Control Engineering Problems Research Articles

Review of Five Sets of Piecewise Constant Orthogonal Functions for Function Approximation, Integration and Solution of First Order Differential Equation Using These Function Sets

This paper reviews five types of piecewise constant orthogonal functions namely Walsh, block-pulse, sample-and-hold, triangular and hybrid functions. Approximation, integration of the functions are performed and compared with the actual result. By performing integration we get the operational matrix for each individual function set. With the help of integration operational matrices we can solve an nth order differential equation which is of importance for solving control engineering problems although a first order ordinary differential equation has been dealt with in this paper.

Minimizing control variation in nonlinear optimal control

In any real system, changing the control signal from one value to another will usually cause wear and tear on the system’s actuators. Thus, when designing a control law, it is important to consider not just predicted system performance, but also the cost associated with changing the control action. This latter cost is almost always ignored in the optimal control literature. In this paper, we consider a class of optimal control problems in which the variation of the control signal is explicitly penalized in the cost function. We develop an effective computational method, based on the control parameterization approach and a novel transformation procedure, for solving this class of optimal control problems. We then apply our method to three example problems in fisheries, train control, and chemical engineering.

Research on Constant Velocity Extruding Process Control for 36,000-Ton Vertical Extrusion Press

Metal extrusion is one of the most significant methods in the field of plastic deformation. The 36,000-ton vertical extrusion press uses one-piece hot extrusion molding method to produce high-pressure, large-diameter, thick-walled, seamless, alloy-steel pipe, which is required by ultrasupercritical power generator units and the third generation of nuclear power plants. The main table (extruding platform) is driven by 36,000-ton thrust. The extrusion process is a typical nonlinear multivariable strong-coupling finite-time system. In this paper, we analyze and solve the large-scaled engineering control problems, including (1) discussion of the mechanical structure of the controlled object and the feature of multivariable strongly coupling for large-scaled parallel-driving hydraulic system, (2) research on the engineering practical simplified control algorithm for multivariable system and propose a way to solve the coupling problem of the hydraulic system, and (3) design of double closed-loop control of velocity and pressure for the new technology of constant velocity extrusion. In our paper, we have proven through practice that the traditional proportional intergral (PI) controlling method, with proper controlling strategy, is still the most efficient and practicable way for a large-dimension complex object in industry.

Calibration and validation of a model describing complete autotrophic nitrogen removal in a granular SBR system

AbstractBACKGROUNDA validated model describing the nitritation‐anammox process in a granular sequencing batch reactor (SBR) system is an important tool for: (a) design of future experiments; and (b) prediction of process performance during optimization, while applying process control, or during system scale‐up.RESULTSA model was calibrated using a step‐wise procedure customized for the specific needs of the system. The important steps in the procedure were initialization, steady‐state and dynamic calibration, and validation. A fast and effective initialization approach was developed to approximate pseudo steady‐state in the biofilm system. For oxygen mass transfer coefficient (kLa) estimation, long‐term data, removal efficiencies, and the stoichiometry of the reactions were used. For the dynamic calibration a pragmatic model fitting approach was used – in this case an iterative Monte Carlo based screening of the parameter space – to find the best fit of the model to dynamic data. Finally, the calibrated model was validated with an independent data set.CONCLUSIONThe calibration procedure presented is the first customized procedure for this type of system and is expected to contribute to achieving a fast and effective model calibration, an important enabling tool for various biochemical engineering design, control and operation problems. © 2013 Society of Chemical Industry

Nonlinear system identification using heterogeneous multiple models

Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, with the heterogeneous multiple model being of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to that of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with off-line identification of nonlinear systems based on heterogeneous multiple models. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called the no output tracking effect. The origin of this difficulty is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of the model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.

