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In this paper the design of a controller for a relay controlled second order nonlinear unstable plant with fourth order nonlinearity is considered. The task of the controller is the simultaneous reduction of output and output derivative to zero with the input being at zero. It is established that, if the initial values of error and error derivative fall in a “controllable region”, it is possible to reduce error and error derivative to zero simultaneously and in the shortest possible time with at most one switching reversal of the relay. It is also shown that, through simple transformation of error and error derivative, the equation of the switching curve can be made independent of the constant gain of the plant, as well as the coefficient of the nonlinear term.

In this paper, it is established that the error and error derivative can be reduced to zero simultaneously and in the shortest possible time with at most one switching reversal of the relay, provided the initial values of error and error derivative fall in a controllable region.

The purpose of this paper is to present a comparison between two well-known Lévy-based meta-heuristics called cuckoo search (CS) and flower pollination algorithm (FPA).

Both the algorithms (Lévy-based meta-heuristics called CS and Flower Pollination) are tested on selected benchmarks from CEC 2017. In addition, this study discussed all CS and FPA comparisons that were included implicitly in other works.

The experimental results show that CS is superior in global convergence to the optimal solution, while FPA outperforms CS in terms of time complexity.

This paper compares the working flow and significance of FPA and CS which seems to have many similarities in order to help the researchers deeply understand the differences between both algorithms. The experimental results are clearly shown to solve the global optimization problem.

In this paper the design of a controller for a relay‐controlled second‐order non‐linear unstable plant with second‐order nonlinearity will be considered. The task of the controller is the simultaneous reduction of output and output derivative to zero with the input being at zero. If the initial values of error and error derivative fall in a “controllable region”, then it is possible to reduce error and error derivative to zero, simultaneously and in the shortest possible time with at most “one” switching reversal of the relay. It will also be shown that, through simple transformation of error and error derivative, the equation of switching curve can be made independent of any constant gain of the plant, as well as the coefficient of non‐linear term.

In this paper the design of a controller for a relay‐controlled second‐order non‐linear stable plant with third‐order nonlinearity is considered. The task of the controller is the simultaneous reduction of output and output derivative to zero with the input being at zero. It will be shown that for all initial values of output and output derivative it would be possible to bring them to zero, simultaneously and with at most one switching reversal of the relay. It will also be shown that, through simple transformation of error and error derivative, the equation of the switching curve can be made independent of any constant gain of the plant and also of the coefficient of the non‐linear term.

This paper aims to design a modified fractional order proportional integral derivative (PID) (FO[PI]^λD^µ) controller based on the principle of fractional calculus and investigate its performance for a class of a second-order plant model under different operating conditions. The effectiveness of the proposed controller is compared with the classical controllers.

The fractional factor related to the integral term of the standard FO[PI]^λD^µ controller is applied as a common fractional factor term for the proportional plus integral coefficients in the proposed controller structure. The controller design is developed using the regular closed-loop system design specifications such as gain crossover frequency, phase margin, robustness to gain change and two more specifications, namely, noise reduction and disturbance elimination functions.

The study results of the designed controller using matrix laboratory software are analyzed and compared with an integer order PID and a classical FOPI^λD^µ controller, the proposed FO[PI]^λD^µ controller exhibit a high degree of performance in terms of settling time, fast response and no overshoot.

This paper proposes a methodology for the FO[PI]^λD^µ controller design for a second-order plant model using the closed-loop system design specifications. The effectiveness of the proposed control scheme is demonstrated under different operating conditions such as external load disturbances and input parameter change.

To develop a new predictive control scheme based on neural networks for linear and non‐linear dynamical systems.

The approach relies on three different multilayer neural networks using input‐output information with delays. One NN is used to identify the process under control, the other is used to predict the future values of the control error and finally the third one is used to compute the magnitude of the control input to be applied to the plant.

