Mixed H2/H∞ control with pole placement in a class of regions

The problem of mixed H₂/H_∞ control with pole placement is considered for linear time-invariant systems. This is the problem of determining a controller for linear time-invariant systems which minimizes the H₂-norm of a certain closed-loop transfor function subject to an H_∞-norm constraint on another closed-loop transfer function and an additional constraint on the location of the closed-loop poles in the complex plane. An optimization problem is posed for the pole-constrained H₂/H_∞, problem in such a way that the objective function is expressed as a weighted sum of the actual H₂ cost and its upper bound. A necessary condition for the optimization problem is derived via the Lagrange multiplier technique. The condition involves a set of highly coupled equations. By sacrificing the H₂ performance, an alternative optimization problem is posed in order to simplify the necessary condition. An iterative algorithm for solving the coupled equations arising in the necessary conditions is proposed and numerical examples are presented.     

A portable pneumatic driving unit for a left ventricular assist device

The authors developed a portable air driving unit for an artificial heart. As the portable energy source of the driver, a commercially available Ni-Cd battery was used. A linear compressor was selected as a portable size compressor. To reduce the number of parts to be assembled, a new type of pneumatic system was employed. In this system, the pressure level was regulated by varying the output flow rate of the compressor instead of using a pressure regulator and large air reservoirs. A one-board microcomputer and pressure sensors were used to control the pressure level. The total weight of the unit is 9.5 Kg. After assembling the components into the portable unit, a blood pump was connected to examine the output characteristics of the system. It was confirmed that the unit could drive the blood pump continuously for more than 2 hours under the following conditions: output flow rate of the blood pump = 5 L/min and output pressure = 100 mmHg.     

Computation of optimal control trajectories using Chebyshev polynomials: parameterization,and quadratic programming

An algorithm is proposed to solve the optimal control problem for linear and nonlinear systems with quadratic performance index. The method is based on parameterizing the state variables by Chebyshev series. The control variables are obtained from the system state equations as a function of the approximated state variables. In this method, there is no need to integrate the system state equations, and the performance index is evaluated by an algorithm which is also proposed in this paper. This converts the optimal control problem into a small size parameter optimization problem which is quadratic in the unknown parameters, therefore the optimal value of these parameters can be obtained by using quadratic programming results. Some numerical examples are presented to show the usefulness of the proposed algorithm. Copyright © 1999 John Wiley & Sons, Ltd.