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Nowadays, some of the most important challenges to society are focused on the use of renewable energies, mitigation of greenhouse-type gases and residual treatment. Microalgae are becoming one of the most powerful solutions to contribute to these problems. So, industrial facilities have been developed in the last decades to produce this type of microorganisms. However the dynamics of these systems is very complex, and advanced models and control strategies are required. The Interpolating Control is a novel technique with capacity to deal with state and control constraints with low computational burden, being suitable to be applied in this type of processes. This technique has been used in the literature to control simulated or laboratory scale systems. This paper shows the operation results for a Interpolated Controller in an industrial raceway photobioreactor to contribute in the control of these real processes.

In this paper, the problem of pH regulation in photobioreactors has been addressed by using a robust Proportional–Integral controller in combination with a linear active disturbance rejection approach. This formulation is based on the Generalized Proportional–Integral (GPI) observers design to estimate online external disturbances and non-modeled dynamics. The methodology uses a model reference optimization procedure with tracking and regulatory target closed-loop transfer functions for first-order plus dead-time models. The proposed controller is validated on a full-scale Raceway photobioreactor, whose results show a significant improvement in the accuracy of pH regulation and, consequently, a positive influence on biomass production. Moreover, a classical feedforward approach has been used for comparison purposes. The performance of the robust technique is evaluated with different indexes, whose results confirm the good performance of the proposed active disturbance rejection control scheme.

This paper presents an active disturbance rejection control scheme to automatically regulate the glucose level in type 1 diabetic patients. Although the blood glucose system is nonlinear, in this control approach, it is represented as a linear perturbed system, whose lumped disturbance input is estimated by an Extended State Observer (ESO) and then compensated by an robust controller tuned with Quantitative Feedback Theory (QFT). The robust control scheme uses a Smith predictor for the time delay compensation and allows taking into account the inter-patient variability presented in the glucose control problem. In order to validate the effectiveness of this approach, the controller is tested in silico on a cohort of adult patients of the UVA/Padova metabolic simulator, which has been accepted by the Food and Drug Administration (FDA). In silico results indicate that safe blood glucose control can be achieved by the proposed controller.

This paper presents the modification of the well-known pole placement method for first-order systems and PI control for the tracking problem. The main drawback of the original method is the presence of a zero in the closed-loop transfer function, which has a negative influence in the desired closed-loop response. Typically, this effect is cancelled by using a reference filter within a two-degree-of-freedom control scheme. However, in this work we present a simple modification of the original method that allows us to consider the zero effect in advance. First, the effect of a zero term in the response of second-order systems is analyzed to see how the time response parameters (overshoot, peak time, rise time and settling time) are affected. Afterwards, this analysis and the resulting equations are combined with the pole placement method to propose the new solution. Finally, simulation results are presented to demonstrate the advantages of the proposed method, where it is shown that faster responses than by using a reference filter are obtained.

Feedforward control schemes to compensate for disturbances are very well known in process control. In those control approaches, PID controllers are usually considered in the feedback loop, where nominal design for both feedback and feedforward controllers are commonly performed. This paper presents a robustness analysis to study how uncertainties can affect the classical feedforward control scheme. Afterwards, a robust PID controller is designed by using Quantitative Feedback Theory to account for these uncertainties and to fulfill robust specificaitons for the regulation control problem. Results based on frequency and time domains are presented.

This document addresses the problem of controlling a one-stage refrigeration cycle by using the opening of the expansion valve and the compressor speed as control variables, while the outlet temperature of evaporator secondary flux and the superheating degree of refrigerant at evaporator outlet are the controlled variables. An uncertain matrix function is obtained in order to represent the full operating range of the nonlinear system. Thus, the control decentralized approach control consists of designing Generalized- Proportional-Integral (GPI) observers for the internal loops of each controlled variable while PID controllers are tuned based on the Quantitative Feedback Theory for the respective external loops. Simulations results show that the robust controllers reacts quickly reference settings, despite the non-measurement of the disturbance variables and the dynamic coupling of the multi-variable system, compared to decentralised single PIDs proposed with the benchmark.

