Internal Model Control Structure Research Articles

PID–PFC control of continuous rotary electro‐hydraulic servo motor applied to flight simulator

Due to the uncertainties caused by high non-linearity, friction, leakage and other external factors existing in the flight simulator with continuous rotary electro-hydraulic servo motor and the traditional control strategies discontenting with the high-performance requirements, the mathematical model of continuous rotary electro-hydraulic position servo system is established and the compound control theory combining proportional-integral-derivative (PID) and the predictive function control (PFC) method is proposed. In order to enable the servo system to estimate the influence of uncertainties and correct it by repeating online optimisation continuously, PID–PFC compound controller basing on the structure of internal model control is designed and then applied to continuous rotary electro hydraulic servo system. The simulation results show that compared with the traditional PID, PFC controller, PID–PFC compound control can effectively inhibit the interferences of the electro-hydraulic servo system, and greatly improve the response speed and tracking performances and expanding the system frequency band width. The accurate control of motor's position can be realised by applying PID–PFC compound control, which can make the servo system has stronger robustness.

Design of an Active Disturbance Rejection Control for Drag-Free Satellite

This paper addresses the problem of designing an active disturbance rejection controller for a high accuracy drag-free satellite with cubic test mass. The uncertain model of the drag-free satellite is defined. The performance requirement imposed on the acceleration of the test mass is broken down into specification of drag-free and suspension loop because of the disturbance decoupling controller, which is based on the linear active disturbance rejection control technique. We derive two-degree internal model control structure of ADRC, which is used for robust stability verification. Search programs determine the parameters that satisfy system stability and the performance requirement. The design technique has shown to be robust to the perturbation of the system and good performance in disturbance suppressing. To check the design of the controller, an overall simulation is preformed, and the results confirmed that the controller is able to meet the system requirements.

Graphic IMC-PID tuning based on maximum sensitivity for uncertain systems

Obtaining all feasible parameters of the proportional-integral-differential (PID) controller is the key goal in uncertain systems. This paper proposes a graphical tuning method based on an internal model control (IMC) strategy for uncertain systems with time delay. Specifically, the Kharitonov theorem is introduced first to simplify the uncertain system into 32 polynomials. Then, for each polynomial, the IMC structure is applied to reduce the tuning parameters of the PID controller in order to rapidly determine the controller parameters. Finally, the maximum sensitivity (Ms) is used to further guarantee the controlled system with a certain robustness and dynamic performance, which can portray constant gain margin and phase margin boundaries, and can even determine the range of parameters of the proposed IMC filter. Three example results from simulations are presented to demonstrate the effectiveness and applicability of the proposed method.

IMC-based Design for Teleoperation Systems with Time Delays

The presence of time delays in communication introduces a limitation to the stability of bilateral teleoperation systems. In this study, we address the design of Internal Model Control (IMC)-based controllers for teleoperation systems with arbitrary time delays. The two degrees of freedom IMC structure is utilized for the master and the slave respectively and thus the passivity-assumption on the external forces is not required. The stability of the overall system is analyzed by regarding the whole system as a multivariable system. A performance-oriented controller design process which guarantees the delayed tracking between the master and the slave is also given. Finally, an example is given to validate the effectiveness of the proposed method.

IMC based Fractional Order Controller Design for Specific Non-Minimum Phase Systems

Internal model control (IMC) structure is derived from classical control by introducing the model of plant in the control loop and thereby having significant advantages over classical control such as dual stability, perfect control and zero-steady state offset. The basic one degree of freedom (ODF) IMC provides good compromise between set-point tracking and disturbance rejection and works well for non-minimum phase (NMP) systems. In this work, an IMC based fractional order (FO) controller is designed for NMP system which satisfy desired phase margin (ϕm) at a desired gain-crossover frequency (ωg). The domain of desired ϕm and ωg is provided from which they can be selected. Simulation studies are done for (i) DC-DC boost converter which is a NMP system with one zero in right half of s-plane and (ii) first order plus time delay (FOPTD) system which is also a NMP system because of the delay. Significance of the proposed methodology is verified by comparing with other well-known techniques in IMC based on the performance measures, such as rise time (Tr), settling time (Ts) and overshoot (%Mp) and performance indices such as integral square error (ISE), integral absolute error (IAE) and integral of the time weighted absolute error (ITAE).

