Problemas resueltos de Teoría de Sistemas

L'obra conté una col·lecció de problemes resolts de Teoria de Sistemes, que és una assignatura troncal del segon curs d'Enginyeria Industrial, el contingut de la qual abraça els conceptes bàsics com ara sistemes dinàmics continus i discrets, modelització de sistemes físics, transformada de Laplace, transformada en Z, representació interna, resposta en freqüència, etc. Els problemes estan classificats en diverses categories i estan resolts amb explicacions detallades per a ajudar l'estudiant a comprendre millor els conceptes teòrics

A new method for experimental tuning of PI controllers based on the step response

In this paper we present a new method for tuning Proportional Integral (PI) controllers from experimental data obtained through an open loop step test over the process to be controlled. The tuning procedure requires first the measurement of the process gain, and the times taken to reach the 5%, 35.3% and 85.3% of the final output and then applying a set of tuning equations. The tuning equations approximate the controller that minimizes the Integral of Absolute Error (IAE) of the disturbance response for a model with three real poles and time delay and are very accurate for a wide range of non oscillatory stable systems. The user can select the desired robustness (through the required maximum of the Sensitivity function ()), as a difference with usual methods that allow only to choose among two or three predefined robustness. The PI controller that minimizes the disturbance IAE is defined by default, but the user can also select a detuning factor to define slower controllers with the same robustness, allowing to find the desired compromise between performance and actuator activity due to sensor measurement noise. An application for Android, that can be downloaded for free, and a web based application, have been developed to implement the tuning procedure.Funding for open access charge: CRUE-Universitat Jaume

Tuning and robustness analysis of event-based PID controllers under different event generation strategies

In this article, we propose practical rules for tuning event-based PID controllers with two sampling strategies: symmetric send-on-delta (SSOD) and regular quantification (RQ). We present a detailed analysis about the effect of the derivative term of the controller when using SSOD or RQ and some guide lines are given to select the derivative filter coefficient. The two sampling strategies are compared, showing that, even when both of them lead to similar controlled output response, systems with RQ have better robustness properties than those with SSOD. The study is based on the describing function and the results are applicable to process with dynamic responses of different types: with time delays, non-minimum phase, under-damped response, etc. The rules presented here are given in terms of phase and gain margins that are measures of robustness used in the design of continuous PID controllers. This allows the application of conventional PID tuning methods to the case of event-based PID. The tuning rules are very simple and can be used for tuning PID, PI, PD and other controller structures.This work has been supported by MICINN project number TEC2015-69155-R from the Spanish government, project number P1-1B2015-42 and grant PI15734 from Universitat Jaume I

A new method for tuning PI controllers with symmetric send-on-delta sampling strategy

In this paper we present a new method for tuning PI controllers with symmetric send-on-delta (SSOD) sampling strategy. First we analyze the conditions that produce oscillations in event based systems considering SSOD sampling strategy. The Describing Function is the tool used to address the problem. Once the conditions for oscillations are established, a new robustness to oscillation performance measure is introduced which entails with the concept of phase margin, one of the most traditional measures of relative stability in closed-loop control systems. Therefore, the application of the proposed robustness measure is easy and intuitive. The method is tested by both simulations and experiments. Additionally, a Java application has been developed to aid in the design according to the results presented in the paper.This work has been supported by the MICINN under grant DPI2011-27845-C02–02

Networked gain-scheduled fault diagnosis under control input dropouts without data delivery acknowledgement

This paper investigates the fault diagnosis problem for discrete‐time networked control systems under dropouts in both control and measurement channel with no delivery acknowledgment. We propose to use a proportional integral observer‐based fault diagnoser collocated with the controller. The observer estimates the faults and computes a residual signal whose comparison with a threshold alarms the fault appearance. We employ the expected value of the arriving control input for the open‐loop estimation and the measurement reception scenario for the correction with a jump observer. The jumping gains are scheduled in real time with rational functions depending on a statistic of the difference between the control command being applied in the plant and the one being used in the observer. We design the observer, the residual, and the threshold to maximize the sensitivity under faults while guaranteeing some minimum detectable faults under a predefined false alarm rate. Exploiting sum‐of‐squares decomposition techniques, the design procedure becomes an optimization problem over polynomials