In this paper, a control scheme based on feedback linearization technique and quantitative feedback theory (QFT) is used to regulate the inner diurnal temperature in a greenhouse located in the south of Spain. In a first step, a non-linear model for the greenhouse is used to design a feedback linearization controller, which provides the vents opening percentage from a virtual control signal provided by a robust proportional integral (PI) controller. The relation between the system output (inside temperature of the greenhouse) and the virtual control signal is given by a first order plus dead time (FOPDT) system. The values for the three parameters of this linear model are identified in the experimental greenhouse by applying several step changes in the virtual control signal and analyzing the process response. Different values for gain, the time constant, and time delay are identified. So, this uncertain linear description for the system is used to design a quantitative feedback theory (QFT) controller with a PI structure. Finally, experimental results are analyzed showing satisfactory performance of the proposed control approach.

Electricity load forecasting, optimal power system operation and energy management play key roles that can bring significant operational advantages to microgrids. This paper studies how methods based on time series and neural networks can be used to predict energy demand and production, allowing them to be combined with model predictive control. Comparisons of different prediction methods and different optimum energy distribution scenarios are provided, permitting us to determine when short-term energy prediction models should be used. The proposed prediction models in addition to the model predictive control strategy appear as a promising solution to energy management in microgrids. The controller has the task of performing the management of electricity purchase and sale to the power grid, maximizing the use of renewable energy sources and managing the use of the energy storage system. Simulations were performed with different weather conditions of solar irradiation. The obtained results are encouraging for future practical implementation.

This paper presents a non-linear control scheme to deal with dead-time processes, specially for systems where fast closed-loop responses are required. The control scheme is based on the combination of two control strategies appeared in the literature to deal with dead-time processes, the Filtered Smith Predictor (FSP), which is a Smith Predictor (SP) including a filter to improve the robustness; and the PI+CI, a PI with a partial reset action on the control signal when the process output reaches the reference input. In the proposed strategy, the reset action allows to achieve very small rise times with small overshoots, improving the results from FSP. On the other hand, the use of the robust predictor allows to deal with the dead-time in a better and systematic way than the existing PI+CI solutions. The improvements of the proposed control scheme are evaluated through simulations and real experiments on an industrial heat exchanger.

The main step of the production of l -aminoacids concentrates from microalgae is the enzymatic hydrolysis. This process has to be done at the optimum temperature and pH of the enzyme in order to obtain the maximum yield. In order to keep a constant pH, NaOH (1 M) or H 2 SO 4 (1 M) are used, depending on the reaction step. When working with pH it is not possible to use the governing equations due to the complexity of the enzymatic hydrolysis. In this work, the modelling of pH is experimentally performed on a laboratory scale plant. Since the obtained model presents delay and uncertainty in the parameters, a Filtered Smith Predictor is proposed as control strategy. This control scheme has been tested in the real system. The Filtered Smith Predictor has reduced the Integral Absolute Error and the time for the solution addition in more than 25% and it has increased 5% the production of l -aminoacids compared to an on-off control, which is the controller most used in these processes.

In this work the input amplitude saturation problem is analysed in the Quantitative Feedback Theory (QFT) framework. This paper reviews previous works in the literature dealing with the input amplitude saturation problem in the presence of an uncertain plant in the frequency domain using QFT. The objective of this paper is to compare the different available approaches and summarize the design process for each case so that this paper can be used as a tutorial; there are six main approaches to this problem. Two of these approaches use the classical two degrees of freedom control scheme for QFT; in both of these, the design constraints of a linear QFT compensator are added in the loop shaping stage: they are added in the first approach to avoid excitation of the actuator saturation and in the second one to guarantee global stability. The other three techniques are considered as anti-windup (AW) approaches. Starting from a base design in QFT with two degrees of freedom, the first AW approach introduces a third degree of freedom that guarantees the stability of the system, allowing for base designs for high performance. The other two AW approaches also introduce a third degree of freedom, but they take simple stability considerations into account and focus on the performance of the system. The last solution consists of using a reference governor technique, which guarantees the computation of a reference signal for an inner control loop that is shaped using QFT in such a way that robust stability will be guaranteed. The reference governor technique is a time domain approach that implies the resolution of an optimization problem. The rest of the approaches are frequency domain techniques based on a loop shaping method in the traditional QFT sense.

