The paper compares the recently modified Åström-Smith predictor (ASP) developed for IPDT models with an automatic offset controller (AOC). While an excellent performance can be achieved with ASP in idealized conditions, unacceptable transients with extraordinary high excessive controller effort and a steady-state control error result in the presence of measurement noise. AOC combines a possibly higher-order (HO) stabilizing controller (SC) with compensation of disturbances using a full disturbance observer (DOB). Nominal full DOB includes both the model dead-time and inversion of the integral mode of the model. By increasing the number of output derivatives used in the SC of the AOC, together with increasing the order of the low-pass filter used both in the SC and the DOB, it is possible to significantly increase the speed and robustness of responses in time-delayed processes, together with decreasing the measurement noise impact. The AOC based on the ultralocal IPDT model can be used to replace the higher-order PID in an universal controller for a wide class of processes with dominant first-order dynamics. Significant improvements in measurement noise attenuation can be demonstrated also in application of equivalent low-pass filters to the ASP. But even after such a modification of the noise attenuation, the filtered ASP can exhibit permanent control error or even instability at higher noise amplitudes. Hence, although even the ASP can be used as a universal controller for processes with dominant first-order dynamics, the benefit of its use should always be verified depending on the amplitude of the measurement noise. From this point of view, the use of AOC is simpler and more reliable. Despite the need for appropriate selection of the degree of derivatives used in SC and the tuning of the low-pass filters used. The conclusions of the article are illustrated by simulation experiments of unstable process control and real-time thermal process control.

This paper explores automatic offset control (AOC) as a modern alternative to classical industrial automatic reset controllers (ARCs). Rather than relying on positive feedback to approximate offset correction, AOC integrates a comprehensive disturbance observer. This modification accelerates transient performance while reducing susceptibility to high-frequency measurement noise. We extend previous AOC designs developed for single and double integrator systems with dead time (IPDT, DIPDT) to triple integrator plus dead-time (TIPDT) formulations, enabling the control of high-order process dynamics. Unlike standard PID configurations tailored for higher-order plants, the proposed AOC does not require separate tuning adjustments when enabling or disabling disturbance compensation. Additionally, its inherent structure avoids integrator windup, demonstrates low sensitivity to measurement noise, and exhibits robust behavior regarding initial state variations, thereby simplifying system start-up.

The article discusses the control of nonlinear processes with first-order dominant dynamics, focusing on implementation using modern hardware available in various programmable devices and embedded systems. The first two approaches rely on linearization with an ultra-local process model, considering small changes of the process input and output around a fixed operating point, which can be adjusted through gain scheduling with the setpoint variable. This model is used to configure either the historically established automatic reset controller (ARC) or a stabilizing proportional (P) controller enhanced by an inversion-based disturbance observer (DOB). This solution can be interpreted as an application of modern control theory (MCT), as DOB-based control (DOBC) or as advanced disturbance rejection control (ADRC). Alternatively, they can be viewed as a special case of automatic offset control (AOC) based on two types of linear process models. In the third design method, setpoint tracking by exact linearization (EL) is extended with a nonlinear DOB designed using the inverse of the nonlinear process dynamics (EEL). The fourth approach augments EL-based tracking with a DOB derived from the transfer functions of nonlinear processes (NTF). An illustrative example involving the control of a liquid reservoir with a variable cross-section clarifies motivation for the definition of (linear) local and ultra-local process models as well as their advantages in designing robust control that accounts for process uncertainties. Thus, the speed, homogeneity, and shape of transient responses, the ability to reconstruct disturbances, control signal saturation, and measurement noise attenuation are evaluated according to the assumptions specified in the controller design. The novelty of the paper lies in presenting a unifying perspective on several seemingly different control options under the impact of measurement noise. By explaining their essence, advantages, and disadvantages, it provides a foundation for controlling more complex time-delayed systems. The paper emphasizes that certain aspects of controller design, often overlooked in traditional linearization procedures, can significantly improve closed-loop properties.

