Internal Model Control Controller Research Articles

A discrete-time internal model-based ∞ controller and its application to a binary distillation column

Abstract Explicit state-space formulae for an H ∞ two degrees-of-freedom (2-DOF) Internal Model Control (IMC)-based controller are derived. The IMC controller solves a special H ∞ control problem directly in discrete-time, providing robust stability against coprime factor uncertainty, and a degree of robust performance in the sense of making the closed-loop system match a pre-specified reference model. The IMC controller structure is shown to comprise a plant state observer, an on-line step response model, and a generalised state-feedback law associated with the plant and model states. A design for a binary (methanol/water) distillation column is presented as an illustrative example.

On the design of robust internal model-based controllers

We consider methods for synthesizing robust controllers that can be directly implemented in the Internal Model Control (IMC) scheme. We show how to put H design methods into the IMC scheme to improve its robustness. These methods include one degree-of-freedom (one d.o.f.) and two degrees-of-freedom (two d.o.f.) H designs. Explicit state-space formulae for the H one d.o.f. and two d.o.f. IMC-based controllers are derived in discrete time. We show that the IMC controller solves a special H control problem, namely a disturbance feedforward control problem, and it proves robust stability against coprime factor uncertainty and with a degree of robust performance for the two d.o.f. case, in the sense of making the closed-loop system match a pre-specified reference model. A design for a glass tube production process is presented as an illustrative example.

Emulator-based control and internal model control: Complementary approaches to robust control design

Two alternative approaches to controller design, the internal model control (IMC) of Morari and Zafiriou [Morari, M. and E. Zafiriou (1989). Robust Process Control. Prentice Hall, Englewood Cliffs, NJ] and the emulator-based control (EBC) of Gawthrop [Gawthrop, P. J. (1987). Continuous-time Self-tuning Control. Vol. 1: Design, Engineering Control Series. Research Studies Press, Lechworth, U.K.] (based on the generalized minimum variance control of Clarke and Gawthrop [Clarke, D. W. and P. J. Gawthrop (1975). Self-tuning controller. Proc. IEE, 122(9), 929–934. Clarke, D. W. and P. J. Gawthrop (1979). Self-tuning control. Proc. IEE, 126(6), 640–6333. Gawthrop, P. J. (1977). Some interpretations of the self-tuning controller. Proc. IEE, 124(10), 889–894]) are shown to differ only superficially in approach and notation. This result provides a link between robust control based on IMC and adaptive control based on EBC.

DSP-based robust control of an AC induction servo drive for motion control

A design method based on the internal model control (IMC) theory has been developed for the robust control of a low-power AC induction servo drive in application of high-performance motion control systems. Indirect vector control with software current control technique has been developed to achieve fast response decoupling control of the induction motor. An equivalent model representing the control dynamics of the decoupled AC induction motor is used for the analysis and synthesis of the IMC controller. To improve the control performance of the servo drive with given frequency-domain robustness specifications, a design procedure for the servo controller is developed based on the IMC theory. The proposed control scheme has been realized using the Texas Instruments TMS320C14 single-chip digital signal processor. Experimental results are given to verify the proposed design method.

Internal model predictive control (IMPC)

A computationally simple model predictive control algorithm incorporates the attractive features of the internal model control (IMC) law. The algorithm first computes the IMC control effort via a model state feedback implementation that automatically compensates for past control effort saturation. Before applying the calculated control, the algorithm checks to see if this control effort, when applied over a single sampling interval and followed by a control effort at the opposite limit (relative to its steady-state level), will cause the model output to exceed its desired trajectory. If not, the calculated control is applied. Otherwise the control is reduced appropriately. Application of the new algorithm to a variety of linear single-input single-output systems shows a smooth, rapid response, without significant overshoot. Comparisons with a QDMC algorithm, tuned to give the same unconstrained behavior as the IMC system and the best possible constrained performance, favor the IMPC system. Application of the new algorithm to a simple multivariable problem drawn from web control in film manufacturing demonstrates the flexibility of the algorithm in dealing with control effort saturation in multivariable systems.