This scheme has been tested by controlling discrete‐time SISO and MIMO processes already known in the control literature and the results have been compared with other control approaches with no predictive effects. Transient behavior of the new algorithm, as well as the steady state one, are observed and analyzed in each case studied. Also, online and offline neural network training are compared for the proposed scheme.

The theoretical proof of stability of the proposed scheme still remains to be studied. Conditions under which non‐linear plants together with the proposed controller present a stable behavior have to be derived.

The main advantage of the proposed method is that the predictive effect allows to suitable control complex non‐linear process, eliminating oscillations during the transient response. This will be useful for control engineers to control complex industrial plants.

This general approach is based on predicting the future control errors through a predictive neural network, taking advantage of the NN characteristics to approximate any kind of relationship. The advantage of this predictive scheme is that the knowledge of the future reference values is not needed, since the information used to train the predictive NN is based on present and past values of the control error. Since the plant parameters are unknown, the identification NN is used to back‐propagate the control error from the output of the plant to the output of the controller. The weights of the controller NN are adjusted so that the present and future values of the control error are minimized.

This paper presents a method for designing a fixed controller, which is able to control in a stable fashion a family of linear time‐invariant n‐th order plants with arbitrary relative degree. This plant family is defined in terms of a nominal transfer function of rational type and bounded variations of the coefficients of numerator and denominator polynomials. The design method is based on the algebraic relationship existing in the model reference adaptive control technique between the true plant parameters, the ideal controller parameters and the model reference parameters. While applying the proposed method, the resulting plant families are broader if compared with other techniques used to design robust controllers.

This paper aims to propose an analytical method for designing parametric optimization-based proportional integral (PI) controllers.

In this method, a performance index containing the weighted summation of the integral square of the error and its derivative is minimized. This performance index is analytically calculated in terms of the controller parameters by solving a Lyapunov equation. Then partial derivatives of the performance index with respect to controller parameters are calculated. Equating these partial derivatives to zero gives explicit relations for the PI controller parameters.

The experimental tests on a DC servomotor system are given to demonstrate the efficiency of the proposed method.

This paper proposes an analytical parametric optimization approach for designing PI controllers for the first time. The application of the proposed method in a laboratory experiment is examined.

The wind turbine (WT) is a complex system subjected to wind disturbances. Because the aerodynamics is nonlinear, the control is thus challenging. For the variation of wind speed when rated power is delivered at rated wind speed, the power is limited to the rate by the pitching of the blades of the turbine. This paper aims to address pitch control with the WT benchmark model. The possible use of appropriate adaptive controller design that modifies the control action automatically identifying any change in system parameters is explored.

To deal with pitch control problem when wind speed exceeds the rated wind speed of the WT, six digital self-tuning controller (STC) with different structures such as proportional integral (PI), proportional derivative (PD), Dahlin’s, pole placement, deadbeat and Takahashi has been taken herein. The system model is identified as a second-order autoregressive exogenous (ARX) model by three techniques for comparison: recursive least square method (RLS), RLS with exponential forgetting and RLS with adaptive directional forgetting identification methods. A comparative study of three identification methods, six adaptive controllers with the conventional PI controller and sliding mode controller (SMC), are shown.

As per the results, the best improvement in control of the output power by pitching in full load region of benchmark model is achieved by self-tuning PD controller based on RLS with adaptive directional forgetting method. The adaptive control design has a future in WT control applications.

A comparative study of identification methods, six adaptive controllers with the conventional PI controller and SMC, are shown here. As per the results, the best improvement in control of the output power by pitching in the full load region of the benchmark model has been achieved by self-tuning PD controller. The best identification method or the system is RLS with an adaptive directional forgetting method. Instead of a step input response design for the controllers, the controller design has been carried out for the stochastic wind and the performance is adjudged by the normalized sum of square tracking error (NSSE) index. The validation of the proposed self-tuning PD controller has been shown in comparison to the conventional controller with Monte-Carlo analysis to handle model parameter alteration and erroneous measurement issues.