Pedro Balaguer

Tuning of PID controllers based on simplified single parameter optimisation

A simple method to design PID controllers in the frequency domain based on a simplified constrained optimisation is proposed. The method is based on the use of a single tuning parameter, defined as the quotient between the final crossover frequency and the zero of the controller. The tuning procedure is based on the maximisation of the controller gain subject to an equality constraint in the phase margin and an inequality constraint in the gain margin. The main advantage of the proposed method is that, even though the maximisation of the controller gain is straightforward, since there is only one parameter to be tuned, the solution is close to the optimal tuning obtained with direct numerical optimisation methods. Moreover the method is applicable to any linear model structure, including dead time and non-minimum phase systems.

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.

Controller parameters dependence on model information through dimensional analysis

In this article we make use of dimensional analysis in order to investigate the controller parameters dependence on model information (i.e. model parameters). The objective is to relate the influence that each model parameter has on each controller parameter. In order to accomplish this goal the model transfer function is first analyzed using dimensional analysis and characterized by means of of dimensionless numbers. Secondly each controller parameter is related with the model parameters. As a result it is derived the underlaying structure that any homogeneous tuning rule must follow. The general results are particularized for PID control of first order and second order systems. The results can be applied to PID tuning and PID tuning rules comparison.

Model order reduction for decentralized PID control design on TITO processes

Abstract The decentralized PID control design of multivariable processes is an appealing approach due to its practical applicability and the existence of a good theoretical basis. However, although industrial processes may be modeled using simple first order and second order models, in decentralized control, the models increase their complexity due to loop interaction, compromising the applicability of existing PID tuning rules. In fact, even inverse response behavior may appear due to loop interaction. The contribution of the article is twofold. First, we derive conditions to assess the inverse response behavior of reduced effective transfer functions. As a result, we know when tuning rules for first order and minimum phase second order models are suited for decentralized control tunning. Secondly, at the sight of matrix transfer function parameters, we derive simplified models in a straightforward way. The results are useful for decentralized MIMO process control design using simple tuning rules derived for first order and second order systems.

A New Frequency Dependent Approach to Model Validation

In order to have confidence in a model it is necessary to validate it. Different model validation approaches exist. Their difference is based upon the assumptions about the plant and models. Classical validation methods, based on classical model identification (Ljung, 1994; Soderstrom and Stoica, 1989) rely on statistical uncertainty assumptions due to stochastic noise only. On the other hand, control oriented identification methods (Chen and

Disturbance compensation on uncertain systems: Feedforward control design for stable systems

Abstract This paper considers the design of feedforward controllers when model uncertainty is present. The main contribution is an alternative approach to the generation of the feedorward control action on the basis of the Internal Model Control formulation. This new structure allows for completely independent tuning of the feedback and feedforward controllers and provides an explicit expression for the achieved nominal performance degradation when the uncertain case is considered. The formulation of the feedforward controller as an Internal Model Controller allows existing design approaches to be applied and uncertainty effect taken into account by means of the corresponding analysis equation.

Robustness Considerations on PID Tuning for Regulatory Control of Inverse Response Processes

Abstract In general, to control industrial processes that show an inverse response output is difficult. This difficulty arises because achievable performance and robustness levels are competing factors that the designer has to deal with. In this paper we focus on proportional integral derivative (PID) control of inverse response processes, in particular with the Direct Synthesis design for disturbance rejection DS-d tuning method of Chen and Seborg. The paper presents equations that link the control system design performance parameter (closed-loop control system speed) with its minimum robustness level, measured with the maximum sensitivity M S , for the mentioned tuning method. In this way, the proposed result allows to obtain robust PID control systems with M S ≤ 2 for inverse response processes. The examples show the effectiveness of the proposed design parameter lower limit estimation for the DS-d tuning method.

A simple procedure to design PID controllers in the frequency domain

In this paper, a simple method to design PID controllers in the frequency domain is proposed. The method is based on the use of a single tuning factor, defined as the quotient between the final cross over frequency and the zero of the controller. Classical methods described in the basic control books propose to fix the above parameter in a predetermined value (usually 10), independently of the process model. Several examples show that this fixed value is not the best choice in general, in the sense that the behavior can be greatly improved if an adequate tuning of that parameter is done. A tuning procedure for the parameter is also proposed, based on the maximization of a controller gain. The procedure is valid for PI, PD and PID controller design, and is tested with a set of well known benchmark systems for PI and PID design and compared with other (more complex) approaches.

On-Line Model Selection Techniques By Using Multiple Models And Supervision Algorithms

In this paper, an intelligent adaptive multi-model based control scheme is proposed to obtain the lowest-order model for a system under control by means of adaptation and switching between multiple models. The multi-model scheme is composed of three models of increasing consecutive orders operating in parallel along with a switching mechanism between them. The switching policy selects on-line the necessary order of the nominal model required to achieve the desired degree of performance of the closed-loop depending on the reference signal selection. In this way, the order selection is performed automatically in real-time by comparing the actual behaviour of the system with the desired performance for the closed-loop. The estimation of the parameters of the model is performed by an adaptive algorithm integrating a so-called multi-estimation scheme. This architecture leads to a simple procedure to on-line select the appropriate order of the nominal model required for a certain control application with assessment of a prescribed level of closed-loop performance.

Singularly Perturbation Method Applied To Multivariable PID Controller Design

Proportional integral derivative (PID) controllers are commonly used in process industries due to their simple structure and high reliability. Efficient tuning is one of the relevant issues of PID controller type. The tuning process always becomes a challenging matter especially for multivariable system and to obtain the best control tuning for different time scales system. This motivates the use of singularly perturbation method into the multivariable PID (MPID) controller designs. In this work, wastewater treatment plant and Newell and Lee evaporator were considered as system case studies. Four MPID control strategies, Davison, Penttinen-Koivo, Maciejowski, and Combined methods, were applied into the systems. The singularly perturbation method based on Naidu and Jian Niu algorithms was applied into MPID control design. It was found that the singularly perturbed system obtained by Naidu method was able to maintain the system characteristic and hence was applied into the design of MPID controllers. The closed loop performance and process interactions were analyzed. It is observed that less computation time is required for singularly perturbed MPID controller compared to the conventional MPID controller. The closed loop performance shows good transient responses, low steady state error, and less process interaction when using singularly perturbed MPID controller.