Pavol Bistak

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.

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.

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 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 ∈ [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 mth-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.

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.

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.

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.

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.