Use of Constant Anticipating and Delayed Control in Shock Isolation Problem Applied to an Object on a Movable Base
- PDF / 520,886 Bytes
- 11 Pages / 612 x 792 pts (letter) Page_size
- 82 Downloads / 128 Views
of Constant Anticipating and Delayed Control in Shock Isolation Problem Applied to an Object on a Movable Base V. A. Korneev Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia e-mail: [email protected] Received August 22, 2019; revised September 10, 2019; accepted September 14, 2019
Abstract—The present article deals with the problem on constructing a guaranteeing time of a given control beginning for a shock isolator protecting an object on a movable base from impacts acting on this base. The initial moment of control action can either be ahead (anticipation) or lag behind (delay) the moment of the disturbance beginning. It is assumed that the shock shape is unknown, but its duration is given and the acceleration of the base is described by an constant-sign function of time with a given integral. As a control force bounded in magnitude that acts between the base and an object to be protected, we set the constant control of a given duration that has been previosly obtained for an instantaneous shock (impact) for a problem without anticipation. The performance index to be minimized is the maximum displacement of the object relative to the base. Based on the value of the performance index, a comparison of the proposed optimization at the moment of the control beginning with other control methods, in particular, with the optimal solution with a single switching is performed. Keywords: shock isolation, optimal control, guaranteeing anticipating control, delay, worst disturbances DOI: 10.3103/S0025654420020120
INTRODUCTION The article deals with the analyzing the simplest method of controlling a shock (impact) isolator under the worst disturbances. A system with one degree of freedom that consists of a base and an object to be protected that is placed on this base is considered. The impact on the base is characterized by acceleration and is described by a function of time. The base and the object to be protected move along one straight line and the control force created by the isolator between the base and the object is bounded in magnitude. In [1–3], the problem on minimizing the maximum modulus of displacement of an object relative to the base under a given disturbance is posed. The foundations of the theory of the optimal shock isolation are developed in [4–7]. The possibilities of isolating an object located on a movable base from short-term impacts using an active isolator with nonanticipating control are studied in [8]. In [8], the maximum possible worst disturbance duration, below which it is optimal to use a constant maximum possible control of a given duration, is obtained. In this case, the control duration is determined from the stopping condition of the object to be protected after the action of disturbance and control. For some specific disturbances, optimal anticipating controls are constructed numerically or analytically in [9]. For problems with a given disturbance duration and fixed control, it is also proved in [9] that the worst disturbances are delta fun
Data Loading...
