Raul Villafuerte

Tuning of Proportional Retarded Controllers: Theory and Experiments

This brief provides simple tuning rules for the proportional retarded (PR) control of second order systems requiring strong closed-loop damping. A frequency domain analysis allows determining the σ-stabilizability regions of the controller. The analysis provides explicit formulae for tuning the three parameters of the PR controller, namely, the proportional gain, the retarded gain, and the delay. The performance of the PR closed-loop control is experimentally compared with that of a proportional derivative (PD) controller. The experiments show that the PR controller outperforms the PD controller fed using velocity estimates obtained from a high-pass filter in terms of noise amplification, control effort, and position error, and has a similar performance compared with a PD controller supplied with velocity estimates produced by an observer. Numerical implementation of the PR controller is computationally less demanding than the corresponding implementation of PD algorithms using velocity estimation based on filters or observers, since it does not need solving ordinary differential equations and only requires performing two products and a few memory registers for implementing the time delay.

Tuning and noise attenuation of a second order system using Proportional Retarded control

Abstract This paper presents a tuning strategy for Proportional Retarded (PR) control laws in closed loop with second order systems and experimental results on the noise attenuation performance of a DC servomotor. The PR controller is compared with other commonly employed strategies for avoiding the time-derivative measurement in Proportional Derivative control laws. The experiments show that the PR controller combines good noise attenuation and tracking performance with a simple implementation.

Tuning the leading roots of a second order DC servomotor with proportional retarded control

The stabilization of a second order system through a proportional delay controller insuring a specified closed loop exponential decay s is studied. The analysis in the frequency domain allows the determination of the s-stabilizability regions of the controller. The locus of the dominant roots is analyzed in detail and the characterization of some key loci, including the maximum achievable decay is obtained. The tuning of a DC servomotor experimental setup illustrates the results.

Robust stabilization of nonlinear time delay systems: A complete type functionals approach

Abstract The robust stabilization of some classes of nonlinear delay systems with nominal linear delay system is addressed. The form of the controller is not an a priori proposal, but it is the result of a synthesis relying on the use of complete type Lyapunov–Krasovskii functionals, leading to distributed delay linear or nonlinear robust control laws. Simulation results of the stabilization of a chemical refining process demonstrate the good performance of the proposed approaches.

Practical stability of neutral type time delay systems: LMI’s approach

In this paper we discuss the practical stability of a class of neutral type time delay systems. We obtain sufficient conditions based on Lyapunov-Krasovskii functionals stated in terms of the feasibility of a set of linear matriz inequalities (LMIpsilas). A ldquopracticalrdquo exponential estimate of the solution is also obtained.

Estimate of the region of attraction for a class of nonlinear time delay systems: a leukemia post-transplantation dynamics example

In this contribution we present an estimate of the region of attraction of the exponentially stable trivial solution for a class of nonlinear time delay systems. The case of multiple delays is addressed. This constructive approach is based on the use of Lyapunov-Krasovskii functionals of complete type. The analysis of the region of attraction of the stable equilibrium of the model describing the post-transplantation dynamics of the immune response to chronic myelogenous leukemia completes this work.

On the computation of estimates for time delay systems with Lyapunov-Krasovskii functionals of complete type

Robust stability conditions for linear time delay systems and estimates of the domain of attraction for a class of nonlinear time delay systems are obtained with the help of a Lyapunov-Krasovskii functional of complete type with a given cross term in the time derivative

Performance without tweaking differentiators via a PR controller: Furuta pendulum case study

Performance of mechatronics systems can deteriorate significantly under the presence of delays in measurements. On the other hand, intentional introduction of a delay in a feedback control law may be beneficial in achieving good performance without relying on accurately tuned estimates for derivatives of measured signals. In this context, a proper design of retarded control laws represents an important challenge, and this paper gives a step forward to obtain better control laws for underactuated mechanical systems under the presence of time delays in measurements. Particularly, a Proportional-Retarded (PR) control law is designed for stabilization of an underactuated rotational inverted pendulum, known as the Furuta pendulum. Experiments over a laboratory platform as well as a comparison with a Linear Quadratic Regulator (LQR) are performed to show the advantages of the proposed scheme.

Identification-based linear control of a twin rotor MIMO system via dynamical neural networks

This paper presents a real-time implementation of an identification-based linear control law on a twin rotor MIMO system. Identification is performed via dynamical neural networks which-under mild conditions-guarantee exponential convergence to zero of the identification error. Once the plant model is obtained and linearized, a stabilizing linear state feedback control law is synthesized via linear matrix inequalities. Based on the same linearization, trajectory tracking is performed by a PID controller. Simulation as well as real-time results are discussed.

Proportional retarded control of a second order system

A strategy for the tuning of a second order system in closed loop with a proportional retarded control law, based on the root location analysis of the system, is proposed. It is validated by achieving a significant reduction of the oscillatory behavior of a cart pendulum experimental setup.