First-order Reset Element Research Articles

Reset control performance improvement using fractional derivatives

When a linear controller is replaced by a reset controller, it is possible to keep the gain behaviour essentially the same, while improving the phase behaviour. However, because reset control is nonlinear, higher order harmonics appear, which may deteriorate the results. In this paper, reset controllers are combined with fractional derivatives, decreasing the magnitude of higher order harmonics. In this way, better results are found in simulations of a Clegg integrator, of a FORE (first order reset element), and of a CgLp (constant in gain lead in phase) controller. The reason why better results are found is explained.

A Nonlinear Integrator Based on the First-Order Reset Element

This work proposes a novel nonlinear Proportional-Integral (PI) controller, which utilizes a generalized first-order reset element. The proposed element can achieve similar magnitude-characteristics as its linear counterpart but with less phase lag at the open-loop crossover frequency (i.e. the control bandwidth), according to a sinusoidal-input describing function (SIDF) analysis. The same can be achieved with an existing reset-based integrator, the Clegg integrator (CI). However, it is known that a Proportional-CI (PCI) element can excessively generate higher-order harmonics of its input, which are neglected in the SIDF-analysis. Furthermore, a PCI can cause a limit cycle when placed in closed-loop with certain types of plants. The novel PI controller proposed in this work can prevent the limit cycle and can reduce the generation of higher-order harmonics, while retaining the beneficial phase advantage that is associated with existing reset-based PI controllers.

Generalization of Reset Controllers to Fractional Orders

Reset control is a simple non-linear control technique that can help overcome the structural limitations of linear control. Fractional control uses the concept of fractional derivatives to expand the range of possibilities when modeling a controller, making it more robust. Fractional reset control merges the advantages of both areas and is the object of this paper. Fractional-order versions of different reset controllers were implemented, namely a fractional Clegg integrator, a fractional generalized first-order reset element, a fractional generalized second-order reset element, and fractional “constant in gain lead in phase” controllers with first- and second-order reset elements. These were computed directly from a numerical implementation of the Grünwald–Letnikov definition of fractional derivatives, and their performances were analyzed.

Reset-control-based current tracking for a solenoid with unknown parameters

Abstract We propose a hybrid controller for reference tracking for the output current of a solenoid. The solenoid can be modeled as a first-order linear plant with unknown parameters. The proposed hybrid controller comprises 1) a feed forward action, based on an estimate of the unknown plant parameters exploiting a hybrid formulation of the recursive least-squares method, and 2) a feedback action, exploiting a reset control scheme based on a first-order reset element. We prove stability properties for the closed-loop system and we show through simulations that the current output converges to the reference for sufficiently exciting reference signals.

Stabilization of Magnetic Suspension System by Using Only a First-Order Reset Element without a Derivative Element

The stabilization of a magnetic suspension system is achieved by using a low-pass filter (LPF) with a nonlinear integrator without any other element. A proportional-derivative (PD) control is commonly used as the simplest method of stabilizing a magnetic suspension system. Meanwhile, a first-order reset element (FORE) was applied to improve transient characteristics. The original FORE was a first-order LPF with a nonlinear reset integrator element. A magnetic suspension system cannot be stabilized by a linear LPF, nor the original FORE. In this work, the reset conditions of the FORE were modified for magnetic suspension. This modified FORE succeeded in stabilizing a magnetic suspension system. The efficacy of the modified FORE was demonstrated by simulations and experiments. A single degree of freedom magnetic suspension system was used in the experiment.

Reset Control of Combustion Oscillation Model

Combustion oscillations occur themselves as pressure and heat release oscillations in lean premixed combustors, and may cause some unexpected damage. This paper proposes a design method of a reset controller to eliminate a combustion oscillation in a lean premixed combustor model. We consider a plant model consisting of a linear system with a nonlinear feedback element and a reset controller using a first-order lag element, which is called a first-order reset element (FORE). We show parameter conditions of the reset controller for which limit cycles are eliminated, using a describing function of the nonlinear element. We apply the proposed design method of the reset controller and a flame describing function to eliminate the combustion oscillation in the lean premixed combustor model and show its effectiveness appropriately.

Improved High-Order-Reset-Element Model Based on Circuit Analysis

In this brief, a generalized first-order reset element (GFORE) is first introduced, and its reset model is established based on circuit analysis. Then, a new class of models for the high-order reset element (HORE) is established by connecting several GFOREs and, defining a proper flow set and jump sets, the proposed model is more appropriate for describing the behavior of HORE than existing ones. Moreover, stability analysis results are presented for reset control systems containing high-order reset controllers. Finally, examples are given to show the superior performance of the proposed reset model and indicate the application prospect in networked control systems.