Exponential-weighted input-to-state stability of hybrid impulsive switched systems

Stability of the non-linear systems with external inputs is an important problem in control theory and engineering. Input-to-state stability (ISS) is one of the stability concepts that have been introduced to non-linear systems. This study extends the ISS to a more general case, namely, exponential-weighted input-to-state stability (eλt-weighted ISS). By employing the Lyapunov function and Lyapunov–Razumikhin techniques, eλt-weighted ISS is proposed and studied for the impulsive switched hybrid systems with and without time delay. An example and simulation results are given to illustrate the effectiveness of the obtained theoretical results.

Optimal Design of Concrete Pumping Displacement Control

To solve the problems of concrete piston striking cylinder and pumping insufficiency caused by the mismatch between varying loads and system’s open-loop control property, the optimal model of concrete pumping displacement control was built.To be precise, the displacement control signal parameters were taken as control variables, and the location parameter of the main cylinder’s displacement sensor was taken as structure variable. under the physical constraint condition of non-collision between piston and cylinder, the piston stroke maximizing was taken as objective function and the optimal model of concrete pumping displacement control was built.Optimization result shows that piston of concrete pumping system don’t strike cylinder and pump sufficiently under varying loads.This optimal model, which is built in the integration design space of structure variable and control variables, is of guiding significance for solving open-loop system’s engineering control problems.

Tuning of a Proportional-Integral-Derivative Controller using Multi-Objective Non Dominated Sorting Particle Swarm Optimization Applied to pH Control in Continuous Stirred Tank Reactor

Problem statement: Most of the control engineering problems are characterized by several, contradicting, conflicting objectives, which have to be satisfied simultaneously. Two widely used methods for finding the optimal solution to such problems are aggregating to a single criterion and using Pareto-optimal solutions. Approach: Non-Dominated Sorting Particle Swarm Optimization algorithm (NSPSO) based approach is used in the design of multiobjective PID controller to find the constant proportional-integral-derivative gains for a chemical neutralization plant. The plant considered in this study is highly non-linear and with varying time delay, provides a challenging test bed for nonlinear control problems. Results: Experimental results confirm that a multi-objective, Paretobased GA search gives a better performance than a single objective GA. Conclusion: Finally, the results for single objective and multiobjective optimization using NSPSO for the neutralization plant are compared. Gain scheduled PID controllers are designed from Pareto front obtained with NSPSO which exhibit good disturbance rejection capability.

ROBUST STATE FEEDBACK CONTROL DESIGN VIA PSO-BASED CONSTRAINED OPTIMIZATION

Computational intelligence has been successfully applied to many engineering applications including control engineering problems. In this paper, a robust state feedback control design using particle swarm optimizer based constrained optimization is proposed. The feedback controller is optimized based on state space model of the plant with structured uncertainty such that the closed-loop system would have maximum stability radius. A wedge region is assigned as a constraint to locate the desired closed-loop poles, which correspond to time-domain control system performance. The proposed controller design is applied to anti-swing control for a gantry crane system. The experimental result is shown, and comparison with that of conventional linear quadratic regulator based controller and H ∞ loop shaping controller are made. The proposed method achieves a satisfactory robust performance based on the structured singular value analysis and the experimental results.

A new general glucose homeostatic model using a proportional-integral-derivative controller

Abstract The glucose–insulin system is a challenging process to model due to the feedback mechanisms present, hence the implementation of a model-based approach to the system is an on-going and challenging research area. A new approach is proposed here which provides an effective way of characterising glycaemic regulation. The resulting model is built on the premise that there are three phases of insulin secretion, similar to those seen in a proportional-integral-derivative (PID) type controller used in engineering control problems. The model relates these three phases to a biological understanding of the system, as well as the logical premise that the homeostatic mechanisms will maintain very tight control of the system. It includes states for insulin, glucose, insulin action and a state to simulate an integral function of glucose. Structural identifiability analysis was performed on the model to determine whether a unique set of parameter values could be identified from the available observations, which should permit meaningful conclusions to be drawn from parameter estimation. Although two parameters – glucose production rate and the proportional control coefficient – were found to be unidentifiable, the former is not a concern as this is known to be impossible to measure without a tracer experiment, and the latter can be easily estimated from other means. Subsequent parameter estimation using Intravenous Glucose Tolerance Test (IVGTT) and hyperglycaemic clamp data was performed and subsequent model simulations have shown good agreement with respect to these real data.

