Impact of the Sampling Period on the Design of Digital PID Controllers

The impact of the sampling period on the parameterization of a digital PID controller in the frequency domain is attempted using three different digital approximations of the integral action. The controller is implemented in the industrial process of regulation of the cement sulphates in the cement mill outlet. The maximum sensitivity, Ms, has been utilized as a main robustness criterion. For the same Ms, proportional and differential gain, a rise of the sampling period leads to a decrease of the integral gain ki for all the three approximations. For the same sampling period, the function between proportional and integral gain differs for the three approximations studied. If the design satisfies two criteria simultaneously, maximum sensitivity and phase margin in the current study, then the permissible PID gains zone becomes narrower.

Design of Composite Feedback and Feedforward Control Law for Aircraft Inertially Stabilized Platforms

The design of the control systems of the inertially stabilized platforms (ISPs) as part of airborne equipment for the majority of aircraft has its peculiarity. The presence of rate gyros in the inertial measurement unit gives the possibility to measure the rotation rate of the ISP base, which is the main disturbance interfering with the ISP accuracy. Inclusion of the feedforward disturbance gain in the control law with the simplest PI feedback significantly improves the accuracy of stabilization by the invariance theory. A combination of feedback and feedforward controllers produces a synergetic effect, thus, improving ISP accuracy. This article deals with the design of the airborne ISP control systems consisting of two stages: the parametric optimization of the PI feedback control based on composite “performance-robustness” criterion and the augmentation of the obtained system with feedforward gain. To prove the efficiency of the proposed control laws, the simulation of the ISP was undertaken. We have used a simulation of the heading-hold system of the commuter aircraft Beaver and the yaw rate output of this closed-loop system we have used as a source of the disturbance. The results of modeling proved the efficiency of the proposed design method.

A Construction Schedule Robustness Measure Based on Improved Prospect Theory and the Copula-CRITIC Method

A robustness measure is an effective tool to evaluate the anti-interference capacity of the construction schedule. However, most research focuses on solution robustness or quality robustness, and few consider a composite robustness criterion, neglecting the bounded rationality of subjective weights and inherent importance and nonlinear intercriteria correlations of objective weights. Therefore, a construction schedule robustness measure based on improved prospect theory and the Copula-criteria importance through intercriteria correlation (CRITIC) method is proposed. Firstly, a composite robustness criterion is established, including start time deviation rs and structural deviation rp for measuring solution robustness from project execution and completion probability rc for measuring quality robustness from the project result. Secondly, bounded rationality is considered, using prospect theory to calculate subjective weights, which is improved by the interval distance formula. Thirdly, the Copula-CRITIC method is proposed to determine objective weights incorporating both inherent importance and nonlinear intercriteria correlations. Finally, an information-entropy-based evidence reasoning method is applied to combine subjective and objective weights together while identifying their validity. An underground power station in China is used for a case study, whose robustness is measured using the proposed methods, single robustness criterion, and composite robustness criterion using traditional weighting methods. The comparison results verify the consistency, representativeness, and advantage of the proposed criterion and methods.

A Novel Design of Fractional PI/PID Controllers for Two-Input-Two-Output Processes

In this paper, a new formulation of fractional order proportional integral (PI)/ proportional integral derivative (PID) controller is proposed. The proposed controller will be justified for some well-known two-input-two-output (TITO) processes. In order to deal with interactions between process variables in a multivariable system, as well as multiple delay times in process transfer functions, the simplified decoupling Smith predictor (SDSP) structure is also used. The issue of decoupling realizability is solved by the PSO algorithm and fractional order processes are also suggested for model reduction. The tuning rules of the controller are derived in analytical terms based on the internal model control (IMC) structure. The effectiveness and robust stability of the proposed approach are illustrated by comparing it with other methods. To have a fair comparison, the robustness criterion using the M-Δ structure with μ-synthesis is adopted and the μ value of the proposed method is always kept smaller than the value of the others.

A Chaos Robustness Criterion for 2D Piecewise Smooth Map with Applications in Pseudorandom Number Generator and Image Encryption with Avalanche Effect

This study proposes a chaos robustness criterion for a kind of 2D piecewise smooth maps (2DPSMs). Using the chaos robustness criterion, one can easily determine the robust chaos parameter regions for some 2DPSMs. Combining 2DPSM with a generalized synchronization (GS) theorem, this study introduces a novel 6-dimensional discrete GS chaotic system. Based on the system, a 216-word chaotic pseudorandom number generator (CPRNG) is designed. The key space of the CPRNG is larger than 2996. Using the FIPS 140-2 test suit/generalized FIPS 140-2 test suit tests the randomness of the 1000 key streams consists of 20,000 bits generated by the CPRNG, the RC4 algorithm, and the ZUC algorithm, respectively. The numerical results show that the three algorithms do not have significant differences. The CPRNG and a stream encryption scheme with avalanche effect (SESAE) are used to encrypt an image. The results demonstrate that the CPRNG is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs. The SESAE with one-time-pad scheme makes any attackers have to use brute attacks to break our cryptographic system.

Sensitivity Analysis of Predictive Scheduling Algorithms

In the paper a survey of predictive and reactive scheduling methods is done in order to evaluate how ability of prediction of reliability characteristics influence over robustness criteria. Survey analysis is done for two job shop scheduling problems: 5x8 and 5x10. The paper answers the question: what method generates robust schedules in case of a failure of a bottleneck occurrence before or after maintenance actions? The Hybrid - Multi Objective Immune Algorithm (H-MOIA) is aided with heuristics: Minimal Impact of Disturbed Operation on the Schedule (MIDOS) for predictive scheduling and Minimal Impact of Rescheduled Operation on the Schedule (MIROS) for reactive scheduling. Sensitivity analysis is done for predictive scheduling methods 1) H-MOIA +MIDOS, 2) algorithm based on priority rules: the Least Flexible Job First (LFJ) and the Longest Processing Time (LPT) and 3) the Average Slack Method. Reactive schedules are generated for various scenarios of the bottleneck occurrence in order to evaluate the efficiency of predictive scheduling methods. Reactive schedules are generated using 1) H-MOIA+MIROS, 2) Right Shifting, 3) rescheduling disturbed operations to parallel machines first available. Efficiency of predictive schedules is evaluated using criteria: makespan, total tardiness, flow time, idle time. Efficiency of reactive schedules is evaluated using: solution robustness criterion and quality robustness criterion.

Robust PID Controller Tuning for 2D Gantry Crane Using Kharitonov's Theorem and Differential Evolution Optimizer

PID (proportional+integral+derivative) controller is well known as a simple and easy-to-implement controller. However, the design procedure is not straightforward for multi-input multi-output (MIMO) systems. It is even more complicated when robustness criterion must be handled. In this paper, a stable robust PID controller for anti-swing control of automatic gantry crane is proposed. The proposed method employs an automatic tuning using DE (differential evolution) to search for a set of PID controller gains that satisfy Kharitonovs polynomials robust stability criterion. This robust stability criterion is used to deal with parametric uncertainty occurs in gantry crane model. The simulation results show that a satisfactory robust PID control performance can be achieved. The PID controller is able to quickly move the cart of the crane while suppressing the swing of the payload for various conditions, i.e. payload mass and cable length variations.