Optimal Control Method for Seismically Excited Building Structures with Time-delay in Control

Optimal control method for seismic-excited linear structures with time delay in control is investigated in this paper. Using zero-order holder, the continuous time differential equation with time delay can be transformed into a standard discrete time form that contains no time delay in terms of two cases that the time delay is integer and noninteger times of sampling period, respectively. The continuous time performance index is used in the design of the optimal controller and it is also transformed into discrete form. Then, the optimal controller can be designed according to the classical discrete LQR method. The controller obtained contains not only current step of state feedback but also a linear combination of some former steps of control. Because the optimal controller is obtained directly from the time-delay differential equation, it is prone to guarantee the stability of the controlled structures. Furthermore, this control method is available for case of large time delay. The performance of the control method proposed and system stability are both demonstrated by numerical simulation results. Simulation results demonstrate that the control method proposed in this paper is a viable and attractive control strategy for application to seismically excited linear structures.

[1]  Michael J. Chajes,et al.  STABILITY OF ACTIVE-TENDON STRUCTURAL CONTROL WITH TIME DELAY , 1993 .

[2]  J. Yan,et al.  Robust stability of uncertain time-delay systems and its stabilization by variable structure control , 1993 .

[3]  J. N. Yang,et al.  Sliding Mode Control for Seismically Excited Linear Structures , 1995 .

[4]  J. T. P. Yao,et al.  Reliability aspects of structural control , 1982 .

[5]  T. T. Soong,et al.  Modified Bang-Bang Control Law for Structural Control Implementation , 1996 .

[6]  Mohamed Abdel-Mooty,et al.  Time‐Delay Compensation in Active Damping of Stuctures , 1991 .

[7]  Mohamed Abdel-Rohman,et al.  TIME-DELAY EFFECTS ON ACTIVELY DAMPED STRUCTURES , 1987 .

[8]  James T. P. Yao,et al.  CONCEPT OF STRUCTURAL CONTROL , 1972 .

[9]  Mohamed Abdel-Rohman,et al.  Research Topics for Practical Implementation of Structural Control , 1987 .

[10]  Zexiang Li,et al.  Aseismic hybrid control of nonlinear and hysteretic structures. II , 1992 .

[11]  Kestutis Pyragas,et al.  Experimental control of chaos by delayed self-controlling feedback , 1993 .

[12]  Jie Chen,et al.  On sufficient conditions for stability independent of delay , 1994, American Control Conference.

[13]  Lap-Loi Chung,et al.  Time‐delay control of structures , 1995 .

[14]  T. T. Soong,et al.  Experiments on Active Control of Seismic Structures , 1988 .

[15]  Benjamin C. Kuo,et al.  Digital Control Systems , 1977 .

[16]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[17]  Erik Noldus,et al.  A way to stabilize linear systems with delayed state , 1983, Autom..

[18]  M. Mahmoud,et al.  Design of robust controllers for time-delay systems , 1994, IEEE Trans. Autom. Control..

[19]  Jann N. Yang,et al.  EFFECT OF TIME DELAY ON CONTROL OF SEISMIC-EXCITED BUILDINGS , 1990 .

[20]  B. Anderson,et al.  Linear Optimal Control , 1971 .

[21]  Faryar Jabbari,et al.  Robust control techniques for buildings under earthquake excitation , 1994 .