Monte Carlo Simulation and Well Testing Applied in Evaluating Reservoir Properties in a Deforming Longwall Overburden

During longwall mining, the intact strata start to deform and fracture as the mining face progresses. Gob gas ventholes (GGVs) are drilled from the surface over a longwall panel before mining to capture methane from the fractured zone. Due to fracturing and bedding-plane separations, reservoir properties change extensively. This poses a major problem for venthole designers and methane control engineers and may become a safety and health concern for underground work force due to unexpected methane emissions: it is difficult to predict the location of major strata separations and their temporal magnitudes to best locate the ventholes. Measurements obtained at different times during longwall mining may not be helpful for this purpose as strata deformation is a dynamic process and the results from different tests may not be lumped together to analyze the data collectively. This article uses a combination of Monte Carlo (MC) simulation and well testing methods to analyze multiple data sets obtained from a GGV at different longwall face locations. The aim was to determine the magnitude of average strata separation before conducting well test analyses to determine the properties of a deformed reservoir. MC simulation was used to process cross-correlated and uncertain data distributions obtained from measurements to generate a set of normally distributed values for each data type. These values were further used to project the amount of strata separation to the timing of well test. Finally, well-test analyses were used to interpret test data and to evaluate reservoir properties.

TUNING OF A PROPORTIONAL–INTEGRAL–DERIVATIVE CONTROLLER USING A MULTIOBJECTIVE GENETIC ALGORITHM NONDOMINATED SORTING GENETIC ALGORITHM‐II APPLIED TO A pH PROCESS

ABSTRACT Most control engineering problems are characterized by several, often contradicting, objectives, which have to be satisfied simultaneously. Two widely used methods for finding the optimal solution to such problems are aggregating to a single criterion, and using Pareto‐optimal solutions. Here we propose the nondominated sorting genetic algorithm (NSGA‐II) to find the constant proportional–integral–derivative (PID) control gains for a chemical neutralization plant. Known to be highly nonlinear and with varying time delay, this plant provides a challenging test bed for nonlinear control strategies. The results confirm that a multiobjective, Pareto‐based GA search gives a better performance than a single objective GA. The former method was also used to design a gain‐scheduled PID controller. PRACTICAL APPLICATIONSThe control of the pH neutralization process plays a very important role in chemical industries, such as wastewater treatments, polymerization reactions, fatty acid production, biochemical processes, pharmaceuticals, biotechnology and so on. The pH neutralization process shows a strong nonlinear behavior and time‐varying nonlinear characteristics resulted from the variation of the feed components or total ion concentrations. In the case of fermentation by the microorganisms, the growth of microorganisms has a pH optimum similar to most biochemical processes. A pH value drifting away from this optimum often inhibits growth of the essential microorganisms, alters the bacterial population and inhibits the desirable enzymatic activities. The result is a delay in the fermentation process, which in turn results in financial loss.

A New General Glucose Homeostatic Model using a Proportional-Integral-Derivative Controller

The glucose-insulin system is a challenging process to model due to the feedback mechanisms present, hence the implementation of a model-based approach to the system is an on-going and challenging research area. A new approach is proposed here which provides an effective way of characterising glycaemic regulation. The resulting model is built on the premise that there are three phases of insulin secretion, similar to those seen in a proportional-integral-derivative (PID) type controller used in engineering control problems. The model relates these three phases to a biological understanding of the system, as well as the logical premise that the homeostatic mechanisms will maintain very tight control of the system. It includes compartments for insulin, glucose, insulin action and a compartment to simulate an integral function of glucose.Structural identifiability analysis was performed on the model to determine whether a unique set of parameter values could be obtained from the available observations, which would allow meaningful conclusions to be drawn from parameter estimation. Although two parameters - glucose production rate and the proportional control coefficient - were found to be unidentifiable, the former is not a concern as this is known to be impossible to measure without a tracer experiment, and the latter can be easily estimated from other means. Subsequent parameter estimation and the model simulations have shown good agreement with respect to real data.

