Alejandro Rincon

Control of an anaerobic upflow fixed bed bioreactor

In this paper the feedback linearization control technique is used for controlling an anaerobic upflow fixed bed reactor, which is used for the degradation of wine distillery waste water. The concentration of the volatile fatty acids is used as the output and the dilution rate is used as the control input. Given the closed loop system to be controlled and the specification for the desired behavior, the control law makes the system to behave correctly. The zero dynamics is found to be stable, guaranteeing that the control technique can be used.

Adaptive Quasi-Sliding Mode Control for Permanent Magnet DC Motor

The motor speed of a buck power converter and DC motor coupled system is controlled by means of a quasi-sliding scheme. The fixed point inducting control technique and the zero average dynamics strategy are used in the controller design. To estimate the load and friction torques an online estimator, computed by the least mean squares method, is used. The control scheme is tested in a rapid control prototyping system which is based on digital signal processing for a dSPACE platform. The closed loop system exhibits adequate performance, and experimental and simulation results match.

Adaptive control for nonlinear systems with time-varying control gain

We propose a scheme for nonlinear plants with time-varying control gain and time-varying plant coefficients, on the basis of a plant model consisting of a Brunovsky-type model with polynomials as approximators. We develop an adaptive robust control scheme for this plant, under the following assumptions: (i) the plant terms involve time-varying but bounded coefficients, being its upper bound unknown; (ii) the control gain is unknown, not necessarily bounded, and only its signum is known. To achieve robustness, we use a combination of robustifying control inputs and dead zone-type update laws. We apply this methodology to the speed control of a permanent magnet synchronous motor (PMSM), and we achieve proper tracking results.

Controller Design for a Second-Order Plant with Uncertain Parameters and Disturbance: Application to a DC Motor

This paper shows the controller design for a second-order plant with unknown varying behavior in the parameters and in the disturbance. The state adaptive backstepping technique is used as control framework, but important modifications are introduced. The controller design achieves mainly the following two benefits: upper or lower bounds of the time-varying parameters of the model are not required, and the formulation of the control and update laws and stability analysis are simpler than closely related works that use the Nussbaum gain method. The controller has been developed and tested for a DC motor speed control and it has been implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform. The motor speed converges to a predefined desired output signal.

A Dynamic Analysis for an Anaerobic Digester: Stability and Bifurcation Branches

This work presents a dynamic analysis for an anaerobic digester, supported on the analytical application of the indirect Lyapunov method. The mass-balance model considered is based on two biological reaction pathways and involves both Monod and Haldane representations of the specific biomass growth rates. The dilution rate, the influent concentration of chemical oxygen demand (COD), and the influent concentration of volatile fatty acids (VFA) are considered as stability parameters. Several characteristics are determined analytically for the normal operation equilibrium point: (i) equilibrium coordinates, (ii) parameter conditions that lead to positive values of the equilibrium state variables, (iii) parameter conditions for locally stable nature of the equilibrium, (iv) coordinates for the local bifurcation points—fold and transcritical—, and (v) coordinates of the crossing between bifurcation points. These factors are computed analytically and explicitly as expressions of the dilution rate and the influent concentrations of COD and VFA.

A New Robust Controller with Applications to Bioreactors

In this work an anaerobic digester is controlled using input-output linearization and Lyapunov-like function methods. It is assumed that model parameters are unknown, time-varying, and bounded, and upper or lower bounds are also unknown. To tackle the effect of input saturation, a state observer is designed. The tracking and observer errors are defined in terms of the noisy measured output instead of ideal output, given by the mathematical model. The design of the observer mechanism and the update laws is based on the Lyapunov-like function technique, whereas the design of the control law is based on the input-output linearization method. In this paper two important properties of the controlled system are proven. First, the observer error converges asymptotically to a residual set whose size is user-defined, and such convergence is not disrupted, neither by the input saturation nor by the parameter uncertainties. Second, when the control input is nonsaturated the tracking error converges to a residual set whose size is user-defined. The model parameter uncertainties are included to prove the convergence of errors. Finally, a numerical example to validate the developed control is presented.

Two-Valued Control for a Second-Order Plant with Additive External Disturbance

In this work a two-valued state feedback control for a plant of second order with known constant coefficients and an additive bounded disturbance is designed. In this controller the control signal can take only two possible values. The controller design is based on Lyapunov-like function method, achieving the convergence of the tracking error to a user-defined residual set. A boundedness condition for the user-defined reference signal is defined, which is necessary to allow out-put tracking. The developed scheme avoids large commutation rate of the control input. The controller design and stability analysis have important contributions with respect to closely related controllers based on the direct Lyapunov method, namely, (i) conditions to guarantee the expected convergence of the tracking error are established. These conditions are imposed on the reference signal and the extreme values of the control input. The stability analysis is developed by means of the Lyapunov-like function method and the Barbalats Lemma and includes (ii) the bounded nature of the Lyapunov function, (iii) the monotonic convergence of the Lyapunov function to a residual set, and (iv) the asymptotic convergence of the tracking error to a residual set of user-defined size.

A robust adaptive controller for bio-reactors with saturated input and uncertain varying plant parameters

In this paper an adaptive controller for bioreactors is developed, using a mass balance model based on an unique biological reaction pathway. The control scheme is constructed from Lyapunov-like function method and an extended Luenberger observer which allows handling the control input saturation. The measured methane flow rate is used to handle the uncertainty on the reaction rate and an update law to handle the uncertainty on the proportional coefficient of the reaction rate. Under the assumptions of the system model are considered: i) the control input is saturated, ii) the values of the kinetic parameters, the biomass concentration and upper or lower bounds are unknown and iii) the output methane flow rate is measured. The main controller characteristics are the following: i) the closed loop states are bounded, ii) the observer error converges to a residual set whose size is user-defined, iii) the tracking error converges to a residual set which is user-defined; provided, the control input does not reach the extreme values. The controller performance is evaluated via numerical simulations showing excellent results.