This paper presents a robust control scheme for a distributed solar collector (DSC) field. As DSC are systems subjected to strong disturbances (mainly in solar radiation and inlet oil temperature), a series feedforward is used as a part of the plant, so that the system to be controlled has one input (fluid flow) and one output (outlet temperature) as the disturbances are partially compensated by the series feedforward term, so that the nonlinear plant is transformed into an uncertain linear system. The Quantitative Feedback Theory technique (QFT) has been used to design a control structure that guarantee desired control specifications, as settling time and maximum overshoot, under different operating conditions despite system uncertainties and disturbances. To account for input and output constraints, both an antireset-windup mechanism and a reference governor have been used. Experimental tests are presented.

Quantitative feedback theory (QFT) is an engineering design technique of uncertain feedback systems that uses frequency domain specifications. A key step in QFT is the mapping of these specifications into regions of the Nichols plane, whose borders are usually referred to as boundaries. Boundaries computation is a key design step, thus a precise and efficient computation is critical for both obtaining low bandwidth feedback compensators and simplification of the design process. In this work, the problem of boundaries computation is analysed, introducing a new algorithm based on the computation of level curves of a three-dimensional surface. Besides magnitude boundaries, associated with some specification over the magnitude of a closed-loop transfer function, phase boundaries are also considered. In addition, comparison with previous published algorithms is done in terms of precision and computational efficiency. Copyright © 2006 John Wiley & Sons, Ltd.

The paper is devoted to extend the synthesis theory developed by Prof. I. Horowitz to guarantee prescribed performance of a feedback system with type I linear plant and with a saturating element Sat. Using a three degrees of freedom scheme a design method is proposed, in the framework of Quantitative Feedback Theory (QFT), that extends the previous synthesis theory to take the plant uncertainty into account. The major factor in this method is Ln, the system loop transmission with respect to saturating element Sat. It is shown how a 3DoF linear compensator {F, G, H} can be synthesized to achieve desired performance even under hard saturation using a new type of specifications over a function of Ln. The proposed method is illustrated using examples to emphasize the practical application of the resulting techniques.

In this paper a new design methodology to cope with global stability in presence of rate and amplitude saturation in systems with uncertain plants is proposed. The design method proposed provides an accurate graphic design procedure in frequency domain. To deal with the problem a 4DoF control scheme, two ( F and G ) designed in a first step with QFT so that the uncertainty is taken into account for the linear operation mode, and the other two (H a and H v ) designed in a second step to deal with the non-linear operation mode.

This paper presents the development and implementation of robust control techniques based on the quantitative feedback theory (QFT) aimed at achieving adequate values of inside greenhouse temperature in spite of uncertainties and disturbances acting on the system. A modification of classical design approaches has been included to incorporate feedforward action (exploiting the availability of measurements of disturbances, which in the particular case of greenhouses are the main energy source) and an antiwindup action to account for frequent saturations in the control signal. Results obtained with this scheme using a validated nonlinear simulator of greenhouse dynamics are also included. Copyright © 2002 IFAC

In this work, a new technique for the computation of the region of attraction for linear and time invariant systems controlled by a saturated reset control system is presented. The estimation of the region of attraction is based on a polytopic representation. In addition, the information of the solutions is synthesized in a directed graph formed by the polytopes. After presenting several useful conditions on the polytopes, such as positive invariance and convergence to the origin, a procedure is proposed to process the graph and obtain a region of attraction estimation. The effectiveness of the proposed technique is illustrated by a numerical example.

Most control techniques require the use of a plant model during the design phase in order to tune the controller parameters. The mathematical models are an approximation of real systems and contain imperfections by several reasons: use of low-order descriptions, unmodelled dynamics, obtaining linear models for a specific operating point (working with poor performance outside of this working point), etc. Therefore, control techniques that work without taking into account these modelling errors, use a fixed-structure model and known parameters (nominal model ) supposing that the model exactly represents the real process, and the imperfections will be removed by means of feedback. However, there exist other control methods called robust control techniques which use these imperfections implicity during the design phase. In the robust control field such imperfections are called uncertainties, and instead of working only with one model (nominal model), a family of models is used forming the nominal model + uncertainties. The uncertainties can be classified in parametric or structured and non-parametric or non-structured. The first ones allow representing the uncertainties into the model coefficients (e.g. the value of a pole placed between maximum and minimum limits). The second ones represent uncertainties as unmodelled dynamics (e.g. differences in the orders of the model and the real system) (Morari and Zafiriou, 1989). The robust control technique which considers more exactly the uncertainties is the Quantitative Feedback Theory (QFT). It is a methodology to design robust controllers based on frequency domain, and was developed by Prof. Isaac Horowitz (Horowitz, 1982; Horowitz and Sidi, 1972; Horowitz, 1993). This technique allows designing robust controllers which fulfil some minimum quantitative specifications considering the presence of uncertainty in the plant model and the existence of perturbations. With this theory, Horowitz showed that the final aim of any control design must be to obtain an open-loop transfer function with the suitable bandwidth (cost of feedback) in order to sensitize the plant and reduce the perturbations. The Nichols plane is used to achieve a desired robust design over the specified region of plant uncertainty where the aim is to design a compensator C(s) and a prefilter F(s) (if it is necessary) (see Figure 1), so that performance and stability specifications are achieved for the family of plants. 17

