Kazuhiko Hiramoto

Integrated design of structural and control systems with a homotopy like iterative method

We consider an integrated design problem of structural and control systems. It is well known that even the simplest formulation of this problem results in a kind of a BMI problem. In this paper, a homotopy-like iterative design method based on LMIs is proposed to obtain an optimal plant and a controller simultaneously for a full-order output feedback problem. We can deal with a multiobjective problem, e.g., H/sub 2//H/sub /spl infin// control problem etc. in the proposed design method. We can also optimize structural design parameters appearing nonlinearly in the coefficient matrices of the plant state-space form using the first order approximation of the nonlinear dependence in the proposed algorithm. Several design examples show that the proposed algorithm works quite effectively for various integrated design problems.

Simultaneous optimal design of structural and control systems for cantilevered pipes conveying fluid

We consider a shape optimization problem for a cantilevered pipe conveying fluid. The outer diameter distribution of the pipe and the location of the sensor and the actuator are optimized such that the critical flow velocity of the closed-loop system is maximized. The outer diameter distribution is optimized such that the total volume of the pipe is unchanged with the initial diameter distribution. The critical flow velocity of the closed-loop system is defined as the flow velocity which cannot be stabilized by active control law with a predetermined energy quantity. By this definition, it is physically reasonable comparing the quality of several design candidates since all candidates are actively controlled with the same energy consumption. We propose a method for obtaining the critical flow velocity with consideration of the amount of computation for the optimal design. This optimal design problem results in a maximization problem with equality and inequality constraints. We adopt simulated annealing method which is known as one of discrete optimization techniques for obtaining the optimal design.

Integrated design of system parameters, control and sensor/actuator placement for symmetric mechanical systems

In this paper, we address the problem of integrated design of output feedback control, structural damping parameters, and sensor/actuator placement to satisfy an upper bound on the closed-loop H ∞ or H 2 norm performance of externally symmetric systems. By combining results on the upper bound of the closed-loop norm for externally symmetric systems with a homotopy-like approximation of an optimization problem, we provide a formulation of the integrated design problem of minimizing the upper bound H ∞ or H2 norm via iterative LMI optimization problems. In this formulation, the corresponding decision variables are the structural damping parameters, the static rate feedback gain, and the sensor and actuator locations. By iteratively solving the approximated LMI problem, a locally optimal solution is obtained. The method is validated on a numerical example of active collocated vibration control of a simply supported beam.

Simultaneous Optimal Design of the Lyapunov-Based Semi-Active Control and the Semi-Active Vibration Control Device: Inverse Lyapunov Approach

We address a simultaneous optimal design problem of a semi-active (SA) control law and design parameters in a semi-active control device for civil structures. The vibration control device (VCD) that is being developed by authors is used as the semi-active control device. The VCD is composed of a ball screw with a flywheel for the inertial resistance force and an electric motor with an electric circuit for the damping resistance force. A new bang–bang type semi-active control law referred to as inverse Lyapunov approach is proposed. In the inverse Lyapunov approach, the Lyapunov matrix in the bang–bang type semi-active control based on the Lyapunov function is searched so that the control performance of the semi-active control system is optimized. Design parameters to determine the Lyapunov function and those of the VCD are optimized with the genetic algorithm (GA). The effectiveness of the proposed approach is presented with simulation studies.

Active Gain Scheduling: A Collaborative Control Strategy between LPV Plants and Gain Scheduling Controllers

We propose a new collaborative control strategy between time varying design parameters of the plant and the feedback controller. As the feedback control law we adopt the LMI based gain scheduling control scheme to guarantee the closed-loop L2 gain performance against the variation of the time varying parameter of the control object. Under the gain scheduling control we propose a method for the adjustment of the time varying parameter using the theory of dissipative systems. The objective of the time varying parameter tuning is to obtain smaller L2 norm of the controlled output. We refer to this control strategy as Active Gain Scheduling Control (AGSC) because the scheduling parameter is actively changed while the control system is working. We show that the tuning rule of the time varying design parameter becomes a bang-bang type in some cases.