An IMC-PID Tuning Procedure Based on the Integral Square Error (ISE) Criterion: A Guide Tour to Understand its Features

The idea of this paper is to present, in a more convenient way for undergraduate students of chemical engineering, the IMC control philosophy as an alternative tuning procedure of PID controllers based on the Integral Square Error (ISE) criterion. The Internal Model Control (IMC) structure is the starting point of this tuning procedure. Classic Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) feedback controllers are then obtained for most chemical dynamic system representations with different approximations of the deadtime. The set of the PID parameters is further related to the ISE-optimum value of the IMC filter parameter r. Since the tuning of an IMC-РID can be obtained from a relatively analytic easy procedure, it is of major interesting for teaching aids for control theory. This paper includes a step-by-step description of the IMC design procedure together with an example that shows how reasonable are the tunings based on this approach when compared with the traditional Ziegler-Ni chois (Z-N) tuning rules.

Identification of Uncertainty Bounds for Robust Control with Applications to a Fixed Bed Reactor

A model-based robust controller is designed for a packed bed methanation reactor. To accomplish this objective, model uncertainty bounds are identified from experimental data. A physically motivated methodology of regions mapping was developed to compute the uncertainty bounds in the complex plane. This technique is compared to other existing nonparametric approaches for a simple nonlinear system and is shown to produce a more accurate description of the model uncertainty for the purpose of robust control design. This regions-mapping approach is then applied to a fixed bed reactor and uncertainty bounds are computed. A robust controller with a single adjustable parameter is designed for the reactor using internal model control (IMC) theory. The computed uncertainty bounds are experimentally validated using the IMC controller.

Internal model control with enhanced robustness

Abstract Based on the conventional structure of internal model control (IMC), a novel IMC scheme with enhanced robustness is developed in this paper. The necessary structure modification for robustness enhancement is very simple as well as effective, and the synthesis of the additional components is not only very simple but also independent from the design of the original IMC controller. Both analytical and numerical studies have been presented to demonstrate the contribution of the structure modification to the robustness enhancement of IMC systems

Experimental application of robust nonlinear control law to pH control

An experimental application of RNCL to pH control is presented. The experimental setup consists of a computer controlled CSTR (continuous stirred tank reactor) and the control objective is to maintain the pH of a strong-acid strong-base system at the neutralization point in the presence of disturbances. The algorithms considered are PI (proportional-integral) control, nonlinear IMC (internal model control), and RNCL (robust nonlinear control law). The experimental results point to the excellent capability of RNCL for controlling pH comparison to nonlinear IMC and PI control.

Improved independent design of robust decentralized controllers

Abstract The procedure for independent design of robust decentralized controllers proposed by Skogestad and Morari [10] is improved by requiring the controller to be a decentralized Internal Model Control (IMC) type controller. It is shown how to find bounds on the magnitude of the IMC filter time constants such that robust stability or performance is guaranteed. This allows the use of real perturbation blocks for modeling the uncertainty associated with the controllers. In contrast, Skogestad and Morari [10] found bounds on the sensitivity functions and complementary sensitivity functions for the individual loops, and therefore had to use complex perturbation blocks. The concept of Robust Decentralized Detunability is introduced. If a system is Robust Decentralized Detunable, any subset of the loops can be detuned independently and to an arbitrary degree without endangering robust stability. A simple test for Robust Decentralized Detunability is developed for systems controller by a decentralized IMC controller

Improved Independent Design of Robust Decentralized Controllers

The procedure for independent design of robust decentralized controllers proposed by Skogestad and Morari [10] is improved by requiring the controller to be a decentralized Internal Model Control (IMC) type controller. It is shown how to find bounds on the magnitude of the IMC filter time constants such that robust stability or performance is guaranteed. This allows the use of real perturbation blocks for modeling the uncertainty associated with the controllers. In contrast, Skogestad and Morari [10] found bounds on the sensitivity functions and complementary sensitivity functions for the individual loops, and therefore had to use complex perturbation blocks.The concept of Robust Decentralized Detunability is introduced. If a system is Robust Decentralized Detunable, any subset of the loops can be detuned independently and to an arbitrary degree without endangering robust stability. A simple test for Robust Decentralized Detunability is developed for systems controller by a decentralized IMC controller

Improved independent design of robust decentralized controllers

Abstract The procedure for independent design of robust decentralized controllers proposed by Skogestad and Morari is improved by requiring that each individual controller is of the internal model control (IMC) type. It is shown how to find bounds on the magnitude of the IMC filter time constants such that robust stability or performance is guaranteed. In contrast, Skogestad and Morari found bounds on the sensitivity functions and complementary sensitivity functions for the individual loops, and therefore allowed a much larger class of designs, resulting in more conservative conditions. A property called robust decentralized detunability (RDD) is introduced. If a system has this property, any subset of the loops can be detuned independently and to an arbitrary degree without endangering robust stability. A simple test for RDD is developed for systems controlled by decentralized IMC controllers.

