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The unit step response is a standard tool for experimental identification; its shape is equivalent to a solution of an appropriate governing equation. In this study, we investigate two variants of nonlinear first-order governing equation, y ′ = k ( 1 - y β ) / β , and mainly its rescaled version y ′ = k 1 - y β . We explore a continuum of response shapes, ranging from constant zero to constant one, including standard shapes such as 1 - exp ( - t ) and tanh ( t ) , but also uncommon shapes such as a part of the logarithmic integral. Two methods for estimating the parameter β are proposed: one based on analyzing the curvature of a single response and the other based on analyzing initial slopes for multiple responses, while varying the amplitude of the step. Our investigation is conducted in the context of gas permeation through a homogeneous porous medium, where nonlinear response shapes have been observed. This context allows for a meaningful interpretation of the results, consistent with expectations for specific thermodynamic processes. However, neither method is constrained by this context, and either might be considered for any first-order system that fails to have amplitude-scale invariance or for which the shapes seem to exhibit an effect of saturation.

This work considers an optimization problem based on step response characteristics. We lay a foundation for it by designing a rapid transient response analysis algorithm with variable time steps. This method applies to linear ordinary differential equations with real order. Numerical tests of the algorithm in the integer case show significant improvement even for higher order systems. This suggests a new method for acquiring step response characteristics for the fractional order case for which we have constructed an explicit expression of the inverse Laplace transform.

Automatic Voltage Regulator (AVR) is employed to stabilize the output voltage of generators at electric power plants. However, reliable performance of AVR depends on professional tuning of its PID controller parameters. Therefore, different optimization algorithms are used to determine those parameters. The objective of the optimization is defined as minimizing the characteristics of transient step response such as settling time, rise time, overshoot, and steady state error. Then, to verify the optimization results, a simulator is built experimentally for AVR and PID system which can also be used for other studies on AVR systems. Experimental results are compared with those of MATLAB and Pspice software. Close agreement between the simulation and experimental results confirms the success of the optimization.

This research is concerned with design optimization of control systems. Our case study deals with magnetic levitation, in which an essential part is a solenoid. Its dimensions, along with controller parameters, form the optimization variables. We present a novel way of writing the explicit expression of the solenoid’s force acting on a magnetic dipole, as well as its first derivatives. Numerical tests using non-gradient search algorithms show the difference in optimal designs provided by these methods. Since such optimization depends on output signals, a comparison of step response analysis methods is presented.

The sensor response has been reported to become highly nonlinear when the acceleration added to a thermal accelerator is very large, so the same response can be observed for two accelerations with different magnitudes and opposite signs. Some papers have reported the frequency response for the horizontal acceleration to be a first-order system, while others have reported it to be a second-order system. The response for the vertical acceleration has not been studied. In this study, computational experiments were performed to examine the step and frequency responses of a three-axis thermal accelerometer. The results showed that monitoring the temperatures at two positions and making use of cross-axis sensitivity allow a unique acceleration to be determined even when the range of the vertical acceleration is very large (e.g., −10,000–10,000 g). The frequency response was proven to be a second-order system for horizontal acceleration and a third-order system for vertical acceleration.

The tuning of the parameters of two types of event-based proportional–integral (PI) controllers based on symmetric send-on-delta (deadband) sampling is investigated in this study. In particular, well-known tuning rules devised for standard (continuous-time) PI controllers are compared with tuning rules properly devised for these event-based controllers in order to minimise the step response settling time. Simulations and experiments show that a satisfactory performance, namely, a performance similar to the corresponding time-driven controller, is achieved by all the tuning rules considered because of the structure of the event-based PI controller, thus making it very suitable for its use in the industry.

Proportional-integral-derivative (PID) controllers in water resource recovery facilities (WRRFs) feedback control loops are commonplace. While simple to implement, such control loops are rarely tuned optimally or systematically. Heuristic tuning approaches are commonly applied with varying degrees of success using trial-and-error, ad hoc tuning rules, or duplication of tuning values from a similar system. However, there are effective methods, such as lambda tuning, produce acceptable tuning with limited effort. These are based on the step-response method, where a manual process perturbation is used to define the relationship between the manipulated and controlled variables. Based on such an experiment, a simple process model is constructed and used to determine the controller tuning values. In this work, we used the step-response method and lambda tuning for two control systems in full-scale WRRFs. This led to responsive and stable behavior of the controlled system as defined by the absolute average error of the controlled variable to setpoint and standard deviation of the manipulated variable. Tuning of feedback control loops can be completed successfully through a systematic approach, and this work suggests that tuning tools, like lambda, should be part of all wastewater treatment control engineers' toolbox.

This study focuses on shaping the transient response of special case of fractional-order systems by using fractional-order PD (FOPD) and fractional-order PID (FOPID) controllers. For a plant with a fractional-order pole, a FOPID controller is designed in which the orders of its derivative and integral terms are considered equal to the commensurate order of the plant while for an integrating plant with a fractional-order pole, a FOPD controller is designed. The region of controller parameters is extracted to obtain a closed-loop system with a monotonically decreasing magnitude–frequency response. This leads to a non-overshooting or low-overshoot step response. The gain crossover frequency and phase isodamping conditions are employed to select appropriate controller parameters among the mentioned region. The numerical examples are provided to show the efficiency of the proposed FOPD and FOPID controllers.

This paper deals with the problem of determining whether or not a linear system has a nondecreasing step response. Results are given in the form of root determination of a polynomial. These results can be applied to a more general class of systems, i.e., the system can be of arbitrary order, the zeros can be real or complex, and the poles of the system can be distributed arbitrarily along the negative real axis, including multiple poles.

This study introduces a proposed control method for microgrids (MGs) in islanded (off-grid) mode. The proposed control method is developed by modifying the droop control method using H-infinity controller. In this control method, the droop control loop, current and voltage control loops are adjusted to respond to system load variation. The proposed method is an adaptive control one as it regulates the system voltage and frequency to their nominal values after system load variations. Also, it is a repetitive control method as it depends on the internal model principle that provides good performance for voltage and current error tracking. To prove the applicability and effectiveness of the proposed method, it is applied to a test system using MATLAB/Simulink under three different loading conditions. The results are compared with those of droop control and they prove the effectiveness of the proposed method in adjusting MGs under the off-grid mode of operation. Also, a system stability analysis is performed based on root locus and system step response. Robustness analysis is performed to prove the ability of the proposed controller to restore the system performance after the fault clearance.