Semi-Active Control of Civil Structures With a One-Step-Ahead Prediction of the Seismic Response

We propose a semi-active control of civil structures based on a one-step-ahead prediction of the seismic response. The vibration control device (VCD), which has been developed by authors, generates two types of resistance forces, i.e., a damping force proportional to the relative velocity and an inertial force proportional to the relative acceleration between two stories. The damping coefficient of the VCD can be changed with a command signal to an electric circuit connected to the VCD. In the present paper the command signal for changing the damping coefficient of each VCD is assumed to take two values, i.e., the command to take the maximum or minimum damping coefficient. The optimal command signal is selected from all candidates of command signals so that the Euclidean norm of the one-step-ahead predicted seismic response is minimized. As an example a semi-active control of a fifteen-story building with three VCDs is considered. The simulation results show that the proposed semi-active control achieves superior performance on vibration suppression compared with a passive control case where the damping coefficient of each VCD is fixed at its maximum value.Copyright

Global Optimal Design of Dynamic Parameters of Robot Manipulators

In this paper we deal with a global optimal design of dynamic parameters of robot manipulators. The dynamic characteristic of robot manipulators is uniquely determined by base parameters, which are functions of physical parameters, e.g., the mass, the moment of inertia and the damping of each link, etc.. Using the fact that the equation of motion of manipulators generally becomes an afflne function on the base parameters we propose an LMI based global optimal design of the base parameters of robot manipulators. In this paper we obtain the global optimal base parameters minimizing the required energy to achieve a given task (given by the reference trajectory of the end-effector). We adopt the computed torque method as the control law for the robot manipulators. The proposed design method guarantees the global optimality of the optimized base parameters. As a design example an optimal design of the base parameters of planar two link manipulator is presented.

Active/semi-active hybrid control for motion and vibration control of mechanical and structural systems

As a new control design framework for motion and vibration control of mechanical and structural systems, an active/semi-active hybrid control (ASHC) methodology is proposed in this paper. In the proposed ASHC framework, a mechanical system that has both an actuator for motion and vibration control, and a semi-active control device, e.g., MR damper, for vibration control is defined as a control configuration. Depending on the location of the actuator and the semi-active device, two ASHC problems are formulated as optimization problems of the control performance on the motion and vibration control. In the ASHC approach, the higher control performance is accomplished by the cooperative and complementary control of the actuator and the semi-active control device. Some solution candidates and design examples are presented to show the effectiveness and the importance of the ASHC framework.

Semi-Active Control of Civil Structures Based on the Prediction of the Structural Response: Integrated Design Approach

Various methodologies for vibration control of civil structures have been proposed so far. The traditional scheme is passive vibration control, i.e., dissipation of the vibration energy to the outside of the structural systems with dampers or mass dampers etc.. Passive control is quite simple and popular still, however it has some limitations, e.g., insufficient performance and/or difficulty in tuning such devices for a case of multi-mode vibration control etc.. Active vibration control is a candidate for a breakthrough to overcome the above drawbacks of passive control and has been studied extensively these decades ((Spencer et al., 1998) and the references therein). Although many studies show that the active control methodology achieves the quite high control performance on vibration suppression, it requires a large energy source to produce the control force and this fact has been an obstacle in applying active methods to general vibration control problems. Semi-active control, which is not necessarily new (Karnop et al., 1974) either, can be recognized as an intermediate between passive and active schemes in the sense of not only the performance on vibration suppression but also the complexity of the control system. In most semi-active control vibration suppression is achieved by changing the damping coefficient of the semi-active damper. In civil structures semi-active control technique is getting more realistic recently (Casciati et al., 2006) along with the development of a large scale damper whose damping property is able to be changed (Sodeyama et al., 1997). In semi-active control, the damping coefficient of the semi-active damper is changed mainly based on the following two strategies:

Biomechanical analysis and muscle tension estimation of the lower extremities using EMG data

Functional electrical stimulation (FES) rowing is a whole-body exercise in which the lower extremities are moved by electric stimulation and the upper extremities are moved voluntarily by paraplegics. The purpose of this study was to identify the kinematic factors of the lower extremities required to perform FES-rowing through the biomechanical analysis. Eighteen healthy adult men participated in this study. A mathematical model was developed to analyze the conventional rowing with or without handle and FES lower extremity extension exercise. The calculated data has the potential to be applied in the low-load and safe FES rowing exercise for the paraplegics.