Pedro Mercader

A PI tuning rule for integrating plus dead time processes with parametric uncertainty

A novel method to tune a Proportional-Integral (PI) compensator for an integrating plus dead time (IPDT) process, in presence of interval parametric uncertainty, is presented. The design is based on optimization of load disturbance rejection with constraints on the magnitude of the sensitivity and complementary sensitivity functions, that must be satisfied for any element belonging to a set of plants. Instead of solving this problem with a brute force approach (grid the uncertainty set), we prove that this problem can be solved by considering only two plants. That lets us to obtain a tuning rule, after using some approximations. To conclude, some examples will be given in order to elucidate the usefulness of the proposed tuning rule.

Robust PID Design Based on QFT and Convex–Concave Optimization

This paper presents an automatic loop-shaping method for designing proportional integral derivative controllers. Criteria for load disturbance attenuation, measurement noise injection, set-point response and robustness to plant uncertainty are given. One criterion is chosen to be optimized with the remaining ones as constraints. Two cases are considered: M-constrained integral gain optimization and minimization of the cost of feedback according to quantitative feedback theory. Optimization is performed using a convex–concave procedure (CCP). The method that relies on solving a sequence of convex optimization problems converges to a local minimum or a saddle point. The proposed method is illustrated by examples.

Robust PI compensators design for FOPDT systems with large uncertainty

This work presents a control design method to determine the parameters of a proportional integral (PI) compensator satisfying desired specifications on the gain and phase margins or, alternatively, an upper bound on the sensitivity transfer function, for an uncertain plant. The process under consideration can be modeled by a first order plus dead time (FOPDT) model having interval parametric uncertainty, therefore a set of plants is considered. The proposed approach is based on the translation of the desired specifications into the compensator parameter space, obtaining in such a way a feasible region where design specifications are met for each of the plant considered. This feasible region is obtained by using a fractional-order system which is representative of the uncertain plant, instead of using each plant belonging to the set. To conclude, an example is given to illustrate the proposed method, this example is motivated from a real process.

Tuning of PI compensators for integrating systems with large parametric uncertainty

A simple PI tuning rule for integrating plus dead time (IPDT) systems, with large parametric uncertainty, is developed. In order to deal with parametric uncertainty a family of plants is considered. The design specifications are upper bounds on the sensitivity and the complementary sensitivity functions, that must be satisfied for any element belonging to the plants set. When applied to a system without uncertainty (or with no significant uncertainty) the well-known SIMC tuning rule is recovered. To conclude, several examples are analyzed to illustrate the proposed tuning rule.

IQC analysis for time-delay reset control systems with first order reset elements

This work studies input-output stability of time-delay reset control systems, with first order reset elements (FORE). The results are derived by using integral quadratic constraint (IQC) framework. A new delay-dependent stability criterion is formulated in the form of a linear matrix inequalities (LMI) condition, using Kalman-Yakubovich-Popov (KYP) lemma. A numerical example is given, which illustrates the effectiveness of the new criterion.

PID synthesis under probabilistic parametric uncertainty

In many system identification methods, process model parameters are considered stochastic variables. Several methods do not only yield expectations of these, but in addition their variance, and sometimes higher moments. This paper proposes a method for robust synthesis of the proportional-integral-derivative (PID) controller, taking parametric process model uncertainty explicitly into account. The proposed method constitutes a stochastic extension to the well-studied minimization of integrated absolute error (IAE) under ℋ∞-constraints on relevant transfer functions. The conventional way to find an approximate solution to the extended problem is through Monte Carlo (MC) methods, resulting in high computational cost. In this work, the problem is instead approximated by a deterministic one, through the unscented transform (UT), and its conjugate extension (CUT). The deterministic approximations can be solved efficiently, as demonstrated through several realistic synthesis examples.

Performance analysis of PI and PI+CI compensation for an IPDT process

In this work, it is performed a comparison between the performance of PI and PI+CI compensators, in terms of a balanced index (servo/regulatory) based on the integrated absolute error (IAE). The plant is modelled by an integrating plus dead time (IPDT) process. The purporse of this work is to provide insight into the benefit of reset compensation both in servo and regulatory problems. This is accomplished by providing a tuning rule for the PI+CI, that allows to analyze the performance index in the compensator parameter space. The analysis done is independent of the process parameters.

IQC analysis of reset control systems with time-varying delay

ABSTRACT The study of input–output stability of reset control systems with time-varying delay is addressed in this work. The time-varying function that defines the delay is assumed to be bounded on magnitude and variation. This approach also covers the particular case of constant time delay, but it is studied separately to obtain less conservative results. After proposing a convenient loop transformation, the stability analysis is performed by means of the integral quadratic constraint framework. Then by applying the Kalman–Yakubovich–Popov lemma, easily checkable conditions in form of linear matrix inequalities are obtained. To conclude, some numerical examples are provided illustrating the proposed criteria.

Robust PID Design by Chance-Constrained Optimization

Abstract A method for synthesizing proportional–integral–derivative (PID) controllers for process models with probabilistic parametric uncertainty is presented. The proposed method constitutes a stochastic extension to the well-studied maximization of integral gain optimization (MIGO) approach, i.e., maximization of integral gain under constraints on the H ∞ -norm of relevant closed-loop transfer functions. The underlying chance-constrained optimization problem is solved using a gradient-based algorithm once it has been approximated by a deterministic optimization problem. The approximate solution is then probabilistically verified using randomized algorithms (RAs). The proposed method is demonstrated through several realistic synthesis examples.

Autotuning of an in-line pH control system

A novel autotuning procedure is presented through application to an industrial in-line pH control system. The procedure has three advantages over classical relay auto-tuners: experiment duration is very short (no need for limit-cycle convergence); all data is used for identification (instead of only peaks and switch instances); a parameter uncertainty model is identified and utilized for robust controller synthesis.