Position Regulation of an EGR Valve Using Reset Control With Adaptive Feedforward

We propose a hybrid control system performing set-point regulation of an exhaust gas recirculation valve of a Diesel engine. The control technique is based on a first-order reset element (FORE) embedded with an adaptive feedforward action whose aim is to provide asymptotic rejection of disturbances acting at the plant input. The feedforward action is adapted by suitable resetting laws occurring whenever the FORE is reset to zero. We first provide a formal analysis of the effectiveness of the adaptive reset system to guarantee asymptotic set-point regulation, and then, we illustrate how the adaptive feedforward can be parameterized for improved transient performance. We experimentally illustrate the proposed solution on a Diesel engine testbench, which reveals substantial position accuracy improvement during a standard driving cycle, as compared with the production standard solution.

A reset observer with discrete/continuous measurements for a class of fuzzy nonlinear systems

This paper proposes the design of a reset fuzzy observer for the class of nonlinear systems able to be described by a Takagi–Sugeno fuzzy model. The observer uses both continuous and discrete measurements and in contrast with the observers based on the First Order Reset Element (FORE), it updates its states resetting the initial condition of the integrator at each instant when the discrete measurements are available. The proposed fuzzy observer is applied to estimate the substrate and biomass concentration of an anaerobic wastewater treatment process and the effectiveness of the proposed method is tested by simulations comparing the results of a reset fuzzy observer with two fuzzy observers using continuous measurements only. Finally, the estimation scheme is validated using experimental data from an actual anaerobic digestion process, suggesting that the proposed reset fuzzy observer is a practical and encouraging approach to the state estimation of the class nonlinear processes under study.

Stability and Performance of SISO Control Systems With First-Order Reset Elements

We consider set-point regulation and L2 robust stability properties of a class of reset control systems consisting of a minimum-phase relative degree-one linear SISO plant controlled by a novel first-order reset element (FORE). These results rely on necessary and sufficient conditions for exponential and L2 finite gain stability of a class of planar reset systems consisting of a scalar linear plant controlled by the novel FORE. We show that the L2 gain of the planar reset system decreases to zero as the pole and/or the gain of the FORE are increased to infinity. A number of stability results, including Lyapunov conditions for Lp and exponential stability, for a larger class of reset and hybrid systems are presented and used to prove our main results.

Analytical and numerical Lyapunov functions for SISO linear control systems with first‐order reset elements

AbstractIn this paper we provide analytical and numerical Lyapunov functions that prove stability and performance of a First‐order Reset Element (FORE) in feedback interconnection with a SISO linear plant. The Lyapunov functions also allow to establish finite gain ℒ︁2 stability from a disturbance input acting at the input of the plant to the plant output. ℒ︁2 stability is established by giving a bound on the corresponding ℒ︁2 gains. The proof of stability and performance is carried out by showing that the Lyapunov functions constructed here satisfy the sufficient conditions in the main results of Nešić et al. (Automatica 2008; 44(8):2019–2026). In the paper we also point out and illustrate via a counterexample an analysis subtlety overlooked in the preliminary results of Zaccarian et al. (American Control Conference, Portland, OR, U.S.A., 2005). Copyright © 2010 John Wiley & Sons, Ltd.

Analysis of Reset Control Systems Consisting of a FORE and Second-Order Loop1

Reset controllers consist of two parts—a linear compensator and a reset element. The linear compensator is designed, in the usual ways, to meet all closed-loop performance specifications while relaxing the overshoot constraint. Then, the reset element is chosen to meet this remaining step-response specification. In this paper, we consider the case when such linear compensation results in a second-order (loop) transfer function and where a first-order reset element (FORE) is employed. We analyze the closed-loop reset control system addressing performance issues such as stability, steady-state response, and transient performance.

Non-linear design for cost of feedback reduction in systems with large parameter uncertainty †

Feedback systems containing linear, minimum-phase plants with large parameter uncertainty may be designed to achieve specified performance tolerances over the entire range of parameter uncertainty. The principal ‘cost of feedback’ is in the feedback loop bandwidth, which is generally much larger than that of the system as a whole. This makes the system very sensitive to sensor noise and high-frequency parasitics. It is shown how a non-linear ‘first-order reset element’ (FORE) may be used to drastically decrease the feedback loop transmission bandwidth. One is logically led to FORE by simple, linear feedback frequency response concepts. The paper assumes that the primary design problem is to satisfy quantitative response tolerances to command inputs. However, disturbances at the plant are not neglected, but the specification on such disturbances is in the damping of the step response. An important feature of the non-linear design is that the system response to command inputs is almost exactly that of a lin...