Technical Stability of Forced Motion in Nonstationary Automatic-Control Systems of Variable Structure

The paper investigates the benefits of implementing the semiactive control systems in relation to passive viscous damping in the context of seismically isolated structures. Frequency response functions are compiled from the computed time history response to pulse-like seismic excitation. A simple semiactive control policy is evaluated in regard to passive linear viscous damping and an optimal non-causal semiactive control strategy. The optimal control strategy minimizes the integral of the squared absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied. The optimization procedure involves a numerical solution to the Euler-Lagrange equations Keywords: optimal control, Euler-Lagrange equations, nonlinear systems Introduction. Passive and active control techniques have been studied in various engineering fields [4, 5, 8, 9, 11-13, 15, 17]. Application of various techniques to civil engineering has been the subject of considerable research since the pioneer work of Yao [16]. Now, the trend in practice for passive isolation systems is toward very large isolators incorporating large viscous dampers. Recent studies show that the use of supplemental dampers in seismic isolation to increase the isolation damping reduce displacements, but at the expense of increases in interstory displacements and accelerations at high frequencies in the superstructure [7]. An increase in the interstory drifts and superstructure accelerations is counter to the primary goal of isolation systems: to protect the sensitive internal equipment and non-structural elements.Semiactive control systems, on the other hand, are a class of control systems in which the control actions are applied by changing the mechanical properties (i.e., stiffness and damping) of the control device [10]. Civil engineering structures incorporating semiactive devices exhibit nonlinear behavior and this motivates the development of nonlinear control strategies that can be practically implemented, which is a challenging task. As is well known, optimal control problem of a linear system with respect to a quadratic performance index has a flexible solution, which leads to the construction of a linear state regulator when there are no constraints on admissible controls [1][2][3]. It is known to the control community that except for relatively few special cases, the mathematical theory of nonlinear oscillations provides little help for practical nonlinear vibration control problems [6]. Therefore, the difficulties in synthesizing optimal feedback controls for nonlinear non-autonomous dynamical systems have motivated many researchers to use the formalism of optimal control theory to derive sub-optimal feedback controllers by obtaining approximate solutions to either the two-point boundary-value problem or to the Hamilton-JacobiBellman equations. Numerical solution to the two-point boundary-value problem for nonlinear non-autonomous dynamical systems can also be found using numerical optimization techniques. The resulting optimal c...

Section: Numerical Solution Of the Euler-lagrange Equationsmentioning

confidence: 99%

Optimal semiactive control of structures with isolated base

Aldemir

Gavin

2006

“…For fixed C and µ −1 , arbitrary time intervals T h , h ≥ 0, are specified as in [21][22][23][24], where T T 0 = for h = 0. Definition 1.…”

Section: Introductionmentioning

confidence: 99%

“…The problem to be formulated below will be solved using the comparison and direct Lyapunov methods and is independent of the sliding-mode conditions on the switching hyperplane in the phase space. The present study is based on the results reported in [14,[21][22][23][24][25].1. Problem Formulation.…”

mentioning

confidence: 99%

Technical stability of stationary automatic control systems of variable structure with switched filters

Matviichuk

2006

Self Cite

Sufficient conditions for the technical stability in measure of a nonstationary control system with variable structure are established. The controller of the system has feedback-switched filters functioning together with shaper and actuator. It is assumed that the nonstationary parameters of the system vary within given ranges, at a finite rate, with appropriate control laws, with adjustment against mismatch signal, its derivatives of finite order, and all variable parameters of the filter. The parameters of the switching hyperplane remain constant. This approach for analysis of technical stability does not involve sliding mode conditions. Criteria of technical instability in measure for the control system under consideration are formulated using the properties of systems of comparison from below. The general criteria of technical stability and instability are applied to nonstationary filtered-control systems of variable structure of the third order. The comparison method based on normalized Lyapunov functions is used Keywords: technical stability and instability, nonstationary control systems with variable structure, switched filters, normalized Lyapunov functions, comparison method Introduction. Among various control systems that allow optimal control, of widespread use are nonstationary automatic-control systems of variable structure with a control filter subjected to internal feedback and functioning together with a shaper and an actuator [1, 3, 8, etc.]. Control actions are discontinuous functions of the phase coordinates and external actions [4,17,19]. Filters introduced into the control loop increase the amount of information needed to design controllers [2, 21, 22, etc.]. Such variable-structure systems with filters make it possible to gain the maximum effect, including optimality, from the use of automatics [9, 11, 12, etc.]. Under certain conditions, these systems may give rise to a specific motion, so-called sliding mode [8,9,19].The present study is concerned with the technical stability and instability in measure of nonstationary variable-structure automatic-control systems with filters in the control loop. The problem to be formulated below will be solved using the comparison and direct Lyapunov methods and is independent of the sliding-mode conditions on the switching hyperplane in the phase space. The present study is based on the results reported in [14,[21][22][23][24][25].1. Problem Formulation. Let us consider a nonstationary automatic-control system of variable structure that includes a feedback-switched filter to provide high-quality control of real processes [1, 9, etc.]. Let the following differential equation of the nth order describe the operation of the basic part of the system-the actuator and the control plant, which have time-dependent parameters [8,19]:

“…Consider a nonstationary automatic-control system of variable structure that functionally includes filters of control signals [1,13]. The dynamic states of the system are described by the following equations [5,[18][19][20]: …”

mentioning

confidence: 99%

“…The established stability criteria are applied to a nonstationary filtered-control system of variable structure of the third order. The study is based on the results from [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

mentioning

confidence: 99%

Stability in sliding mode of nonstationary automatic-control systems of variable structure with switched filters

Matviichuk

2006

Self Cite

Stability conditions for a nonstationary automatic-control system of variable structure in sliding mode are established. The controller of the system has feedback-switched filters functioning together with the shaper and actuator. The nonstationary parameters of the system vary within given ranges, at a finite rate, under appropriate control laws, with adjustment for the error signal, its derivatives of finite order, and all variable parameters of the filter. The parameters of the switching hyperplane remain constant. This approach to stability analysis is based on the existence conditions for the sliding mode at the switching boundary in the phase space. The general stability and instability criteria are applied to nonstationary automatic filtered-control systems of variable structure of the third order Keywords: nonstationary automatic-control systems of variable structure, switched filters, sliding mode, stability and instability, error gain, nonstationary filtered-control system of variable structure of the third order Introduction. Filtered-control systems of variable structure are important, in particular, for solving practical problems in flight automation and automatic control of surface and subsurface ships, in various nonstationary filtration of program automatic control signals to reject artificial or natural interference, and in dynamic elastic processes and objects that should be controlled taking the time-dependence of their parameters into account [5, 10, 11, etc.]. The nonstationary parameters of the variable-structure system under consideration vary within given ranges, at a finite rate, under appropriate control laws, and with adjustment for the error signal, its derivatives of finite order, and all independent variable parameters of the filter [5,9,13], the parameters of the switching hyperplane remaining constant.The present paper addresses the stability of dynamic states of nonstationary automatic-control systems with variable structure in sliding modes. The controller in such systems includes control filters functionally commuted with the shaper and actuator. The approach proposed here for the stability analysis of such variable-structure systems is based on the existence conditions for the sliding mode at the switching boundary in the phase space [1][2][3][4]. Error gain is used for stabilization purposes [5,17]. The established stability criteria are applied to a nonstationary filtered-control system of variable structure of the third order. The study is based on the results from [1-20].1. Problem Formulation. Consider a nonstationary automatic-control system of variable structure that functionally includes filters of control signals [1,13]. The dynamic states of the system are described by the following equations [5,[18][19][20]: