Guillermo J. Silva

New results on the synthesis of PID controllers

This paper considers the problem of stabilizing a first-order plant with dead time using a proportional-integral-derivative (PID) controller. Using a version of the Hermite-Biehler theorem that is applicable to quasi-polynomials, the complete set of stabilizing PID parameters is determined for both open-loop stable and unstable plants. The range of admissible proportional gains is first determined in closed form. For each proportional gain in this range, the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid, a triangle or a quadrilateral. For the case of an open-loop unstable plant, a necessary and sufficient condition on the time delay is determined for the existence of stabilizing PID controllers.

Brief PI stabilization of first-order systems with time delay

This paper considers the problem of stabilizing a first-order plant with dead time using a PI controller. Using a version of the Hermite-Biehler Theorem applicable to quasipolynomials, a complete and constructive characterization of all stabilizing PI gain values is obtained.

Stabilization of time delay systems

We first consider the problem of stabilizing a first-order plant with dead time using a constant gain controller. Using a version of the Hermite-Biehler theorem applicable to quasipolynomials, a complete analytical characterization of all stabilizing gain values is provided as a closed form solution. A similar approach is then used to tackle the problem of stabilizing a first-order plant with time delay using a PI controller, and once again the complete stabilizing set is determined.

On the stability and controller robustness of some popular PID tuning rules

In this note, we study the stability and controller robustness of some popular proportional-integral-derivative (PID) tuning techniques that are based on first-order models with time delays. Using the characterization of all stabilizing PID controllers derived in a previous paper, each tuning rule is analyzed to first determine if the proportional gain value dictated by that rule, lies inside the range of admissible proportional gains. Then, the integral and derivative gain values are examined to determine conditions under which the tuning rule exhibits robustness with respect to controller parameter perturbations.

Adaptive internal model control: the discrete-time case

This paper considers the design and analysis of a discrete-time H2 optimal robust adaptive controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete-time robust adaptive law with a discrete-time H2 internal model controller to obtain a discrete-time adaptive H2 internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for the continuous-time case. Nevertheless, there are some differences which, together with the widespread use of digital computers for controls applications, justifies a separate exposition. Copyright

Controller design via Pade approximation can lead to instability

The Pade approximation is often used to approximate a pure time delay by a rational transfer function. In this paper, we show via examples that PID controllers that stabilize such an approximation may actually be destabilizing for the true system. Recent results, giving the entire set of stabilizing PID controllers for finite dimensional linear time invariant systems as well as for systems with time delay, are used to make a comparative study, through examples, of the stabilizing sets for the true plant and its Pade approximants.

Power-performance management on an IBM POWER7 server

The processor and cooling subsystems of high-performance servers consume a significant portion of total system power. In this paper, we use the server energy-efficiency benchmark SPECpower ssj2008 to assess dynamic power management strategies for these sub-systems on an IBM POWER 750 platform. First, we evaluate the impact of feedback-driven fan control to reduce power while continuously maintaining a suitable thermal environment. Next, we demonstrate the importance of refining traditional utilization-based DVFS algorithms when managing systems with large core and thread counts. We present a new approach and demonstrate its effectiveness with real-world scenarios for dynamic power management. With reliable runtime power management, we can safely boost (turbo) core frequencies beyond their nominal values to achieve higher throughput. The combined effect of dynamic fan and enhanced processor DVFS control yields an overall improvement of 43% for the energy-efficiency score of the SPECpower ssj2008 benchmark on our test system.

Stabilization of first-order systems with time delay using the PID controller

This paper considers the problem of stabilizing a first-order plant with dead-time using a PID controller. Using a version of the Hermite-Biehler theorem applicable to quasi-polynomials, the complete set of stabilizing PID parameters is determined for both open-loop stable and unstable plants. The range of admissible proportional gains is first determined in closed form. For each proportional gain in this range the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid, a triangle or a quadrilateral. For the case of an open-loop unstable plant, a necessary and sufficient condition on the time delay is determined for the existence of stabilizing PID controllers. An example illustrates the applicability of the procedure.

Robust control design using the PID controller

We present useful tools and criteria for designing a PI or a PID controller for a first-order system with time delay. These tools show the importance of knowing apriori the set of controller parameter values that stabilize the closed-loop system. The characterization of these stabilizing sets was derived in earlier works (Ref.1, 2) and serves as the basis of the synthesis tools presented in the paper.

Determination of stabilizing feedback gains for second-order systems with time delay

In this paper we consider the problem of stabilizing a second-order plant with dead-time using a constant gain controller. Due to the presence of the time delay, the number of roots of the characteristic equation of the closed-loop system is infinite, making the problem posed in this paper a difficult one. A complete analytical characterization of all stabilizing feedback gains is provided using a version of the Hermite-Biehler Theorem applicable to quasipolynomials. Both open-loop stable and unstable plants are considered. The results reported in this paper will serve as a stepping stone for tackling the more complicated cases of stabilization using a PI or a PID controller.