The article examines approximations of dead-time inversion proposed for integrator plus dead-time process models managed by generalized proportional-integral-derivative (PID) and automatic offset controllers (AOC) with derivatives of increasing order. The proposed controllers are tuned using the multiple real dominant pole method and are implemented and made robust with low-pass filters, which also help attenuate measurement noise. PID controllers have traditionally been the most popular, but nevertheless, closed loop performance, as measured by integral of absolute error or total variation, can be increased by factors reaching two to three orders of magnitude using AOC. The range of performance achievable with both approaches, along with the popular SIMC and iSIMC controllers, can be assessed by studying speed-effort and speed-wobbling charts. These charts clearly demonstrate the advantages of controllers that include second-order derivatives. Two additional time-domain charts are then used to characterize the impact of the controller derivative order on closed-loop performance for a fixed equivalent delay of the controller filter and for a fixed speed of setpoint responses. The same charts are also used to illustrate the performance of PID and AOC when controlling a nonlinear thermal process in real time. In this context, AOC proves to be a much less sensitive and much more flexible and effective alternative to PID controllers, interesting even to carry-out start-up of experiments with PID controllers.

Unknown external disturbances and hydrodynamic uncertainties pose significant challenges to accurate path tracking of autonomous underwater vehicles (AUVs). To address this problem, a guidance law ensuring trajectory convergence is proposed by incorporating position error and AUV dynamics. A deviation compensation disturbance rejection (DCDR) controller is developed by introducing an independent tunable gain to decouple disturbance rejection from state observer dynamics, thereby enabling separate design and coordination of nominal control and robust enhancement. The transfer function-based DCDR implementation is derived to demonstrate a systematic parameter tuning guideline, and the closed-loop stability is established through invariant set analysis. The effectiveness of the proposed method is validated through straight and circular path tracking simulations with and without wave-induced external disturbances. By maintaining an explicit control structure, the proposed DCDR can achieve improved tracking performance and reduced control effort compared with the linear active disturbance rejection control (LADRC) and the compensation function observer-based controller (CFO-C).

The article extends the performance that can be achieved with the setup for the design of higher-order proportional-integral-derivative (HO PID) controllers using ultra-local integrator-plus-dead-time (IPDT) models. The previously derived reference family of controllers, referred to as 1PID, is complemented by a new family of 2PIDs corresponding to the double integrator plus dead time (DIPDT) model. The individual members of the 1PID and 2PID families are derived using the multiple real dominant pole method (MRDP) and normalized by the parameters of the ultra-local models used. The degree of the considered controller derivatives m is an element of[1,6] significantly outperforms most of the known methods for PID control design, which mainly use m <= 1 and only exceptionally consider the cases with m>1 . Therefore, the obtained results are even comparable to the HO controllers created by approximating fractional-order PID controllers. To implement the m th-order derivative, binomial low-pass filters of order n >= m are used in the controllers, specified by an equivalent filter delay added to the process. The traditional controllers with two degrees of freedom, for the separate design of setpoint and disturbance responses, are extended by two additional degrees of freedom provided by m and n, allowing to modify the speed of the transients together with their shapes and the closed-loop robustness. The choice of 1PIDs and 2PIDs brings another degree of freedom related to the process model used. The multiple controller parameters are set by a new modification of the Performance Portrait Method (PPM), which makes it possible to shape the closed-loop responses by specifying tolerances for deviations of step responses from their ideal shape in the time domain. The illustrative examples, which deal with two stable higher-order processes and an unstable system, show the possibility of a multiple increase in performance compared to previously known methods. They show that HO-2PID controllers are inherently better suited for processes characterized by multiple dominant time constants. The novel design opens the door to wider use of HO controllers enabled by embedded control and programmable device technology, and allows the development of new HO controllers tuned by parallel computation.

This paper presents possibilities for how to model and experiment with a portable pocket-sized dynamical system representing the operation of magnetic levitation. It describes different models (mathematical, 3D, simulation) of the magnetic levitation system and discusses Arduino IDE and Matlab/Simulink platforms with the use of Arduino Uno and Arduino Due microcontrollers for a magnetic levitation control.

The paper compares control approaches with disturbance reconstruction and compensation using disturbance observer (DOB) based on integrator plus dead-time (IPDT) models. The first option generalizes the automatic reset controller (ARC), representing the historical industrial controllers developed a century ago and later denoted as the series proportional-integral (PI) controller. Denoted as the automatic offset control (AOC), by increasing the number of output derivatives used in the stabilizing controller, it increases the speed and robustness of responses together with enhancing measurement noise attenuation. All AOC options treated are tuned by the multiple real dominant pole (MRDP) method with the aim of balancing the speed of transient responses and attenuation of the measurement noise. The performance achievable with AOC is comparable to the recently modified Aström-Smith predictor.

Almost a century ago, the first industrial controllers were introduced to the market, labeled as automatic reset and later generalized to hyper-reset or pre-act. Recently, it has been shown that such control solutions can be characterized as model-based solutions with a simplified disturbance observer developed for an integrating model. The aforementioned controllers, albeit under the name of proportional–integral–derivative (PID) controllers, are still the most commonly used control solutions in practice. With the help of a new interpretation, however, it can be shown that PID controllers are also very well suited for controlling processes with complex non-linear dynamics. This paper investigates the design and feasibility of a family of gain-scheduling controllers for saturated non-linear systems described by a first-order differential equation. It is shown that the process can be linearized either by using locally applicable linear models or by using more narrowly applicable ultralocal models. By combining both approaches, an innovative linearization method around the steady states of the process input and output is proposed. This novel approach emphasizes that the entire process input signal has to be constructed by adding the control increment calculated by the linearization to the value of the considered operating point. Thus, it avoids the uncertainties of those methods, which are based on achieving the actual controller output by integrating the calculated differential values. Another advantage of model-based design is that the saturation of the control signal is included in the design from the outset. Therefore, the undesired integration (windup), which is typical for controllers with explicit integral action, is prevented. The proposed design is illustrated using the control of a liquid tank with variable cross-section as a function of the liquid level. The model-based approach is also used in the evaluation of the transients, where homogeneous responses were obtained over the whole range of process output values. Responses were more homogeneous when simple ultralocal models were used, regardless of controller saturation constraints. Finally, all important innovative aspects of the design are highlighted by a comparison with gain-scheduled PI controller design based on velocity implementation.

The first part of the two-part paper introduces a new setup for optimization of higher-order $(\text{HO})$ controllers using a base of controller families derived by the multiple real dominant pole (MRDP) method for ultralocal process models with increasing degree of the pure integrator. It is illustrated by the design of a family of HO PID (proportional-integral-derivative) controllers derived for integrator plus dead-time (IPDT) models applied to control an unstable process. The specification of the optimal family term is accomplished by comparing all the available options by the performance portrait method, which shows the possibility of a huge increase in loop performance compared to earlier published papers. The reduction of the IAE value for disturbance responses below 4 % of the previously reported values obviously introduces a completely new generation of controller design. The second part of the paper then continues with the development of another family of HO-PIDs using the double-time-delayed integrator model.

One of the most important contributions of modern control theory from the 1960s was the separation of the dynamics of state-space controller design from the dynamics of state reconstruction. However, because modern control theory predates the mass spread of digital controllers and was predominantly focused on analog solutions that avoided modeling dead-time elements, it cannot effectively cover all aspects that emerged with the development of programmable devices and embedded systems. The same historical limitations also characterized the development of proportional-integral-derivative (PID) controllers, which began several decades earlier. Although they were used to control time-delayed systems, these solutions, which are most commonly used in practice today, can also be referred to as simplified disturbance observers that allow the avoidance of the the direct use of dead-time models. Using the example of controlling systems with a double integrator plus dead-time model, this article shows a novel controller design that significantly improves control performance compared to conventional PID controllers. The new control structure is a combination of a generalized state-space controller, interpreted as a higher-order derivative controller, and a predictive disturbance observer that uses the inversion of double integrator dynamics and dead-time models. It enables the elimination of the windup effect that is typical for PID control and extends the separation of the dynamics of setpoint tracking from the dynamics of state and disturbance reconstruction to time-delayed processes as well. The novelty of the presented solution offers several orders of magnitude lower amplification of measurement noise compared to traditional PID control. On the other hand, it offers high robustness and a stable transient response despite the unstable internal feedback of processes like the magnetic levitation system. The improvements achieved are so high that they call into question the classical solutions with PID controllers, at least for DIPDT models. In addition to the comparison with PID control, the relationship with traditional state space controllers, which today form the basis of active disturbance rejection control (ADRC), is also discussed and examined for processes including dead time.

The performance portrait method (PPM) can be characterized as a systematized digitalized version of the trial and error method—probably the most popular and very often used method of engineering work. Its digitization required the expansion of performance measures used to evaluate the step responses of dynamic systems. Based on process modeling, PPM also contributed to the classification of models describing linear and non-linear dynamic processes so that they approximate their dynamics using the smallest possible number of numerical parameters. From most bio-inspired procedures of artificial intelligence and optimization used for the design of automatic controllers, PPM is distinguished by the possibility of repeated application of once generated performance portraits (PPs). These represent information about the process obtained by evaluating the performance of setpoint and disturbance step responses for all relevant values of the determining loop parameters organized into a grid. It can be supported by the implementation of parallel calculations with optimized decomposition in the high-performance computing (HPC) cloud. The wide applicability of PPM ranges from verification of analytically calculated optimal settings achieved by various approaches to controller design, to the analysis as well as optimal and robust setting of controllers for processes where other known control design methods fail. One such situation is illustrated by an example of predictive integrating (PrI) controller design for processes with a dominant time-delayed sensor dynamics, representing a counterpart of proportional-integrating (PI) controllers, the most frequently used solutions in practice. PrI controllers can be considered as a generalization of the disturbance–response feedback—the oldest known method for the design of dead-time compensators by Reswick. In applications with dominant dead-time and loop time constants located in the feedback (sensors), as those, e.g., met in magnetoencephalography (MEG), it makes it possible to significantly improve the control performance. PPM shows that, despite the absence of effective analytical control design methods for such situations, it is possible to obtain high-quality optimal solutions for processes that require working with uncertain models specified by interval parameters, while achieving invariance to changes in uncertain parameters.

This article explores the resilient fault-tolerant containment control problem for nonlinear multi-agent systems with actuator faults and denial-of-service (DoS) attacks. To circument unknown agent dynamics, the nonlinear data mapping of agents with time-varying actuator fault information is established by the locally dynamic linearization technique. In the cyber layer, the stochastic DoS attack is supposed to follow the Bernoulli distribution with duration and frequency constraints, and a backward attack compensation strategy is built. In the physical layer, an adaptive varying actuator fault compensation mechanism derived from the improved projection algorithm is developed. Within this design, a data-driven distributed model-free adaptive fault-tolerant control (DMFA-FTC) method is formulated to ensure the dual security guarantees. By the nature of irreducible sub-stochastic matrices, the convergence condition of the method is provided. Finally, experiments affirm the DMFA-FTC method.

The paper presents a new control concept based on the process moment instead of the process states or the process output signal. The control scheme is based on separate control of reference tracking and disturbance rejection. The tracking control is achieved by additionally feeding the input of the process model by the scaled output signal of the process model. The advantage of such feedback is that the final state of the process output can be analytically calculated and used for control instead of the actual process output value. The disturbance rejection, including model imperfections, is controlled by feeding back the filtered difference between the process output and the model output to the process input. The performance of tracking and disturbance rejection is simply controlled by two user-defined gains. Several examples have shown that the new control method provides very good and stable tracking and disturbance rejection performance.

The paper presents an application of the new control paradigm, which is based on process moments, to a model of a DC motor. The basis of the new control paradigm is that it eliminates the process transfer function within the closed loop, as it estimates the final steady-state value of the process output and compares it with the reference signal. As a result, the closed loop response is much more stable and generally without overshoots. This property makes it suitable for application to motor-driven processes where overshoots is undesirable. It was shown that the control method provides very stable closed-loop responses even when the actual motor and the model parameters differ. It was also shown that the proposed method can be applied to constrained systems as the anti-windup protection is implicitly embedded in the control solution.

