Comparison of Steady State and Dynamic Interaction Measurements in Multiloop Control Systems

Sensitivity of Relative Gain Array for Processes with Uncertain Gains and Residence Times

Process control structures are still mainly based on multiple interacting single-input single-output loops. The well-known relative gain array (RGA) is often used as an indication of the amount of interaction in the system. The RGA is limited in the sense that it is based only on static responses. We extend the RGA to compare the entire time domain open- and closed-loop step responses as interaction measurements. The closed-loop response is based on the best achievable control performance using internal model control. The results are shown graphically by regarding the open- and closed-loop responses of each pairing as a parametric representation. For each possible pairing, a graph is produced and placed in an array. This dynamic array is completely consistent with the static RGA and a useful extension in the case that the static RGA might prefer the wrong pairing (because the dynamics have been excluded) or does not prefer any pairing (when all RGA elements have more or less the same value).

Control strategy for a column flotation process

Designing controllers for multi-input multi-output (MIMO) integrated Dc-Dc converter is complicated due to shared elements, integrated structure, and relation between the input and output variables of the converter. In this work, a robust PID controller based on a Contoured Robust Controller Bode Plot (CRCBP) is designed for control of the three-input integrated Dc-Dc (TIID) converter. This method combines robust control with classical loop-shaping. In this procedure, the outlines of the robust metric are drawn on the Bode charts of the controller, and the controller is adjusted till its frequency response does not cross the contours of the robust metric to meet the stability and performance goals. The TIID converter is modeled using state-space analysis and a Transfer Function Matrix (TFM) is acquired from the small signal continuous time model. The interactions between the inputs and outputs of the converter are quantified and input-output pairing is identified by Relative Gain Array (RGA). The input-output pairing suggested by RGA decides the controller structure. Further, the weight functions (loop-shaping filters) are designed based on the TFM which represents the desired robustness and performance of the controller. These weight functions are used to define the robust metric for the controller design. Based on this, the CRCBP controller is designed iteratively. A standard TIID converter of power rating 288 W with input voltage levels of 24V, 30V, and 36V is considered to show the effectiveness of the proposed controller under varying operating conditions. The real-time simulation results disclose the proposed controller's superiority over the existing approaches in the literature.

Model predictive control (MPC) is an advanced control that has found widespread use in industries, particularly in process industries like oil refining and petrochemicals. Although the basic premise behind MPC is easy to comprehend, its inner workings are still generally viewed or regarded as too advanced for actual plant operator understanding. This lack of understanding is exposed when MPC performance deteriorates sometime after commissioning, as is often the case in some commercially operated process plants. Currently operators might have difficulty over reasoning about MPC performance degradation and formulating steps to investigate the cause. A tool is described that aims to make MPC more transparent to the operators. Commonly reported causes of MPC performance degradation are discussed and ways in which the operator can recognise them when they occur are outlined. Issues that are addressed include: making the set of controlled variables to be used for a given set of manipulated variables simpler and clearer; ways to recognise when a MPC controller is performing poorly and to identify the source of performance deterioration. An aim is to determine under what instances the operator can return the MPC performance to previous levels or request for specialist support or simply switch the MPC off. A goal is to avoid the kind of often reported situation where the operator gets worried that the controller is deteriorating and ends up taking knee jerk actions that cause further problems in MPC. At the top of the maintenance tool hierarchy is the trends comparison group, where MPC reference graphical performance trends are compared with actual graphical performance trends counterpart. If any abnormality is observed in these trends, the operator is encouraged to choose an option from a list of preliminary diagnostic questions contained in a group below trends comparison group, which best describes the observed abnormality. Each abnormality is associated with a list of suspected causes. When a suspected cause is chosen from the associated list, the operator is led to the symptoms investigation window, which contains scripts detailing steps for systematic examination of each symptom, with a view to either rejecting or confirming the suspicion. Assisted in the investigation are four background information windows: the virtual plant without MPC window, the virtual plant with MPC window, the transfer function matrix window and steady state gain, relative gain array (RGA) and relative weight array (RWA) window. The windows contain information and guidance that the operator might refer to from time to time during symptom investigation. Development of the maintenance tool is still at the design stage. The key components described have been research implementing MPC on three nonlinear process models, a continuous stirred tank reactor (CSTR), an evaporator process and a fluid catalytic cracking unit (FCCU). Case studies representing different MPC degradation scenarios are simulated, followed by a systematic procedure for diagnosing, isolating and recovering from such degradation, based on assumed operator’s perspective and expert’s technical reasoning. The knowledge gained from the case studies is used to develop an outline of a vision for a data-driven model predictive maintenance tool to help the operator make sensible judgements about performance degradation, the form and direction of diagnosis and fault isolation, and possibly, the recovery procedure.