The paper is devoted to the robust stability problem of linear time invariant feedback control systems with actuator saturation, especially in those cases with potentially large parametric uncertainty. The main motivation of the work has been twofold: First, most of the existing robust antiwindup techniques use a conservative plant uncertainty description, and second, previous quantitative feedback theory (QFT) results for control systems with actuator saturation are not suitable to achieve robust stability specifications when the control system is saturated. Traditionally, in the literature, this type of problems has been solved in terms of linear matrix inequalities (LMIs), using less structured uncertainty descriptions as given by the QFT templates. The problem is formulated for single input single output systems in an input-output (I/O) stability sense, and is approached by using a generic three degrees of freedom control structure. In this work, a QFT-based design method is proposed in order to solve the robust stability problem of antiwindup design methods. The main limitation is that the plant has poles in the closed left half plane, and at most, has one integrator. The work investigates robust adaptations of the Zames–Falb stability multipliers result, and it may be generalized to any compensation scheme that admits a decomposition as a feedback interconnection of linear and nonlinear blocks (Lur’e type system), being antiwindup systems as a particular case. In addition, an example will be shown, making explicit the advantages of the proposed method in relation to previous approaches.

This work approaches the problem of robust control for distributed collector fields. The goal is to investigate the potentials of a nonlinear/hybrid compensator previously developed by some of the authors, referred to as the PI+CI compensator, in the control of a system with significant uncertainty. To this end, the design of PI+CI has been made in two steps: first, a base robust PI compensator is designed by using QFT (quantitative feedback theory) to satisfy (robust) relative stability and tracking specifications, and then a reset percentage of the integral term is chosen in order to improve the transitory response. In addition, a simple modification of the PI+CI compensator, consisting of the variation of the reset percentage at each reset time, is investigated regarding the improvement of the previous design.

A general framework for designing antiwindup control systems is developed. More traditional anti-windup schemes generally suffer from several limitations, including the lack of (a priori) robustness respect to plant uncertainty, and also have a considerable heuristic component. The design method proposed in this paper provides an accurate graphic design procedure that guarantees closed loop global stability, in the presence of saturation-type non-linearities and plant uncertainty. The case of SISO LTI plant is considered.

This paper is devoted to extend the synthesis theory developed in a previous work, to guarantee prescribed performance of a feedback system with an uncertain linear plant with one integrator and with rate and amplitude saturating elements. Using a three degrees of freedom scheme a design method is proposed, within the framework of Quantitative Feedback Theory (QFT), that extends the existing synthesis theory to take the plant uncertainty into account when this type of non-linear elements are present. The major factor in this method is Ln, the system loop transmission with respect to the saturating elements. It is shown how the compensator [F, G, H] can be synthesized to achieve desired performance even under hard saturation using a new type of specifications over a function of Ln. The proposed method is illustrated using an example to emphasize the practical application of the resulting technique.

This paper presents a non-linear control scheme to deal with dead-time (DT) processes where small rise times are required. The control scheme is based on the combination of two strategies appeared in the literature to deal with DT processes, the Filtered Smith Predictor (FSP), which is a Smith Predictor (SP) including a filter to improve the robustness, and the PI+CI, a PI with a partial reset action on the control signal when the process output is equal to the reference input. In the proposed strategy, the reset action allows to achieve very small rise times with small overshoots, improving the results from FSP. On the other hand, the use of the robust predictor allows to deal with the dead time in a better and systematic way than the PI+CI with variable reset ratio and variable reset band does.