The design of effective controllers for complex Two-Input-Two-Output (TITO) systems presents a significant challenge, particularly in the context of implementing a design methodology suited to this specific type of process. In the majority of cases, if the system in question exhibits highly complex dynamics or a high order, the procedure to be performed is an order reduction. This is done in order to describe the essential dynamic characteristics of the original system in a way that allows for the reliable design of controllers. This work presents a practical approach to the design of decentralized Fractional-Order Proportional-Integral-Derivative (FOPID) controllers for TITO systems. The methodology comprises a reduced-order representation of the original system and an optimization-guided design. The intention is to quantify the performance loss in the decentralized FOPID controller design procedure when reduced-order models are employed. This will facilitate a validity analysis of the fractional controller selection. To enable a fair comparison in the validation example, an equivalent procedure for a decentralized PID controller will be presented in parallel.

In the design of Multiple-Input-Multiple-Output (MIMO) control systems, one of the most critical considerations is system stability. This is typically addressed in the controller design process through the incorporation of a stability index, often based on frequency domain analysis, to quantify system robustness after controller implementation. This work focuses on analyzing the design of Decentralized Proportional-Integral-Derivative (PID) controllers for Two-Input-Two-Output (TITO) processes, which are among the most common multivariable systems. The proposed approach evaluates stability margins using the maximum of the sensitivity function, despite robustness also being measurable through the maximum of the singular values. By utilizing the equivalent sensitivity function for multivariable systems, the method provides a direct means of assessing robustness once decentralized controllers are implemented. The feasibility of this approach is examined for a specific level of robustness and is validated employing two benchmark processes.

In the last decades the use of fractional calculus in control applications has risen especially in the process modelling and the control algorithm design and controller tuning which are indispensable stages in the design of a control system. Several works have proved the effectiveness of the use of fractional order proportional-integral-derivative controllers, to satisfy performance considerations in the set-point tracking and in the load disturbance rejection, as well as for achieving robustness levels. Most of the studies have focused the tuning of FOPID controllers based on stable dynamics well characterized by first and second order plus dead time models as well as integrating Dynamics. However, when the process presents an inverse response there are not so many Works that explain how design the closed-loop system based on performance and robustness considerations and using a FOPID controller. In this work we present a methodology to compare the performance provided by the use of PID and FOPID when a robustness constraint is considered for inverse response dynamics in the control of an isothermal continuous stirred tank reactor (CSTR) and a process model with a transfer function which has large values for the normalized dead time and for the ratio between the zero time constant and the dominant time constant.

Data science has been attracting a great deal of attention in recent years because of its promise to extract value from the data that abounds in society. In the control engineering field, data-driven design, in which control system design can be performed directly from data, can also be considered a part of data science. Using the data-driven approach, a control system can be optimized directly from controlled data. However, even if a system is optimally designed, its behavior cannot be verified until the system is actually controlled. Therefore, in the present study, a data-driven response estimation-based tuning (DRET) is proposed in order to design a control system based on the estimated time response. It is applied to the control system design of not only stable systems but also unstable systems. In the design of DRET, a finite impulse response filter is used and a model matching problem is solved directly from the control data, to compensate for the difference between an original objective function and a data-driven objective function. The proposed method is applied to the control system design of a ball-and-beam system, which is an unstable system, and its usefulness is verified.

Cascade control structures are widely implemented in industries, due to the fact that they increase the performance of single-loop control. Nevertheless, their implementation requires a higher initial investment. Because of this, it is of great importance to be able to quantify their relative performance improvement. Very few studies handle this subject, and they do not obtain results which directly establish this quantification on a general basis. Therefore, the objective of this project is to conduct a study with help of computational tools, in order to determine the relative performance improvement of a cascade control structure with respect to a single-loop structure, for setpoint tracking and disturbance rejection. An overdamped second-order-plus-dead-time process, separable in two first-order-plus-dead-time subprocesses, was considered. The controllers were implemented using a PID algorithm. Simulations were conducted to obtain the ratio of the IAE performance indexes of each control structure, as a function of the time constant ratio, for different process parameters. The controllers were tuned by means of optimization routines, in order to guarantee that they provided the best IAE index. Finally, two general equations were obtained, which quantify the relative performance improvement of a cascade control structure with respect to a single-loop structure, as a function of the process parameters, for set point tracking and disturbance rejection.