Support Vector Machines for Identification and Classification Problems in Control Engineering

Support Vector Machines for Identification and Classification Problems in Control Engineering

Software and Mathematical Support of Automated High-precision Laser Calibration System with optically reverse channels

The problems of the high-precision and automated control are actual for all branches of modern mechanical engineering. The main control problems in mechanical engineering can be effectively solved only with the use of computer laser measuring systems with two optical the turned channels (LMS TOTC). The following issues are described in the article: the developed program-algorithmic solutions for multi channel precision measuring systems automation (which can be integrated into operating automated control systems of technological processes); software of supervision, gathering, record and storage of the measuring information, and also automated data processing and objects visualization means and controlling methods are considered.

Simulation of sediment-laden flow by depth-averaged model based on unstructured collocated grid

The 2-D depth-averaged mathematical model for sediment-laden flows has been widely used in river control and other related engineering problems, and now it is usually solved on structured grids. Since the natural river is usually very complicated in plane boundary, and unstructured grids are more attractive in solving the problems with complicated domains, the following questions about solving 2-D depth-averaged model were discussed in this article: (1) a modified Bowyer algorithm was suggested to generate unstructured grids for natural rivers, (2) the Finite Volume Method (FVM) is employed to discretize the governing equations of the 2-D depth-averaged model and an implicit scheme was suggested with unstructured collocated grids, (3) the observed hydrological data of the Chenglingji Reach in the Yangtze River are used for verification of the presented method. It seems that the suggested numerical scheme works very well, and the simulation results of both hydraulic characteristics and river bed deformation are in good agreement with the observed ones.

Stochastic MPC with inequality stability constraints

Stochastic uncertainty is a common feature of many control engineering problems, and is also present in a wider class of applications, e.g. finance and sustainable development. Recent work proposed a constrained MPC approach that took explicit account of the distributions of uncertain model parameters but used terminal equality constraints to ensure stability. The present paper reformulates the problem in order to relax the stability constraints by invoking appropriate terminal inequalities. The application of the proposed strategy and its advantages over earlier work are illustrated by means of a numerical example.

Robust Design of Fault Detection and Isolation Systems

AbstractInspired by the rationale of Robust Design, a novel methodology is presented for the design of diagnostic systems for fault detection and isolation (FDI). Detection/isolation capability and robustness, i.e. sensitivity to faults and insensitivity to noise, are addressed in an integrated way within a fully stochastic framework. Although FDI is a classical problem in control engineering, this new approach improves the current state of the art both in terms of general applicability and optimality of the design solution. It demonstrates the potential of robust design in fostering innovation in a variety of technical sectors. For illustrative purposes, the methodology is applied to the design of a FDI system for a fluid mixer. Copyright © 2006 John Wiley & Sons, Ltd.

C(sI-A)-1B가 최소위상이 될 LMI 조건을 이용한 해석과 설계

We derive a linear matrix inequality(LMI) condition guaranteeing that any invariant zeros of a triple (A, B, C) lie in the open left half plane of the complex plane, i.e. <TEX>$C(sI-A)^{-1}B$</TEX> is minimum phase. The LMI condition is equivalent to a certain constrained Lyapunov matrix equation which can be found in many results relating to stability analysis or control design. We show that the LMI condition can be used to simplify various control engineering problems such as a dynamic output feedback control problem, a variable structure static output feedback control problem, and a nonlinear system observer design problem. Finally, we give some numerical examples.

ROBUST PERFORMANCE IN BIOPHYSICAL NETWORKS

Robust performance, the attainment of a specified response under uncertainty, is a well studied problem in control engineering. In the field of systems biology, related problems are emerging from the quantitative analysis of complex biophysical networks. In this paper, connections are made between the robust performance questions in biology and engineering. Two examples are used to illustrate these ideas: (i) a signal transduction network, and (ii) the gene network responsible for circadian oscillations.