Failure conditions for inverse-based multivariable controllers: internal model control structure

Properties of inverse-based controllers under failure conditions are addressed. The inverse-based controllers considered are parameterized, designed and implemented under the internal model control (IMC) structure. One important property is that the integral action is lost when failure in actuator and/or sensor occurs. The steady-state errors (offsets) under failure conditions are discussed in detail from aspects of the set-point tracking and disturbance rejection. The steady-state errors for set-point tracking can be characterized by the well-known interaction measures such as RGA and BRG. The overall performance under failure status is assessed based on the sum of squares of steady-state errors ( SSE). An amplification factor (AF) is defined as the ratio of SSE with IMC control over the SSE without control. An amplification that, under failure modes. AF can be greater than one in some cases. This implies IMC feedback system may lead to inferior performance than a system without control. A distillation example is used to illustrate the behavior of IMC system under failure modes. The results presented here provide a better understanding of IMC and give useful information in making on-line decision under failure conditions.

Internal model control: robust digital controller synthesis for multivariable open-loop stable or unstable processes

The two-step internal model control (IMC) procedure is presented for the synthesis of multivariable discrete controllers. This paper adds the following features to the IMC design methodology: (i) extension to open-loop unstable plants; (ii) design of the first-step (no model error) IMC controller so that the L2-error (sum of squared errors) is minimized for every set-point or disturbance vector in a designer-specified set and their linear combinations; (iii) the second-step (model-plant mismatch) multivariable low-pass filter is designed for robust stability and performance by minimizing a non-conservative robustness measure, the ‘structured singular value’; (iv) the potential problem of intersample rippling is avoided by introducing a modification in the first-step controller and formulating the robust performance objective for the continuous plant output.

Synthesis of model‐based controllers for an autothermal reactor

AbstractModel‐based controllers for a bench scale autothermal tubular packed‐bed reactor have been formulated using the Internal Model Control (IMC) approach. The Structural Dominance Analysis technique has been used in developing the reduced‐order models. Controller performance at robust and sensitive steady states have been assessed through simulations and experiments. Both PI and model‐based controllers can regulate reactor operation at robust steady states, but only third order IMC controllers are able to regulate reactor operation at the sensitive steady state.

IMC controller design for multivariable systems

A systematic internal model control (IMC) controller design methodology has been developed for various types of multivariable processes. When we try to apply IMC to various systems several implementation problems are encountered. In this paper, we resolve these problems and suggest a systematic IMC controller design methodology. IMC shows very good performance and is easy to tune for open-loop stable systems. For unstable systems we apply IMC after stabilizing the systems using the pole placement technique. A combination of quadratic programming and IMC can handle constraints on manipulated and controlled variables.

SOME THEORETICAL INSIGHTS INTO RECENT CONTROL DESIGN ALGORITHMS

Abstract Internal Model Control (IMC) design procedure is known to offer valuable advantages over classical control methods, especially for robust controller design. The Perfect Controller is defined using the well-known classical PID algorithm and its equivalence to IMC. After the definition of the Perfect Controller the IMC filter tuning parameter, which is used to maintain robustness, is obtained as a result of reparametrization of the classical PID control algorithm and factorization of the model. Through factorization, invertible part of the model is used directly in defining the perfect controller and the noninvertibility effects of the model are lumped into the new IMC tuning parameter. Closed loop IMC controller design is obtained with appropriate plant parameter uncertainty representation. Theoretical foundation for the transition from classical PID design to IMC design is analyzed using simple common chemical process models.

Control system design for a fixed-bed methanation reactor

A systematic approach is applied to the design of robust controllers for a fixed-bed, non-adiabatic, laboratory methanation reactor, a unit inherently difficult to control. The fundamental limitations to the achievable closed-loop performance are established by both physical arguments and dynamic resilience considerations. The Internal Model Control (IMC) structure provides a suitable framework for this analysis. IMC controllers are designed and their performance in the face of model uncertainty is tested both by simulation and by means of the Structured Singular Value (μ) analysis technique. The paper provides a basic insight into the characterization and solution of control problems that are particular to fixed-bed reactor systems and constitutes the first account of the application of several recent advances in control theory to a complex chemical process.