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A controller with the frequency response of a complex order derivative may have a gain that decreases with frequency, while the phase increases. This behaviour may be desirable to ensure simultaneous rejection of high-frequency noise and robustness to variations of the open-loop gain. Implementations of such complex order controllers found in the literature are unsatisfactory for several reasons: the desired behaviour of the gain may be difficult or impossible to obtain, or non-minimum phase zeros may appear, or even unstable open-loop poles. We propose an alternative nonlinear approximation, combining a CRONE approximation of a fractional derivative with reset control, which does not suffer from these problems. An experimental proof of concept confirms the good results of this approximation and shows that nonlinear effects do not preclude the desired performance.

This paper proposes a fractional-order reset element whose architecture allows for the suppression of nonlinear effects for a range of frequencies. Suppressing the nonlinear effects of a reset element for the desired frequency range while maintaining it for the rest is beneficial, especially when it is used in the framework of a “Constant in gain, Lead in phase” (CgLp) filter. CgLp is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation—the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies. However, CgLp’s ideal behaviour is based on the describing function, which is a first-order approximation that neglects the effects of the higher-order harmonics in the output of the filter. Although CgLp is fundamentally a nonlinear filter, its nonlinearity is not required for all frequencies. Thus, it is shown in this paper that using the proposed reset element architecture, CgLp gets closer to its ideal behaviour for a range of frequencies, and its performance will be improved accordingly.

The reset control is a simple nonlinear control approach where the states of the controller are conducted to zero when a particular condition is satisfied. The PI+CI is a controller that mixes the simplicity of PI controllers with the benefits of a reset action to mitigate the fundamental limitations of linear control. However, the tuning of this kind of controller, with three parameters, two for the linear part and one for the nonlinear one, is not trivial. In this paper, simple tuning rules for PI+CI are proposed for both tracking and regulation problems, assuming first-order dynamics for the plant. The resulting control scheme, for which the reset coefficient is computed from exponential functions, is simulated and compared with an ideal PI+CI where the reset coefficient is obtained using rules available in the literature. Similar results are obtained for the tracking problem, and optimal performance based on the Integral Absolute Error (IAE) is also obtained for the regulation problem. These new rules, in contrast to those already existing in the literature, depend only on closed-loop specifications. Furthermore, the framework based on the minimization of IAE, used to obtain the proposed rules, makes it possible to consider for the first time the tracking and regulation problems simultaneously, i.e., cases where setpoint changes and disturbance arrivals can occur at the same time before reaching a new steady state. The results are validated using a set of study cases.

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.

An intelligent vehicle must face a wide variety of situations ranging from safe and comfortable to more aggressive ones. Smooth maneuvers are adequately addressed by means of linear control, whereas more aggressive maneuvers are tackled by nonlinear techniques. Likewise, there exist intermediate scenarios where the required responses are smooth but constrained in some way (rise time, settling time, overshoot). Due to the existence of the fundamental linear limitations, which impose restrictions on the attainable time-domain and frequency-domain performance, linear systems cannot provide smoothness while operating in compliance with the previous restrictions. For this reason, this article aims to explore the effects of reset control on the alleviation of these limitations for a lane change maneuver under a set of demanding design conditions to guarantee a suitable ride quality and a swift response. To this end, several reset strategies are considered, determining the best reset condition to apply as well as the magnitude thereto. Concerning the reset condition that triggers the reset action, three strategies are considered: zero crossing of the controller input, fixed reset band and variable reset band. As far as the magnitude of the reset action is concerned, a full-reset technique is compared to a Lyapunov-based error minimization method to calculate the optimal reset percentage. The base linear controller subject to the reset action is searched via genetic algorithms. The proposed controllers are validated by means of CarSim.

Purpose This paper aims to investigate the attitude regulation for spacecraft in the presence of time-varying inertia uncertainty and exogenous disturbances. Design/methodology/approach The high gain approaches are typically used in existing researches for theoretical advantages, bringing better performance but sensitive to parameter selection, making the controller conservative. A reset-control policy is presented to achieve the spacecraft attitude control with easy control parameter tuning. Findings The reset-control policy guarantees satisfying control performance despite using performance tuning function and saturation function besides reducing the conservativeness of the controller, thus reducing the effort in tuning control parameters. Originality/value Notably, the adaptive function owns a reset mechanism, which is reset to a preset condition when the controlled variable crosses zero. The mathematical analysis also shows the system trajectory can converge to a set centered at the origin.

In recent years, several powerful control methods have been proposed. One of these methods is the reset control, simple nonlinear control technique very effective for plants subjected to fundamental design limitations, and this paper suggests its implementation for secondary control of the frequency of an island microgrid. The studied microgrid includes various elements such as renewable energy sources and various factors such as the load changes, power fluctuations from renewable energy sources, dynamic disturbances as well as parametric uncertainties affecting the frequency of the grid and the complexity of its control. To overcome the above effects and stabilize the network frequency, this paper uses the reset control method to regulate the network operating frequency. Using the proposed controller, the behaviour of the network under parametric changes and different disturbances has been investigated and compared with conventional and optimized PID control methods. High speed frequency regulatory and low undershot/overshot are some of the advantages of the proposed method. The simulation results show the desired performance of the proposed control method in stabilizing the network frequency under different scenarios.

Input-to-state stability (ISS) is considered for a nonlinear “soft-reset” system with inputs. The latter is a system that approximates a hard-reset system, which is modeled as a hybrid system with inputs. In contrast, a soft-reset system is modeled as a differential inclusion with inputs. Lyapunov conditions on the hard-reset system are given that guarantee ISS for the soft-reset system. In turn, it is shown when global asymptotic stability for the origin of the zero-input reset system guarantees ISS for nonzero inputs. Examples are given to demonstrate the theory.

The proportional–integral plus Clegg integrator (PI + CI) controller is a hybrid extension of the proportional–integral (PI) controller that is able to overcome fundamental limitations of the linear and time-invariant control systems, potentially obtaining faster responses without increasing overshooting. This work focused on the analysis and design of PI + CI controllers and reset controllers in general, for the case of parallel multiple-input single-output (MISO) systems, extending previous design methods developed for the single-input single-output (SISO) case. Several design strategies were developed: one for first-order MISO plants achieving a flat response with a finite settling time, and for second-order MISO plants obtaining a fast response with a reduced overshoot and settling time in comparison with non-hybrid strategies. Several case studies were also developed to illustrate the potential of the proposed methods.

Proton Exchange Membrane as one of the most advanced types of fuel cells plays an effective role in renewable energy generation and supply manifold is one of its main subsystems. Aiming to cover nonlinear behaviour, this study presents a new robust method for controlling the supply manifold pressure at the cathode side. To consider the uncertainty effects as well as the nonlinear behaviour of the supply manifold, a delayed transfer function model is considered. The proposed reset control approach improves the transient response in regulating the supply manifold pressure at the cathode side. The simulation and comparison results in MATLAB environment show the capabilities of the proposed method to improve the transient response of the system from different perspectives and stability despite of uncertainty effects.