider the design of a state feedback $H_{\infty}$ controller for linear systems with saturating actuators. We consider a general saturating actuator and employ the multiplicative decomposition to deal with it effectively. Based on Linear Matrix Inequality (LMI) techniques, we present a condition on designing a controller that guarantees the $L_2$ gain, from the noise to the output, is not greater than a given value. A controller is obtained by checking the feasibility of three LMI's, and this can be easily done by well-known control package. Finally, we show the usefulness of our result by a numerical example.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.229-234
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• 1992

This paper presents a compensator design method for multivariable feedback control systems with saturating actuators based on the concept of the equilibrium point. Am explicit expression for the compensation matrix of the general anti-reset windup(ARW) scheme is derived by minimizing the distances between the equilibrium points. The resulting dynamics of the compensated controller exhibits the reduced model form of the unsaturated system which can be obtained by the singular perturbational method. The proposed method is applicable to any open-loop stable plants with saturating actuators whose controllers are determined by some design technique. An example is given to show the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.4
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• pp.668-676
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• 2008

In this paper, we considered the $H_{\infty}$ tracking control for time-delayed linear systems with saturating actuators. The considered time delay is a time varying one having bounded magnitude and rate, and the considered tracking reference is a general one only known its bounds of magnitude and rate. First, we have converted the $H_{\infty}$ tracking control problem into an equivalent $H_{\infty}$ disturbance attenuation problem using two steps of transformations. Next, based on a new Lyapunov-Krasovskii functional, we have derived the result in the form of LMI with two non-convex parameters. Finally, by numerical examples, we have shown the usefulness and effectiveness of our result.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.73-76
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• 1996

This paper presents a dynamical anti-reset windup (ARW) compensation method for saturating control systems with multiple controllers and/or multiloop configuration. By regarding the difference of the controller states in the absence and presence of saturating actuators as an objective function, the dynamical compensator which minimize the objective function are derived in an integrated fashion. The proposed dynamical compensator is a closed form of the plant and controller parameters. The proposed method guarantees total stability of resulting system. An illustrative example is given to show the effectiveness of the proposed method.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.5
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• pp.380-387
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• 1989

The Conventional-Anti-reset-Windup (CAW) structure gives pretty good performance among the conventional strategies that prevent systems from saturation, but there is no systematic way of designing the control systems. Also, it frequently destabilizes the systems. Moreover, the CAW structure cannot be applied when the output of the saturating actuator cannot be measured. Therefore the CAW structure is modified to accommodate this situation. An effective designing method is proposed to give better performance of the control system. The stability of the control system is also considered. The usefulness of the proposed method is shown by applying this method to a few examples.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1342-1350
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• 1993

One of the undesirable nonlinear phenomena in feedback control systems is called 'wind up', which is characterized by large overshoot, slow response, and even instability. It is caused by interaction between the integrator in the controller and the saturating actuator. Limit cycle and jump resonance are another nonlinear characteristrics of systems with saturating actuators. Several 'anti-windup' compensators have been developed to prevent some of the aforementioned nonlinear characteristics such as instability and limit cycle, but none has studied the effect of anti-windup compensator on the jump resonance. In this paper, we developed an analytical method to design the compensator to prevent not only limit cycle but also jump resonance. An illustrative example is included to show the compensator eliminates jump resonance effectively.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.141-150
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• 1998

This paper presents a dynamical anti-reset windup (ARW) compensation method for saturating control systems with multiple controllers and/or multiloop configuration. By regarding the difference of controller states in the absence and presence of saturating actuators as an objective function, the dynamical compensator which minimizes the objective function is derived in an integrated fashion. The proposed dynamical compensator is a closed form of plant and controller parameters. The resulting dynamics of compensated controller reflects the linear closed-loop system. The proposed method guarantees total stability of the resulting system. The effectiveness of the proposed method is illustrated by applying it to a servo motor control system. The paper is an extension of the results in Park and Choi[1].