Heating, Ventilating and Air Conditioning (HVAC) systems have nonlinear character and nature. Current models for control components and the optimization of HVAC system parameters can be linear approximations based on an operating or activation point, or alternatively, highly complex nonlinear estimations. This duality creates problems when the systems are used with real time applications. The two parameters temperature and relative humidity (RH) have a more direct effect in most applications of HVAC systems than the execution. This study’s objective is to implement and simulate an adaptive controller for decoupled bi-linear HVAC systems for the purpose of controlling the temperature and RH in a thermal zone. The contribution of this study is to apply the adaptive controller for the decoupled bi linear HVAC system via relative gain array (RGA). To achieve this objective, we used a system identification toolbox to increase the speed and accuracy of the identification of system dynamics, as was required for simplification and decoupled HVAC systems. The method of decoupling is relative gain array. The results of the simulation show that when compared with a classical PID controller, the adaptive controller performance is superior, owing to the high efficiency with which the steady state set points for temperature and RH are reached.

Control System Design in Distillation Processes and its Dependence of the Original Process Design

This research presents the application of model predictive control (MPC) to control a proton exchange membrane fuel cell (PEMFC). Firstly, the steady state analysis of PEMFC is considered to select its suitable operating conditions based on cell electrical characteristics. Then, the effect of input parameters on cell voltage and temperature is analyzed to investigate the dynamic behavior of PEMFC that is important for control design. It is found that the cell voltage and cell temperature depend on the inlet molar flow rates and temperature of hydrogen and air, and operating current density. To obtain an efficient control system, the control structure design of the PEMFC is considered to specify a good choice of the controlled and manipulated variables. An analysis of the steady-state relative gain array (RGA) is used for pairing of the controlled and manipulated variables. The result shows that the inlet molar flow rates of hydrogen and air are manipulated variables to regulate the cell temperature and partial pressure of hydrogen, respectively. Finally, a model predictive control (MPC) is developed and designed for controlling the cell temperature and partial pressure of hydrogen. Basically, MPC requires the process model used in its control algorithm. The PEMFC model is known to be complicated and involves uncertain parameters. Thus, an offline robust model predictive control (robust MPC) based on a linear time-varying (LTV) model is proposed for PEMFC control. The simulation results show that the robust MPC shows better control performance than conventional MPC because the robust MPC can guarantee robust stability.

Dynamic analysis and linear control strategies for proton exchange membrane fuel cell using a distributed parameter model

This research focuses on the performance analysis and control of a solid oxide fuel cell (SOFC) with direct internal reforming using methane as fuel. Firstly, the steady state analysis is performed to design the optimal operational condition for this system. The direct internal reforming of methane in SOFC can utilize the heat from the exothermic electrochemical reaction to produce hydrogen-rich gas, leading to an increasing system efficiency. However, the coupling of the endothermic reforming and electrochemical reactions results in a complicated dynamic response. Therefore, the effect of input variables on the cell temperature and cell voltage is analyzed to investigate the dynamic behavior that is important for design a controller. It is found that the cell operating temperature and cell voltage are dependent on the fuel and air inlet temperature as well as the current density. Next, to achieve the efficient control system, the control structure design of the SOFC is considered to identify good controlled variables and manipulated variables. The concept of a controllability analysis is applied to the control system design of the SOFC for the selection of input-output pairings by considering the relative gain array (RGA). The result shows that the inlet molar flow rates of air and fuel are manipulated variables to control the cell temperature and the content of fuel, respectively. Finally, the conventional and advanced control techniques are designed and implemented to control the cell temperature, the content of methane and the cell voltage. In this research, the model predictive control (MPC) that is a model-based control strategy is proposed for SOFC control. In general, MPC requires the accurate and reliable model of the process to be controlled. However, the SOFC model is complicated and involves uncertain parameters. Therefore, an off-line robust MPC algorithm is developed and employed for controlling the SOFC. The robust MPC algorithm based on linear time-varying (LTV) and linear parameter varying (LPV) systems is also studied. The simulation results show that under the model uncertainty, the proposed robust MPC can control the SOFC and guarantee the stability of the SOFC. The robust MPC algorithm using the LPV model of the SOFC can achieve a better control performance because the model parameters are on-line updated and used in the control calculation.

