Order Process Model Research Articles

Model-based and PID controllers for disturbance rejection in processes with time delay: a comparison

Model-based control systems for processes with a time delay and slow disturbance dynamics are examined and compared. Two of them have a two-degrees-of-freedom Internal Model Control (IMC) structure: the first one (IMC-22) was presented by the authors earlier, and the second one (IMC-GAP) is derived from the Generalized Analytical Predictor (GAP). The nature of the difference between the two is illustrated in a control system with first order process and disturbance transfer function models. The performance of the two is compared for a first and a second order process, the process types for which the GAP was designed. The same type of performance comparison is done for a third controller type, the Model-Dependent Control (MDC), and for the IMC-PID controller derived from an IMC structure. Some modifications of the GAP and MDC controllers are proposed in order to improve the input characteristics as in the IMC-22 controller. The controllers are tuned for equal robust stability in several cases of process parameter uncertainty.

Method for on-line identification of a first orderplusdead-time process model

An improved method for on-line identification of a first order plus dead-time process model under proportional-integral control is proposed. The proposed method eliminates some of the disadvantages of the Yuwana and Seborg method while retaining the simplicity of the method. Simulation results show that the proposed method performs well on a range of processes.

A Novel Relay Auto-Tunin Technique for Process with Integration

In this paper a novel idea of inserting a diflerentiator in front of the relay is presented. This technique is applicable to a process with integration. The advantage is that the time taken for the relay experiment can be shortened by as much as 100%. A special case of an asymmetrical relay – relay with DC bias – is also analysed. This paper shows that a common process model used in the industry – the first order plus deadtime process model – can be obtained from the oscillation produced by the relay with DC bias. Once a process model is obtained, many controller design techniques are available. The techniques described in this paper were successfully implemented in a laboratory experiment on a tank level system.

Self‐tuning Smith predictors for processes with long dead time

AbstractA simple relay feedback auto‐tuning method is proposed for the Smith predictor, an advanced controller for processes with long dead time. the relay feedback control gives information on one point of the Nyquist curve in terms of ultimate gain and frequency. With an additional measurement of the static gain, a reduced order process model in terms of a first‐ or second‐order dynamics plus dead time could be computed and used to auto‐tune the Smith predictor. When the process dynamics changes more frequently, a self‐tuning controller is required. In this case the Fast Fourier Transform technique can be further employed to track the points on the Nyquist curve by estimating the process frequency response and then used to update the Smith predictor. Excellent performance of the auto‐tuned and self‐tuned Smith predictor has been substantiated by simulations.

A Self-Tuning Controller Based on PI Algorithm

A simple self-tuner algorithm based on the tuning of the proportional band of a conventional Proportional Integral mode action is proposed. The algorithm, based on intuitive reasoning as adopted by process experts is simpler than many of its type specially from the viewpoint of implementation on a 8 or 16-bit microprocessor. It has been tested in a stable second order process model as also in an actual second order thermal process. Test results show that the proposed algorithm has an edge over its conventional discrete counterpart even when the latter is perfectly tuned.

Application of Adaptive Control Theory to On-Line GTA Weld Geometry Regulation

This study addresses the uses of adaptive schemes for on-line control of backbead width in the Gas Tungsten Arc (GTA) welding process. Open-loop tests using a step input current confirm the validity of a nominal first order process model. However, the time constant and gain prove highly dependent upon welding conditions including torch speed, arc length, material thickness, and other material properties. Accordingly, a need exists for adaptive controllers that can compensate for these process nonlinearities. The performance of two adaptive controllers is evaluated: Narendra and Lin’s Model-Referenced Adaptive Control (MRAC/NL), and Self-Tuning Control with Pole Placement (STC/PP). The addition of a quadratic term to the adaption mechanisms of MRAC/NL is proposed and preliminary simulations and experiments clearly demonstrate the stabilizing effect of this added term. The main experiments compare the performance of the modified MRAC/NL controller and the STC/PP controller with each other and with linear PI controller and the STC/PP controller with each other and with linear PI controller under four experimental conditions: first, where welding conditions are nominal; second, when conditions are disturbed by a step-wise increase in the torch velocity, and third, when conditions are disturbed by a step-wise increase in material thickness. In each case the experimental demonstrates the superiority of the adaptive controllers over the linear PI controller. However, the STC/PP controller exhibits high frequency control action in response to severe disturbances of material thickness and the parameter estimates it generates drift during steady-state operations. The MRAC/NL controller proves more robust under these circumstances. Analysis demonstrates that the superior performance of the MRAC/NL is due both to the inherent normalizing effect of the quadratic feedback terms and to the noise filtering properties of the adaptive mechanism.

