Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].

Eigenstructure assignment in descriptor systems

Coordinate free conditions are given for pole assignment by feedback in linear descriptor (singular) systems which guarantee closed-loop regularity. These conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles. Transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback.

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.

Strong structural controllability and the multilink inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

Improved MATLAB GUIs for learning frequency response methods

The author developed two GUIs for asymptotic Bode plots and identification from such plots aimed at improving the learning of frequency response methods: these were presented at UKACC Control 2012. Student feedback and reflection by the author suggested various improvements to these GUIs, which have now been implemented. This paper reviews the earlier work, describes the improvements, and includes positive feedback from the students on the GUIs and how they have helped their understanding of the methods.

The cyber challenge: a robotics project to enthuse

Robotics is a key theme in many of the degrees offered in Systems Engineering. The topic has proved useful in attracting students to the University, and it also provides the basis of much practical and project work throughout the degrees. This paper focuses on one aspect, a Part 2 project in which students doing various degrees work together to develop a mobile robot which is controlled remotely to navigate an environment and perform specific tasks. In addition to providing practical experience of relevant academic topics, this project helps to contribute to key teaching and learning priorities including problem based learning, motivation and important employability skills.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Proposta de um sistema de segurança eletrônica predial

This work presents a suggestion of a security system of land automation having as objective main the creation of a system capable from easy method, supervise the installations of a building with the goal to preserver security personal and patrimonial necessities, aim at portability low cost and use easiness. Was designed an alarms central and access controller that has digital and analogical inputs for sensors and outputs for buzzer, telephonic dialing and electronic lock. The system is supervised by software that makes solicitations of information to the alarms central through the one computer's serial port (RS-232). The supervisory software was developed in platform LabVIEW with displays the received data on a graphical interface informing the sensors' current states distributed in the building and system events as alarns occurrences. This system also can be viewed through the Internet for people registered by the land security's system administrator

Automação de um sistema rotatório para secagem do rejeito de maracujá

The rotary dryer is one of the most used equipments in processing industries. Its automatic control mode of operation is important specially to keep the moisture content of the final product in the desired value. The classical control strategies, like PID (proportional integral derivative) control, are largely used in the industrial sector because of its robustness and because they are easy to be implemented. In this work, a data acquisition system was implemented for monitoring the most relevant process variables, like: both inlet and outlet drying air temperature, dryer rotation, outlet air speed and humidity, and mass of the final product. Openloop tests were realized to identify a mathematical model able to represent the drying process for the rotary system. From this model, a PID controller was tuned using a direct synthesis method, assuming a first order trajectory. The PID controller was implemented in the system in order to control the inlet drying air temperature. By the end, closedloop tests (operating in automatic mode) were realized to observe the controller performance, and, after setting the best tune, experiments were realized using passion fruit seeds as raw material. The experiments realized in closedloop showed a satisfactory performance by the implemented control strategy for the drying air temperature of the rotary system

Design of fuzzy regulators with optimal initial conditions compensation

In almost all cases, the goal of the design of automatic control systems is to obtain the parameters of the controllers, which are described by differential equations. In general, the controller is artificially built and it is possible to update its initial conditions. In the design of optimal quadratic regulators, the initial conditions of the controller can be changed in an optimal way and they can improve the performance of the controlled system. Following this idea, a LNU-based design procedure to update the initial conditions of PI controllers, considering the nonlinear plant described by Takagi-Sugeno fuzzy models, is presented. The importance of the proposed method is that it also allows other specifications, such as, the decay rate and constraints on control input and output. The application in the control of an inverted pendulum illustrates the effectively of proposed method.

Rehydration and shrinkage behaviour of dried pineapple

The shrinking behavior, apparent densities and rehydration indexes of fresh and osmotically pre-treated pineapple slices during air-drying were obtained. The air drying velocity varied from 1.5 to 2.5 m/s and the air temperature from 40 to 70 degreesC. By means of automatic control, it was possible to obtain drying curves under conditions of constant product temperature. Volumetric shrinkage of fresh samples was temperature independent for drying at high air velocities but, at lower velocities, increased with decreasing drying temperature. Osmotically pre-treating the material resulted in reduced shrinkage, as well as drying with product temperature controlled, due to lower drying times needed that led to shorter high temperature exposition. Moisture dependence of apparent density was highly non-linear and could be fitted by an empirical model. Fresh sample rehydration indexes were higher than osmosed ones and increased with increasing temperature, except for pre-treated samples dried at 70 degreesC, probably due to superficial sugar caramelization, which reduced surface water permeability.

Uniform estimates of attracting sets of extended Lurie systems using LMIs

This research presents a systematic procedure to obtain estimates, via extended Lyapunov functions, of attracting sets of a class of nonlinear systems, as well as an estimate of their stability regions. The considered class of nonlinear systems, called in this note the extended Lurie system, consists of nonlinear systems like those of the Lurie problem where one of the nonlinear functions can violate the sector conditions of the Lurie problem around the origin. In case of nonautonomous systems the concept of absolute stability is extended and uniform estimates of the attracting set are obtained. Two classical nonlinear systems, the forced duffing equation and the Van der Pol system, are analyzed with the proposed procedure.

Air-drying of fresh and osmotically pre-treated pineapple slices: Fixed air temperature versus fixed slice temperature drying kinetics

In this investigation, the air drying characteristics of fresh and osmotically pre-treated pineapple slices in a tray dryer were studied under different operating conditions. The air velocity varied from 1.5 to 2.5 m/s and the air temperature from 40 to 70 degreesC. The analytical solution of the second Fick's law for an infinite slab was used to calculate effective diffusion coefficients and their temperature dependence could be well represented by an Arrhenius-type equation. Comparison of the results showed that the diffusion coefficients were lower for the pre-treated fruit. By means of automatic control, it was possible to obtain drying curves under conditions of constant product temperature, which showed to be an alternative to reduce the drying time of pineapple slices.

Variable speed refrigeration system with HPF input rectifier stage

This paper is based on the analysis and implementation of a new drive system applied to refrigeration systems, complying with the restrictions imposed by the IEC standards (Harmonic/Flicker/EMI-Electromagnetic Interference restrictions), in order to obtain high efficiency, high power factor, reduced harmonic distortion in the input current and reduced electromagnetic interference, with excellent performance in temperature control of a refrigeration prototype system (automatic control, precision and high dynamic response). The proposal is replace the single-phase motor by a three-phase motor, in the conventional refrigeration system. In this way, a proper control technique can be applied, using a closed-loop (feedback control), that will allow an accurate adjustment of the desirable temperature. The proposed refrigeration prototype uses a 0.5Hp three-phase motor and an open (Belt-Drive) Bitzer IY type compressor. The input rectifier stage's features include the reduction in the input current ripple, the reduction in the output voltage ripple, the use of low stress devices, low volume for the EMI input filter, high input power factor (PF), and low total harmonic distortion (THD) in the input current, in compliance with the IEC61000-3-2 standards. The digital controller for the output three-phase inverter stage has been developed using a conventional voltage-frequency control (scalar V/f control), and a simplified stator oriented Vector control, in order to verify the feasibility and performance of the proposed digital controls for continuous temperature control applied at the refrigerator prototype. ©2008 IEEE.