We consider resonance absorption of magnetohydrodynamic waves, and the Alfvén resonance layer in particular. We show that the dissipative layer can be modeled as a simple mechanical system consisting of a few harmonic oscillators which are coupled by friction. The mechanical model reproduces known results for the externally driven system in steady state, such as the structure of the dissipative layer, the “waves” of heating which propagate across the layer, and the fact that the total heating is independent of time. The total work done on the oscillators by the driver is always positive; the external driver sees the total system as a single damped oscillator driven exactly at resonance. Nonetheless, some of the oscillators return energy back to the driver. The total kinetic energy of all the oscillators and the total potential energy are nearly independent of time, because the integrals, across the dissipative layer, of the square of the velocity and the square of the displacement, are truly constants in time. Waves of kinetic and potential energy propagate across the system in the same sense as the waves of heating. We also investigate an initial value problem in which the driver is turned on at t = 0. There is no single number representing the time required for the dissipative layer to reach a steady state. The waves of heating which are found in the steady state are also present in the buildup phase. However, if the driver is turned off after the system has reached a steady state, then the waves of heating are less obvious. We consider the effects of a nonlinear frictional coupling between the oscillators, designed to mimic the effects of Kelvin‐Helmholtz instabilities. The nonlinear coupling has surprisingly little effect on the system. The total steady state heating rate is the same as in the linear system; even with nonlinear dissipation, the dissipative layer adjusts itself to absorb a predetermined amount of energy being pumped in by the external driver. The waves of heating which are found in the linear system are still present. We find no evidence of chaotic behavior.

The basic principles of an efficient new methodology for the calculation of the nonsinusoidal periodic steady state in power systems with nonlinear and time-varying components are described. All linear parts, including the network and part of the loads, are represented in the frequency domain, while nonlinear and time-varying components, mainly loads, are represented in the time domain. This hybrid process is iterative, with periodic, nonsinusoidal, bus voltages as inputs for both frequency domain solutions and time domain simulations: a current mismatch is calculated at each bus and used to update the voltages until convergence is reached. Thus the process, but not the solution, is decoupled for the individual harmonics. Its efficiency is enhanced by the use of Newton type algorithms for fast convergence to the periodic steady state in the time domain simulations. Potential applications of this methodology are in the computation of harmonic power flow and in the steady state initialization needed in the calculation of electromagnetic transients.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper describes an improved measurement method for fast evaluation of thermophysical properties of an insulation sheet. The sheet is used to insulate inverter and water cooling jacket in an electric or hybrid electric vehicles. A large number of iterations of steady state measurement is required to perform parameter study for various composition of the sheet. However, steady state measurement generally needs very long time even only once. From the above reasons, it is necessary to reduce measurement time while keeping accuracy. Here, quasisteady state method is one of the methods of reducing measurement time by performing a prediction while keeping accuracy. Transient temperature response and steady temperature can be obtained by prediction faster than steady state method. Accuracy of prediction and measurement time will be changed by controlling application range. In this report, the availability of quasi-steady state method was investigated by comparing prediction results with steady state results of 3D thermal analysis and experiment. Especially, thermal conductivity was evaluated as a criterion. Then, the predicted thermal conductivity was derived from the predicted steady temperature. Through the investigation, in terms of accuracy, the quasi-steady state method was available when surrounding condition was perfectly insulated. On the other hand, in terms of the reduction of measurement time, a thinner thickness of metal block required a shorter measurement time because of the decrease in the heat capacity.

Computation of parameter bounds of a linear dynamical system, given input–output observations and bounds on model‐output error, has been developed as an alternative to classical parameter estimation using least squares, maximum likelihood or the prediction error method. When bounds on time‐domain plant behaviour are known in advance, they can be used to develop prior parameter bounds for discrete‐time rational transfer‐function parameters. These bounds can be used to initialize standard parameter‐bounding algorithms which process input–output observations to update the exact polytope feasible set or one of its outer bounding approximations such as an ellipsoid, orthotope or parallelotope. This paper presents a method to compute such prior bounds from bounds on time constants and steady‐state (dc) gain, often available from the physics of the system or from previous experience. The method finds subsets making up the prior feasible parameter set, recursively in model order, for any configuration of the pole ranges. An analysis leading to measures of the value of prior bounds, in terms of their chances of remaining active when new bounds derived from observations are imposed, is presented. A simulation study compares polytope updating with and without such initial bounds. The simulations investigate the influence of the tightness of time‐constant and steady‐state‐gain bounds in reducing the volume of the feasible sets obtained as observations are processed. The effects of initial bound tightness and signal‐to‐noise ratio on survival time of the prior bounds are also examined. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Stability and Pattern of Bifurcating Steady States in Systems with Double Involution