Application of an extended Kalman filter for state estimation of a yeast fermentation

The development of a Kalman filter for state and parameter estimation of a biotechnical process is discussed. Because of the large complexity of biotechnical processes, mathematical models for online estimation are based on extensive simplifications. Therefore model errors in the structure and parameters cannot be avoided. In such situations, simulations of the process in combination with the estimator are very helpful during the design phase: these permit fast examinations of the different behaviour of linear filters compared to nonlinear algorithms and also investigations of the influence of sampling interval and initial values of state and filter variables on the estimation. By the use of such simulations, the suitability of process models with various degrees of simplifications can also be easily tested. Based on the simulations, an extended Kalman filter with iteration of the output equations was chosen. Besides the states, two parameters of a third order process model are estimated online. The filter algorithm was tested during batch processes and worked well after a slight modification. The filter behaviour observed in the experiments was very similar to the simulations.

On a Class of Adaptive PID Regulators

Based on some relations discovered between the deterministic servo regulator and the PID design a simple design role is presented for stable processes to ensure 5% relative overshoot for the closed loop step response. The adaptive solution is based on the explicit identification of a second order process model with time delay. Extending the PID regulator by an appropriate correcting term the poorly damped or inverse unstable process zero is allowed to be a zero of the closed loop system, as well. Additional pole placement is also available.

Direct Methods for Self-Tuning PID Regulators

Two algorithms are presented for self-tuning PID regulators. The first method is based on the explicit identification of a second order process model with time delay and an explicit formula ensuring prescribed overshoot of the process output. The second method applies an implicit identification technique which directly estimates the PID regulator parameters using a special form of stochastic approximation algorithms. Simulation results and comparison are also given.

Properties of optimal stochastic control systems with dead-time

Structural, stability and sensitivity properties of optimal stochastic control systems for dead-time, stable minimum phase as well as non-minimum phase processes are presented. The processes are described by rational transfer functions plus dead-times and the disturbances by rational spectral densities. It is shown that although the frequency domain design techniques guarantee asymptotically stable systems for given process and disturbance models, many of the designs might be practically unstable. Necessary and sufficient conditions that must be imposed on the design to assure practically stable optimal systems are derived. The uncertainties in the parameters and in the structure of the process model are measured by means of an ignorance function. Sufficient conditions in terms of the ignorance function, which guarantee stable design and by means of which the bounds of the uncertainties for a given design may be estimated, are stated. Conditions under which the optimal designs possess attractive relative stability properties, namely gain and phase margins of at least 2 and 60°, respectively, are stated, too. It is further shown that any optimal controller, for the type of processes discussed in this paper, may be separated into a primary controller and into a dead-time compensator where the latter is completely independent of the cost and the disturbance properties. Such a decomposition gives excellent insight into the role of the cost and the disturbance in the design. When low order process and disturbance models are used, the conventional PI and PID control laws coupled with the dead-time compensator emerge.

Application of Optimal Multivariate Control with Process Computer in a Thermal Power Plant

A design and application of an optimal multivariable control concept for a boiler-turbine-system is described in this paper.Thereby the optimal control algorithm is computed by solving the algebraic matrix Riccati-equation for a 28th order process model with 6 input- and 8 output-variables. The command variables are fitted to the process in such a way that the controlled output variables will also reach the final steady state required without using integral control. Integral loops are only assigned additionally to avoid deviations from steady state caused by disturbances.The reconstruction of the non-measurable state-variables are done by complete Luenberger observer.The developed optimal control concept has been carried out with process computer directly at a thermal power plant unit. By using this concept the load changes can be three times or more greater than by using conventional control, which was applied before. This will be illustrated in the measuring curves.