Víctor M. Alfaro

Analytical robust tuning of PI controllers for first-order-plus-dead-time processes

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.

Second order inverse response process identification from transient step response.

Simple algorithms for identification of inverse response models from step response are difficult to obtain because analytically the solution of a system of coupled nonlinear equations is required. In this article we propose a simple identification procedure for second order inverse response processes, based on the plant step response. The algorithm provides the model parameters in a sequential way, thus avoiding the solution of a nonlinear equation system. Moreover the algorithm is flexible because it can be suited to user requirements, thus modifying the algorithm performance. Finally error bounds on the identified parameters are provided which are useful if the model is used for control design purposes.

Analysis of the claimed robustness for PI/PID robust tuning rules

This paper analyzes how recognized robust PI/PID tuning rules accomplish with respect to its robustness specification. A concrete analysis is conducted where the chosen PI/PID controller tuning rules are based on a precise quantitative robustness specification such as the Maximum Sensitivity; Ms; value. It is reported that the claimed robustness specification in most of the cases is not accomplished for some set of plants, on other cases it is accomplished with excessive margin, therefore providing a not satisfactory Robustness/Performance tradeoff. The conclusion drawn from this study is that even if the robustness issue has been incorporated in the new approaches for tuning and design of PI/PID controllers, this does not sufficient. In order to appropriately tackle the Robustness/Performance tradeoff, the achieved robustness level should not only be an integral specification, but its accomplishment should be checked.

Two-Degree-of-Freedom PI/PID tuning approach for smooth control on cascade control systems

A design approach for two-degree-of-freedom (2-DOF) PID controllers within a cascade control configuration that guarantees smooth control is presented in this paper. The rationale of operation associated to both, the inner and outer controllers, determines the need of good performance for disturbance attenuation (regulation) as well as set-point following (tracking). Therefore the use of 2-DOF controllers is introduced. However the use of 2-DOF controllers introduces additional parameters that need to be tuned appropriately. Specially for the case of PI/PID controllers there are not known clear auto-tuning guidelines for such situation. The approach undertaken in this paper provides the complete set of tuning parameters for the inner (2-DOF PI) controller and the outer (2-DOF PID) controller. The design equations are formulated in such a way that a non-oscillatory response is specified for both the inner and outer loop. A side advantage of providing the complete set of parameters is that it avoids the need for the usual identification experiment for the tuning of the outer controller.

Simple robust autotuning rules for 2-DoF PI controllers.

This paper addresses the problem of providing simple tuning rules for a Two-Degree-of-Freedom (2-DoF) PI controller (PI(2)) with robustness considerations. The introduction of robustness as a matter of primary concern is by now well established among the control community. Among the different ways of introducing a robustness constraint into the design stage, the purpose of this paper is to use the maximum sensitivity value as the design parameter. In order to deal with the well known performance/robustness tradeoff, an analysis is conducted first that allows the determination of the lowest closed-loop time constant that guarantees a desired robustness. From that point, an analytical design is conducted for the assignment of the load-disturbance dynamics followed by the tuning of the set-point weight factor in order to match, as much as possible, the set-point-to-output dynamics according to a first-order-plus-dead-time dynamics. Simple tuning rules are generated by considering specific values for the maximum sensitivity value. These tuning rules, provide all the controller parameters parameterized in terms of the open-loop normalized dead-time allowing the user to select a high/medium/low robust closed-loop control system. The proposed autotuning expressions are therefore compared with other well known tuning rules also conceived by using the same robustness measure, showing that the proposed approach is able to guarantee the same robustness level and improve the system time performance.

Multi-loop PI-based control strategies for the Activated Sludge Process

This paper proposes a multi loop decentralized control strategy for the control of a wastewater treatment plant based on an Activated Sludge (ASP) model. The ASP is a described by means of a nonlinear model and results on a Two-Input Two-Output multivariable system. Even though advanced control strategies have been presented in the literature, the proposal of this paper is to show that by appropriate tuning of decentralized PI controllers, it is possible to get comparable performance as with other approaches. With this purpose the paper proposes a way of addressing the design of the decentralized controllers as well as a regulation based tuning for a PI controller. Simulations are carried out on the nonlinear model showing the performance of the proposed approach.

Optimal Robust Tuning for 1DoF PI/PID Control Unifying FOPDT/SOPDT Models

The aim of the paper is to present tuning equations for one-degree-of-freedom (1DoF) proportional integral (PI) and proportional integral derivative (PID) controllers. These are based on a performance/robustness trade-off analysis with first- and second-order plus deadtime models. On the basis of this analysis a tuning method is developed for 1DoF PI and PID controllers for servo and regulatory control that allows designing closed-loop control systems with a specified MS robustness that at the same time have the best possible IAE performance. The control system robustness is adjusted varying only the controller proportional gain.

Performance/robustness tradeoff analysis of PI/PID servo and regulatory control systems

This paper presents a performance (Integrated Absolute Error IAE) - robustness (Maximum Sensitivity Ms) tradeoff analysis for First-Order-Plus-Dead-Time (FOPDT) and Second-Order-Plus-Dead-Time (SOPDT) servo-control and regulatory control systems with One-Degree-of-Freedom (1-Dof) and Two-Degree-of Freedom (2-Dof) Proportional Integral (PI) and Proportional Integral Derivative (PID) controllers. Analysis shows that for same model, performance optimized 1-DoF PI controllers are more robust than the PIDs but their optimal performance is lower. The performance optimized regulatory control systems, PI and PID, are less robust than the servo-control ones, requiring also more performance degradation to reach the same robustness level.

Considerations on Set-Point Weight choice for 2-DoF PID Controllers

Abstract Abstract This papers aim is to present an analysis of the influence of the 2-DoF controllers proportional set-point weight over the servo-control performance and to show that the removal of the existing constraint for its selection (0 ≤ β ≤ 1.0) will allow to improve its performance when a high robust regulatory control system is required. A concrete analysis is conducted by using 2-DoF PID tuning approaches that explicitly take the desired robustness level as a design parameter. It is seen that as the desired robustness increases the tuning methods suggest values β > 1.0. Performance looses are evaluated if we are to be constrained to the case β ≤ 1.0.

Conversion formulae and performance capabilities of two-degree-of-freedom PID control algorithms

The aim of the paper is to present two-degree-of-freedom (2DoF) proportional integral derivative (PID) control algorithms and conversion relations between their parameters. The Ideal PID with filter (PID2F) is the more general PID controller. Restrictions to obtain equivalent 2DoF Standard or Series PID controllers are presented taking into account the derivative filter constant. Examples are used to illustrate when or when not equivalent controllers exist.