Closed-loop Time Constant Research Articles

IMC based automatic tuning method for PID controllers in a Smith predictor configuration

In this paper, a new approach is presented based on relay autotuning of a plant to find parameters for its control using a Smith predictor. A Smith predictor configuration is represented as its equivalent internal model controller (IMC) which provides the parameters of the proportional-integral (PI) or proportional-integral-derivative (PID) controller to be defined in terms of the desired closed-loop time constant, which can be adjusted by the operator, and the parameters of the process model. This means that only one parameter, namely the desired closed-loop time constant, is left for tuning, assuming that the model parameters have been obtained from a relay autotuning. The ISE criterion was used to find the filter parameter, and simple equations were obtained to tune the Smith predictor. The method is very simple and has given improved results when compared with some previous approaches.

Dynamic Interaction Measures for Decentralized Control of Multivariable Processes

We present some insights on the relative error matrix between the process transfer function matrix and its diagonal matrix, which has been used in analyzing dynamic interactions by several authors. Proposed interaction measures can be interpreted in terms of differences of the complementary sensitivity function matrices when loops are closed, extending the concept of gain changes in the relative gain array. To employ the interaction measures, control systems are designed in advance using internal model control. With changes in the closed-loop time constant, proper pairings based on closed-loop response speeds can be obtained.

Temperature control in catalytic cracking reactors via a robust PID controller

The stabilization of fluid catalytic cracking reactors is tackled in this paper. A robust PID control law is developed in order to control the outlet reactor temperature. The suggested control is based on a reduced order model of the reactor given by a system of ordinary differential equations. The controller is synthesized using an input/output linearizing control law coupled to a proportional-derivative reduced order observer to infer on-line the unknown heat of reaction. The proposed control algorithm leads to a classical PID structure. New tuning rules are given, based on the system structure, estimations and closed-loop time constants. This control strategy turns out to be robust against model uncertainties, noisy temperature measurements and set point changes. The performance of the reaction temperature in a tubular riser reactor is numerically compared when the proposed control scheme and standard PID controllers are applied. # 2002 Elsevier Science Ltd. All rights reserved.

Robust PI 2 controller for continuous bioreactors

An estimation algorithm related to the kinetics terms of the main uncertainties present in a continuous stirred tank bioreactor, is developed. This algorithm is based on a proportional–integral reduced order uncertainty observer. With the estimate generated of the uncertain term, an input–output linearizing feedback control is designed which provides robust regulation model uncertainties, noisy measurements and sustained disturbances. This control strategy could be represented as PI 2 controller where new tuning rules of the controller gains are given in terms of the estimation and closed-loop time constants. The performance of the estimation algorithm and the corresponding closed-loop behaviour of the system are compared to a standard PI controller and they are illustrated by means of numerical simulations.

Control valves and process variability

A theoretical analysis is developed to explain some experimental results for a flow loop from the literature. Process variability is shown to be dependent on the disturbance or noise parameters, the closed loop time constant, the loop dead time and the control valve dead band. The results can be extended to other process variables.

Control of a fluid catalytic cracking unit based on proportional-integral reduced order observers

The fluid catalytic cracking (FCC) unit is one of the most complex interactive processes in the refining industry, and is difficult to operate and control. This work deals with the regulative control law design for stabilization of the reactor and regenerator temperatures, considering that the kinetics terms are poorly known. The proposed control law makes use of on-line estimates of the input/output modeling errors, obtained from a proportional-integral reduced order observer. The structure of the proposed controller is similar to a proportional-double integral compensator (PI 2) such that a new parameterization of the controllers gains is given in terms of the closed-loop and estimation time constants. The performance of the control scheme proposed here is analyzed via numerical simulations.

Robustness and Parametrization of the Proportional Plus Double-Integral Compensator

The proportional plus double-integral (PI 2 ) controller was proposed by Belanger and Luyben (Ind. Eng. Chem. Res. 1997, 36, 5339-5347) as a low-frequency compensator. The objective of the additional double-integral compensation is to reject the effects of ramplike disturbances. The aim of this work is to provide a parametrization of the PI 2 controller gains in terms of a nominal closed-loop and disturbance estimation time constants. A reduced-order observer is constructed to estimate ramplike disturbances, which is subsequently coupled with a feedback loop to counteract the effects of the disturbance. It is shown that such control configuration is equivalent to a PI 2 compensator. Some robustness issues of the PI 2 compensator with respect to unmodeled dynamics and nonlinearities are discussed and illustrated with two numerical examples.

Robust Proportional−Integral Control

In this paper, the classical proportional−integral controller is derived by using an on-line uncertainty estimation approach. The crucial role of integral action in linearization-based controller design for uncertain and externally disturbed systems is highlighted. Specifically, the integral action is interpreted as a modeling error compensator, which induces certain robustness capabilities against external disturbances, uncertain parameters, and nonlinearities. Our approach leads to a parametrization of the controller gain and the integral time in terms of estimation and nominal closed-loop time constants. As a consequence of our results, the role of the integral time in the robustness of the closed-loop system is clarified.

