Orhan Beker

Fundamental properties of reset control systems

Reset controllers are linear controllers that reset some of their states to zero when their input is zero. We are interested in their feedback connection with linear plants, and in this paper we establish fundamental closed-loop properties including stability and asymptotic tracking. This paper considers more general reset structures than previously considered, allowing for higher-order controllers and partial-state resetting. It gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded-input bounded-state stability and steady-state performance. Unlike previous related research, which includes the study of impulsive differential equations, our stability results require no assumptions on the evolution of reset times.

Stability of a reset control system under constant inputs

Reset controllers are standard linear compensators equipped with mechanism to instantaneously reset their states. With respect to pure linear control, there is evidence that this reset action is capable of improving control system tradeoffs. This papers objective is to analyze the stability of a particular example of reset control system when excited by constant inputs. Our main result shows that the equilibrium point of the closed-loop dynamics is asymptotically stable.

Stability of a MIMO reset control system under constant inputs

Reset controllers are standard linear compensators equipped with a mechanism to instantaneously reset their states. With respect to pure linear control, there is evidence that this reset action is capable of improving control system tradeoffs. In Beker et al. (1999) we established stability conditions for SISO reset control systems and this paper extends these results to the MIMO case. The papers objective is to analyze the stability of such reset control systems when excited by constant inputs. Our main result gives conditions under which the equilibrium point of the closed-loop dynamic is asymptotically stable.

Plant with integrator: an example of reset control overcoming limitations of linear feedback

The purpose of this paper is twofold. First, to give conditions under which linear feedback control of a plant containing integrator must overshoot. Secondly, to give an example of reset control that does not overshoot under such constraints.

On reset control systems with second-order plants

Reset control has the potential of providing better trade-offs among competing specifications compared to LTI control. We consider a specific class of reset control systems consisting of a feedback interconnection between a linear second-order system and a so-called first-order reset element. Despite the simplicity of this feedback system, few theoretical results are available to quantify stability and performance. The paper develops a necessary and sufficient condition for asymptotic stability and a sufficient condition for BIBO stability. We also characterize steady-state response, overshoot, rise time and settling time to step input.

Forced oscillations in reset control systems

Reset controllers are linear systems that reset some or all of their states to zero based on a given reset law. We (1999) previously established asymptotic stability results for reset control systems under constant inputs. The bounded-input bounded-output stability of reset systems was addressed by Chen et al. (2000). In this paper, we study their response to sinusoidal inputs and analyze oscillations forced by sinusoidal sensor noise. Our motivation is to establish reset control system response to (sinusoidal) sensor noise.

Stability of limit-cycles in reset control systems

In this paper, the authors continue their work on establishing the properties of reset control systems. Here, they focus on the local stability of limit-cycles induced under sinusoidal sensor excitation.

FUNDAMENTAL PROPERTIES OF RESET CONTROL SYSTEMS

Abstract Reset controllers are linear controllers that reset some of their states to zero when their input is zero. We are interested in their feedback connection with linear plants, and in this paper we establish fundamental closed-loop properties. This paper considers more general reset structures than previously considered, allowing for higher-order controllers and partial-state resetting. It gives a testable necessary and sufficient condition for quadratic stability and links it to uniform bounded-input bounded-output state stability. Unlike previous related research, which includes the study of impulsive differential equations, our stability results require no assumptions on the evolution of reset times.