Automation and Robot Applications 332 Design of second-order sliding mode controllers for MR damper-embedded smart structures

This paper presents the design of second-order sliding mode controllers for semi-active control using magneto-rheological (MR) dampers. The approach can be useful in applications involving shock absorbers but here our main concern is the suppression of building vibrations induced by dynamic loadings such as earthquakes or strong winds. The MR dampers have been of increasing interest in structural control as they are inexpensive to manufacture and have attractive properties such as small energy requirements, reliability and stability in operations, as well as a fast response of milliseconds. Challenges of MR damper structural control rest with the system’s high nonlinearity due to the force-velocity hysteresis, and the constraint of the magnetisation current, required to be between its zero and maximal values. A variety of control algorithms have been applied, including the decentralized bangbang control, modulated homogeneous friction algorithm, clipped optimal control, Lyapunov-based control, and also non model-based intelligent schemes. In these techniques, the currents are usually obtained from the damping force indirectly rather than directly from the controller output. For direct current control, in this paper we propose second-order sliding mode controllers, which can satisfy the control constraint, provide high accuracy, retain robustness and remove chattering. The effectiveness of the proposed direct current control technique is verified, in simulations, on a benchmark building model subject to excitation of various scaled earthquake records. Introduction Control devices and methodologies for suppression of high-rise building vibrations caused by a dynamic loading source can be classified as passive dampers requiring no input power to operate, active dampers requiring a great deal of power to generate counteracting forces, and semi-active combining features of passive and active damping (Datta, 2003; Symans & Constaninou, 1999; Yoshida et al., 2004). In structural control, active control devices require a certain amount of energy to drive the actuators to accomplish the control objective. On the other hand, semi-active control needs a relatively small amount of driving power and the actuators can also be operated in the passive mode. The philosophy adopted in these approaches is to effectively absorb the vibration energy by modifying the control device physical characteristics. For semi-active structural control, the use of magneto-rheological (MR) dampers has been of increasing interest in smart civil structures as they are inexpensive to manufacture, have reliable, stable and fail-safe operations, small energy requirements, and a fast response of milliseconds. Given the advantages of MR dampers and semi-active control strategies, a number of controller designs have been proposed for the building control problem. In most of MR damper controllers developed so far, the current supplied to the dampers is quite often derived, from the required damping force obtained as the control signal, via a secondary current-control loop. In this paper, the direct current control approach for MR-dampers is proposed using second-order sliding mode (SOSM) controllers. The idea is to control directly the magnetisation current of the semi-active device in order to drive to zero not only the sliding function of the state variables but also higher-order time derivatives of the sliding function. The SOSM approach retains strong robustness of the system in the sliding mode, at the same time removes the chattering effect, provides even higher accuracy in realisation, and is suitable for control signals subject to constraints. These features make it ideal for direct current control of the MR damper used in the smart structures. The remainder of the paper is organized as follows. The system description and the design of the proposed SOSM controller are included in Section 2. Simulation results are given in Section 3 to verify the effectiveness of the proposed approach. Finally, a conclusion is drawn in Section 4. 26th International Symposium on Automation and Robotics in Construction (ISARC 2009) 333 Control Design Consider pairs of MR dampers, placed in a differential configuration on the 1st ,... th k ,... and th n floors of a building, with the control current vector T ] [ i n k i i i L L 1 = whose entries are constrained between zero and the maximal values. By defining the system state n 2 R ∈ = T T T ] x [x y & , the state-space equation for the smart structure can be written as (Ha et al., 2007): E B(y)i Αy y + + = & , (1) in which