Force control in turning based on robust PI controller design

Real-time cutting force control is a very straightforward way to improve safety, performance and quality in rough turning operations. The main problem in controller design for force control is to achieve robustness. Several time-variable process parameters, such as the depth of cut, the spindle rotational speed and the specific cutting force, directly affect the closed-loop system gain and time constant. In this paper, two approaches to robust PI (proportional integral) controller design based on the internal model control (IMC) method are presented. The first approach treats the cutting process as a first-order system with a time- variable gain. By designing for highest process gain, the controller becomes robust, but perhaps a bit sluggish for the lower range of process gain. In the second approach, the cutting process is linearized by introducing non-linear transformations. In this way, the design may be based on a constant-gain system and the time-variable parameters may be considered as additive disturbances. This controller is somewhat faster than the first approach and shows almost identical behaviour over the entire operating range. Both controllers incorporate, in addition, simple parameter adaptation by gain scheduling with respect to spindle speed variations, in order to handle variations in the process time constant. The work presented in this paper shows that it is possible to achieve robust force control in turning using the common PI controller.

Fast controller design for single-phase power-factor correction systems

A fast controller is presented for single-phase boost-type power factor correction circuits. The twice-line-frequency ripple component is removed from the measured output voltage with an adaptive estimator. This enables the closed-loop time constants and overshoots to be reduced by two orders of magnitude compared to traditional designs. The controller copes with considerable uncertainty in input voltage magnitude, line frequency and output capacitance. All sections of the control system are shown to be asymptotically stable. Experimental results are presented to verify the excellent dynamics and robust behavior of the design.

Limitations of dynamic matrix control

Dynamic matrix control (DMC) is based on two assumptions which limit the feedback performance of the algorithm. The first assumption is that a stable step response model can be used to represent the plant. The second assumption is that the difference between the measured and the predicted output can be modeled as a step disturbance acting on the output. These assumptions lead to the following limitations: 1 Good performance may require an excessive number of step response coefficients. 2 Poor performance may be observed for disturbances affecting the plant inputs. 3 Poor robust performance may be observed for multivariable plants with strong interactions. Limitations 1 and 2 apply when the plant's open-loop time constant is much larger than the desired closed-loop time constant. Limitation 3 is caused by gain uncertianty on the inputs. In this paper we separate the DMC algorithm into a predictor and an optimizer. This enables us to highlight the DMC limitations and to suggest how they can be avoided. We demonstrate that a new model predictive control (MPC) algorithm, which includes an observer, does not suffer from the listed limitations.

Nonlinear adaptive observation of an exothermic stirred-tank reactor

Nonlinear control of an exothermic stirred-tank reactor has been previously demonstrated using a number of techniques, including nonlinear static state feedback and output feedback using observers. This paper considers the task of adaptive observation. It is shown that an adaptive observer for concentration can be constructed for an arbitrary order reaction system when only temperature measurements are available. An adaptive observer is constructed to identify the pre-exponential Arrhenius constant and to provide on-line estimation of the unmeasured reactant concentration for a global nonlinear state-feedback controller. The reaction system is transformed into a time-varying adaptive observer canonical form (AOCF) which is linear in the unknown observer states and adaptive parameters. The AOCF was proposed by Bastin and Gevers, who have provided sufficient conditions for its stability. It is shown that the sufficient conditions on the structure of the system and on the signals for global stability of the observer are satisfied by the reaction system, thereby admitting the construction of the adaptive observer for an arbitrary order reaction. Proper choice of observer gains is crucial for an acceptable rate of convergence. Simulations show that the combined observer/controller provides satisfactory closed-loop behavior when the observer time constant is approximately 4 times smaller than the closed-loop time constant. It is also shown why certain transformations result in better adaptive observers.

IMC-PID Controller Design - An Extension

PID controller design based on Internal Model Control (IMC) design procedure by Rivera and co-workers has been extended to cover a wider range of process models. PID tuning parameters for processes up to second-order with first-order numerator dynamics and dead time will be given with only one tuning parameter (closed-loop time constant). In order to obtain the PID formulation, dead time is approximated by either a first-order Padé or a first-order Taylor series expansion depending on whether a PI or PID controller is desired. Various industrial PID implementations which require different PID settings will also be examined in this paper.Several examples including a first-order plus dead time, second-order plus dead time and inverse response, an industrial level control problem, and a nonlinear distillation column model will be used to compare the performance of IMC-PID controller design with more traditional tuning rules, eg, Ziegler-Nichols, Cohen-Coon, and frequency response maximum peak criterion. Model mismatches in process gain, dead time, and time constant will also be introduced to compare the robustness of various controller design methods.