Testing minimum cost strategies of pumping systems with scheduled electric tariffs in a lab scale plant

Ponencia presentada en IFAC Papers Online : Conference Paper ArchiveThis paper describes the development and testing of a lab plant that emulates a water supply pumping system with the objective of testing optimal pumping strategies based on standard solvers. The emulated system consists of two tanks that supply the water to two districts in a town. There are two pumps, that can fill the tanks through a reconfigurable hydraulic system with several valves. The automatic controller determines the valves and pumps that are active at each instant of time in order to minimize the operation cost, taking into account the electric tariff periods. Some aspects on the development of the lab plant are first discussed, including hydraulic aspects and real time control implementation issues. Then, a mathematical model is proposed to be able to formulate, in matrix form, the cost index and the constraints, such that, standard solvers as Mosek or CBC can be used. The full optimization proposal is tested on several experiments, and compare to some simulations, to demostrate the validity of the plant and the optimization approac

Inferential networked control with accessibility constraints in both the sensor and actuator channels

The predictor and controller design for an inferential control scheme over a network is addressed. A linear plant with disturbances and measurement noise is assumed to be controlled by a controller that communicates with the sensors and the actuators through a constrained network. An algorithm is proposed such that the scarce available outputs are used to make a prediction of the system evolution with an observer that takes into account the amount of lost data between successful measurements transmissions. The state prediction is then used to calculate the control actions sent to the actuator. The possibility of control action drop due to network constraints is taken into account. This networked control scheme is analyzed and both the predictor and controller designs are addressed taking into account the disturbances, the measurement noise, the scarce availability of output samples and the scarce capability of control actions update. The time-varying sampling periods that result for the process inputs and outputs due to network constraints have been determined as a function of the probability of successful transmission on a specified time with a Bernoulli distribution. For both designs H∞ performance has been established and LMI design techniques have been used to achieve a numerical solution

Jump state estimation with multiple sensors with packet dropping and delaying channels

This work addresses the design of a state observer for systems whose outputs are measured through a communication network. The measurements from each sensor node are assumed to arrive randomly, scarcely and with a time-varying delay. The proposed model of the plant and the network measurement scenarios cover the cases of multiple sensors, out-of-sequence measurements, buffered measurements on a single packet and multirate sensor measurements. A jump observer is proposed that selects a different gain depending on the number of periods elapsed between successfully received measurements and on the available data. A finite set of gains is pre-calculated offline with a tractable optimisation problem, where the complexity of the observer implementation is a design parameter. The computational cost of the observer implementation is much lower than in the Kalman filter, whilst the performance is similar. Several examples illustrate the observer design for different measurement scenarios and observer complexity and show the achievable performance

H∞ observer design for a class of nonlinear discrete systems

Necessary and sufficient conditions are presented under which a discrete-time autonomous system with outputs is locally diffeomorphic to an output-scaled linear observable system or an output-scaled nonlinear system in the observer form. As a consequence of such characterizations, the nonlinear observer design problem is studied for a broader class of discrete-time nonlinear systems by using the exact linearization technique that is based on the differential geometric approac

Performance Tradeoffs for Networked Jump Observer-Based Fault Diagnosis

Print Request Permissions In this paper, we address the fault diagnosis problem for discrete-time multi-sensor systems over communication networks with measurement dropouts. We use the measurement outcomes to model the measurement reception scenarios. Based on this, we propose the use of a jump observer to diagnose multiple faults. We model the faults as slow time-varying signals and introduce this dynamic in the observer to estimate the faults and to generate a residual. The fault detection is assured by comparing the residual signal with a prescribed threshold. We design the jump observer, the residual and the threshold to attain disturbance attenuation, fault tracking and detection conditions and a given false alarm rate. The false alarm rate is upper bounded by means of Markov's inequality. We explore the tradeoffs between the minimum detectable faults, the false alarm rate and the response time to faults of the fault diagnoser. By imposing the disturbances and measurement noises to be Gaussian, we tighten the false alarm rate bound which improves the time needed to detect a fault. A numerical example is provided to illustrate the effectiveness of the theory developed in the paper