This work faces the problem of frequency deviation in microgrid systems. The considered microgrid includes renewable energy sources such as wind and solar photovoltaic. As long as these sources provide an irregular power supply or there is a sudden change in the system load, the power system frequency deviates. In order to compensate such deviations, alternative, conventional energy sources should be commanded in order to provide the corresponding power deficit. In this paper a very simple and of common industrial practice control approach such as the Internal Model Control based on first order plus time delay models is proposed within an event-based framework. As the commanded energy sources are based on fuel consumption, the control usage has to be maintained at low levels. It is shown that the event-based approach is able to provide accurate frequency deviation control with very low movements for the control signal. Time domain simulations show the effectiveness of the approach as compared with other more sophisticated controllers already proposed in the literature.

In this paper, a One-Degree-of-Freedom PI controller is optimized using the model reference tuning approach for a Second Order Inverse Response and Dead Time Process operating as a servo control. In addition, a graphic user interface tool that computes the PI optimized controller parameters is presented, also showing the response of the control system operating as a servo-control (the optimized one) and the associated response for the regulatory-control case.

This paper deals with the identification of fractional models with one fractional parameter. This kind of models are capable to represent an extensive range of dynamics, including overdamped and oscillatory behaviors. The identification algorithm consists in applying an optimization function, starting from an initial point, that allows the program to calculate a very representative model of the process. The results demonstrate the usefulness and robustness of the tool, which can be employed to identify integer and fractional systems in an easy way and this can be later exploited for further studies, for example the development of tuning rules.

In this work, an analysis of multi-objective optimization methods for PI controllers tuning is presented using the Pareto front concept. A new multi-objective method is proposed to find an evenly spaced Pareto frontier which, at the same time, gives the user an idea of the degradation of one of the objective functions. The results are analyzed from a control theory perspective, which include the comparison with classical PI tuning methods.

This paper introduces the stability analysis for the so-called intermediate-tuning PID controller. Thus, each of the three PID parameters is proposed to lie within the convex hull of two extreme values, being defined as the optimal tuning settings for servo and regulation modes respectively. The result ensures that all the PID controllers generated for each frozen value of the interpolating parameters guarantee the stability of the closed-loop.

This paper analyzes optimal controller settings for controllers with One-Degree-of-Freedom (1-DoF) Proportional-Integral-Derivative (PID) structure. The analysis is conducted from the point of view of the operating mode (either servo or regulation mode) of the control-loop and tuning mode of the controller. Performance of the optimal tuning settings can be degraded when the operating mode is different from that selected for tuning and obviously both situations can be present in any control system. In this context, a Performance Degradation index is minimized and based on this minimization, an autotuning procedure as a function of the normalized process dead-time is proposed.

This paper presents an analytically deducted procedure for tuning two-degree-of-freedom proportional integral (PI) controllers for first-order-plus-dead-time (FOPDT) controlled process. The equations incorporate a design parameter, which relates the feedback control systempsilas time constant, with the controlled process time constant. The design procedure considers the control-loop robustness by means of maximum sensitivity requirements, allowing the designer to deal with the performance-robustness trade-off.

This paper analyzes optimal controller settings for controllers with One-Degree-of-Freedom (1-DOF) Proportional-Integral-Derivative (PID) structure. The analysis is conducted from the point of view of the operating mode (either servo or regulation mode) of the control loop and tuning mode of the controller. Performance of the optimal tuning settings (ISE-like) can be degraded when the operating mode is different from the select one for tuning. An index for measuring the overall Performance Degradation is proposed and from the minimum of this, tradeoff tuning settings are given. The proposed procedure is applied to control a Continuous Stirred Tank Reactor (CSTR), which is a non-linear system.

Robustness and performance analysis for a control system with a PID controller tuning from optimal settings are presented. Those analysis are conducted from the point of view of the stability margins characterization and of the operating mode (either servo or regulation mode) of the control loop and tuning mode of the controller, respectively. It is well known that, specially for optimization based settings, the performance of the control loop is defined in terms of the expected operating mode of the control loop. When the control system is not operating in the same operating mode as the controller was tuned, the performance may exhibit very poor results. The performance degradation with respect to the optimal performance is defined and analyzed for settings based on ISE-like optimization criteria. As a consequence, in order to get a minimal overall performance degradation with respect to both operating modes, tradeoff settings are proposed and the stability margins for the transition between both servo and regulation tunings are obtained.