This paper deals with the tuning of the parameters of a fractional-order PI controller for the speed control of an electric servo drive in which the torque is set by a torque generator. The controller parameters are tuned using the multiple dominant pole method (MDPM), while the fractional order integrator is approximated by the Oustaloup method. The input parameters required for tuning the controller using MDPM are calculated using the optimization algorithm presented in this paper. This algorithm selects the optimal parameters from a set of points in three-dimensional space, based on the symmetry around a central point. The controller tuning is performed for the normalized control loop model. The obtained optimized normalized fractional order PI controller can then be applied to a real servo drive with specific parameters. The proposed tuning was also verified experimentally, comparing the obtained closed-loop responses with those of the integer-order PI controller. Both simulation and experimental results showed a significant reduction in the integral of the absolute error at the disturbance step compared to a control loop using an integer-order PI controller. This results in a faster output response to load torque steps and a smaller control error in a real servo drive.

The paper presents a modification of the Magnitude Optimum Multiple Integration (MOMI) method process non-parametric data in the frequency domain instead of the time domain. The required frequency data are obtained directly from the filtered amplitude-shifted process step response and have been shown to be relatively insensitive to normally distributed process noise. All calculations, including the calculation of the PID controller parameters, are performed analytically. The closed loop responses to tested processes with added normally distributed noise were relatively fast with small or no overshoot, all according to the Magnitude Optimum (MO) method. The proposed method is not limited to open loop step responses or to the PID controller structure.

This work proposes a novel architecture for constructing remote laboratories, employing modular building blocks: Matlab/Simulink software for control system design and simulation, WebSocket communication technology for continuous data exchange, and a front-end application developed using the Angular framework. To facilitate WebSocket communication on the Matlab server side, the MatlabWebSocket library is implemented. Beyond the Angular framework, interactivity within the remote laboratory is further enhanced through 3D visualization of the controlled system using a Three.js based library. These combined technologies are applied in the development of a remote laboratory for a fast, unstable, and nonlinear magnetic levitation system. The laboratory allows users to remotely set desired values and control parameters for experiments, while also providing continuous data visualization in various forms, including numerical readouts, graphs, and 3D animations. This approach demonstrates the effectiveness of the proposed architecture for building remote laboratories for complex systems. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

The proposed practice-oriented controller design (POCD) aims at stabilizing the system, reconstructing and compensating for disturbances while achieving fast and smooth step responses. This is achieved through a simple approach to process identification and controller tuning that takes into account control signal constraints and measurement noise. The proposed method utilizes POCD by eliminating the influence of the unstable zero dynamics of the inverse-response processes, which limits the achievable performance. It extends the previous work on PI and PID controllers to higher-order (HO) automatic reset controllers (ARCs) with low-pass filters. It is also extended according to POCD requirements while maintaining the simplified process model. The final result is an extremely simple design for a constrained controller that provides sufficiently smooth and robust responses to a wide family of HO-ARCs with odd derivatives, designed using integral plus dead time (IPDT) models and tuned by the multiple real dominant pole method (MRDP) and the circle criterion of absolute stability. The proposed design can be considered as a generalization of the Ziegler and Nichols step response method for inverse response processes and HO-ARCs.

Integrating processes can be found in various industries. The main characteristic of such processes is that a limited process input can cause an unlimited process output. In general, they are more difficult to control compared to stable processes. The recently developed Magnitude optimum multiple integration tuning method for integrating processes provides very good closed-loop responses. However, it uses a reference-weighting 2-DOF PI(D) controller structure where the weighting parameters for the P and D term of the controller are equal (therefore the user can only change one parameter). Another drawback of the existing method is that it needs to find the roots of the fourth-order algebraic equation. The method proposed here does not require finding these roots and provides better tracking compared to the original method while maintaining optimal disturbance rejection for different integrating process models.