A simpler formula for the singular values of a certain Hankel operator

This paper deals with the problem of computing the singular values and vectors of a Hankel operator with symbol m^*W where m ε H^∞ is arbitrary inner and W ε H^∞ is rational. A simplified version of the formula given in [6] is obtained for computing the singular values of the Hankel operator. This result is applied to the (one-block) H^∞ optimal control of SISO stable infinite dimensional plants and rational weights. Using this new formula a simple expression is derived for the H^∞ optimal controller whose structure was observed in [9].     

On the mixed sensitivity minimization for systems with infinitely many unstable modes

In this note we consider a class of linear time invariant systems with infinitely many unstable modes. By using the parameterization of all stabilizing controllers and a data transformation, we show that controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes.     

Frequency domain analysis and robust control design for an ideal flexible beam

We study the problem of designing a feedback controller for a highly flexible Euler-Bernoulli beam using a distributed-parameter H^∞-method. Employing skew Toeplitz theory, we derive the H^∞-optimal controller for a weighted mixed sensitivity design for the beam. Based on the structure of the optimal controller we obtain suboptimal, finite-dimensional, linear, time-invariant controllers. With this approach we are able to include the added difficulties of a pure time delay and a noncollocated actuator/sensor pair directly into the design process.     

Controller design for natural and robotic systems with transmission delays

Robust stability and two‐dimensional trajectory following problems are considered for n‐link robotic systems with transmission delays. Such problems appear in telerobotics, where the controller is physically far from the robot, and in neural control of musculo‐skeletal (biological) systems, where muscle actuation and neural sensing are subject to time delays. A typical second‐order nonlinear dynamical model is taken with input and output time delays. In a prior work by the authors, a control strategy was developed for stable movement of the planar linkage system, using the standard Q‐parameterization and solving an H^∞ control problem to determine the free parameter. In this article, a new control scheme is proposed to eliminate the steady‐state errors seen in the tracking performance of the controller derived in the earlier work. Simulation examples are shown to demonstrate the effectiveness of the proposed control methodology. © 2002 Wiley Periodicals, Inc.     

PID controller design for fractional-order systems with time delays

Classical proper PID controllers are designed for linear time invariant plants whose transfer functions are rational functions of s^α, where 0<α<1, and s is the Laplace transform variable. Effect of input-output time delay on the range of allowable controller parameters is investigated. The allowable PID controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants.     

Comparison of PI controllers designed for the delay model of TCP/AQM networks

One of the major problems of communication networks is congestion. In order to address this problem in TCP/IP networks, Active Queue Management (AQM) scheme is recommended. AQM aims to minimize the congestion by regulating the average queue size at the routers. To improve upon AQM, recently, several feedback control approaches were proposed. Among these approaches, PI controllers are gaining attention because of their simplicity and ease of implementation. In this paper, by utilizing the fluid-flow model of TCP networks, we study the PI controllers designed for TCP/AQM. We compare these controllers by first analyzing their robustness and fragility. Then, we implement these controllers in ns-2 platform and conduct simulation experiments to compare their performances in terms of queue length. Taken together, our results provide a guideline for choosing a PI controller for AQM given specific performance requirements.     

Robust flow control in data‐communication networks with multiple time‐delays

Robust controller design for a flow control problem where uncertain multiple time‐varying time‐delays exist is considered. Although primarily data‐communication networks are considered, the presented approach can also be applied to other flow control problems and can even be extended to other control problems where uncertain multiple time‐varying time‐delays exist. Besides robustness, tracking and fairness requirements are also considered. To solve this problem, an ??^∞ optimization problem is set up and solved. Unlike previous approaches, where only a suboptimal solution could be found, the present approach allows to design an optimal controller. Simulation studies are carried out in order to illustrate the time‐domain performance of the designed controllers. The obtained results are also compared to the results of a suboptimal controller obtained by an earlier approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimizing low-order controllers for haptic systems under delayed feedback

In this paper, a PD controller design for haptic systems under delayed feedback is considered. More precisely, a complete stability analysis of a haptic system where local dynamics are described by some second-order mechanical dynamics is presented. Next, using two optimization techniques ($H_{\infty }$ and stability, margin optimization) an optimal choice for the controller gains is proposed. The derived results are tested on a three degree-of-freedom real-time experimental platform to illustrate the theoretical results.