Enhanced IMC synthesis for tracking control of magnetic levitation system

This paper presents an enhanced internal model control (EIMC) scheme for a time-delayed second order unstable process, which is subjected to exogenous disturbance and model variations. Even though the conventional internal model control (IMC) can provide an asymptotic tracking response with desired stability margins, the major limitation of conventional IMC is that it cannot be applied for an unstable system because a small exogenous disturbance can trigger the control signal to grow unbounded. Hence, modifying the conventional IMC structure to guarantee the internal stability, we present an EIMC scheme which can offer better trade-off between setpoint tracking and disturbance rejection characteristics. To improve the load disturbance rejection characteristics and attenuate the effect of sensor noise, we solve the selection of controller gains as an H∞ optimization problem. One of the key aspects of the EIMC scheme is that the robustness of the closed loop system can be tuned via a single tuning parameter. The performance of the EIMC scheme is experimentally assessed on a magnetic levitation plant for reference tracking application. Experimental results substantiate that the EIMC scheme can effectively counteract the inherent time delay in the model and offer precise tracking, even in the presence of exogenous disturbance. Moreover, by comparing the trajectory tracking performance of EIMC with that of the proportional integral velocity (PIV) controller through cumulative power spectral density (CPSD) of the tracking error, we show that the EIMC can offer better low frequency servo response with minimal vibrations.

A Modified IMC Structure to Independently Select Phase Margin and Gain Cross-over Frequency Criteria

In this paper, a modified internal model control (IMC) is proposed to improve transient response by introducing an additional PD controller in the control loop of a first order plus time delay (FOPTD) system. The controller is tuned to satisfy phase margin (φm) and gain cross-over frequency (ωg) independently. In the proposed methodology, φm and ωg can be selected from a ωg - φm plane whereas basic IMC gives freedom to select φm and ωg from a ωg -φm line. Therefore, it improves the freedom for selection of these specifications by broadening the domain of selection from a line to a plane, also improving the overall response. Further the impact of the proposed controller is verified by considering transient parameters such as rise time (Tr), settling time (Ts) and maximum overshoot (%Mp) and the controller effectiveness is measured in terms of performance indices like integral square error (ISE), integral absolute error (IAE) and integral of the time weighted absolute error (ITAE).

Experimental Evaluation of Internal Model Control Scheme on a DC–DC Boost Converter Exhibiting Nonminimum Phase Behavior

In this work, an internal model controller (IMC) with two-degree-of-freedom has been implemented as a voltage mode controller for the output voltage regulation of a boost-type dc–dc converter that exhibits nonminimum phase behavior due to occurrence of a right-half plane (RHP) zero. The IMC structure provides an alternate parameterization of the conventional feedback controller and is comparatively simple to tune to achieve satisfactory servo and regulatory behavior that are close to the performance limits set by the RHP zero. An internal model controller was designed using a linear model developed in the neighborhood of a nominal operating point for the converter. To assess the efficacy of the IMC scheme, simulation studies and experimental evaluations were carried. In majority of the problems investigated, the IMC was found to perform significantly better than a PID designed using the conventional approach. The responses obtained using the experimental setup were found to match closely with the responses obtained using the nonlinear dynamic model based closed-loop simulations, which corroborated the conclusions reached through the simulations. Thus, the simulation as well as experimental studies indicated that the IMC scheme is ideally suited for controlling a boost-type dc–dc converter exhibiting the nonminimum phase behavior.

IMC-PID controller design based on loop shaping via LMI approach

This paper presents a new approach to designing a PID controller based on internal model control (IMC). For this purpose, the parameters of PID controller in the standard structure of IMC are calculated such that the gain crossover frequency, phase margin, and phase and amplitude of the open-loop system at various frequencies are separately adjusted to the desired values. This loop shaping procedure is wholly formulated as a linear matrix inequality (LMI) generalized eigenvalue problem (GEVP). Hence, using this approach, one can combine the advantages of PID, IMC, and LMI. Unlike the traditional methods, here the LMIs are derived directly in the frequency domain without using state-space models. The proposed method was applied to various widely used process models to verify its efficiency, and the results were compared with competing methods.

Hybridization of IMC and PID control structures based on filtered GPC using genetic algorithm

Classical and advanced hybridization methods are employed in the control literature to calibrate the tuning parameters of internal model control (IMC) and proportional-integral-derivative (PID) controllers. This paper presents an alternative tuning design for the generalized predictive controller (GPC) that is based on both the positional process model and cost function. The proposed method involves the selection of an integral polynomial weighting filter for reference and output signals to deal with reference tracking, disturbance rejection, model-plant mismatch (MPM), minimum control energy and closed-loop robustness. The filter positional GPC (FP-GPC) obtained is transformed into a two-degree-of-freedom polynomial filtered RST structure and then into filtered internal model control (F-IMC) and PID controllers. Also, a multi-objective optimization based on genetic algorithm is applied to tune the filter parameters. Numerical and experimental essays show the effectiveness of the proposed control methodology.

A modified two-degree of freedom-internal model control configuration for load frequency control of a single area power system

In this paper, we propose a modified two degree-of-freedom internal model control structure, with dual feedback loop configuration for the load frequency control problem of a single-area power system. Our main objective is to achieve better transient and steady state performance. The predictive model of the proposed configuration is derived through the stability equation method, which preserves the stability of the model. The proposed scheme is simulated for a single-area power system with nonreheated turbine and 50% parametric uncertainty. It is observed from the responses and the performance indices that the proposed control configuration gives better results compared to well-known existing techniques.

Dynamic Recurrent Neural Network Based Indirect Adaptive Control for Nonlinear Systems

In this study, an indirect adaptive controller based on dynamic recurrent neural network (DRNN) is developed in the form of the internal model control structure. This control method includes two learning phases, i.e., off-line and on-line learning. In the offline learning, the DRNN is learned by the epoch wise back propagation through time (BPTT) method to represent the forward dynamics of the system to be controlled. In the online phase, the DRNN is used as the internal model of the controlled system and its parameters can be trained by the Truncated BPTT to cope with the possible change in the system dynamics. Hence, the mathematical inversion of the DRNN internal model is computed online to act as the forward controller. Finally, the controller is then obtained by cascading this inverse model with a robust filter and a linear compensator to improve the closed loop performance. The proposed method is applied to a continuous stirred tank reactor (CSTR) with time varying behavior to evaluate the performance of controller.

Internal Model Control for a Light-Weight Active Noise-Reducing Casing

Abstract The active noise-reducing casing developed and promoted by the authors in recent publications have multiple advantages over other active noise control methods. When compared to classical solutions, it allows for obtaining global reduction of noise generated by a device enclosed in the casing. Moreover, the system does not require loudspeakers, and much smaller actuators attached to the casing walls are used instead. In turn, when compared to passive casings, the walls can be made thinner, lighter and with much better thermal transfer than sound-absorbing materials. For active noise control a feedforward structure is usually used. However, it requires an in-advance reference signal, which can be difficult to be acquired for some applications. Fortunately, usually the dominant noise components are due to rotational operations of the enclosed device parts, and thus they are tonal and multitonal. Therefore, it can be adequately predicted and the Internal Model Control structure can be used to benefit from algorithms well developed for feedforward systems. The authors have already tested that approach for a rigid casing, where interaction of the walls was significantly reduced. In this paper the idea is further explored and applied for a light-weight casing, more frequently met in practice, where each vibrating wall of the casing influences all the other walls. The system is verified in laboratory experiments.

Operator-based robust control for nonlinear uncertain systems with unknown backlash-like hysteresis

In this paper, operator based robust control for nonlinear uncertain system with unknown backlash-like hysteresis is considered. In detail, a continuous backlash-like hysteresis operator is proved to be corresponding to a one-to-one operator, that is, it is suitable to be used in operator theoretic based control theory. Moreover, an internal model control (IMC) structure with one parallel compensating operator is proposed for nonlinear uncertain system with unknown backlash-like hysteresis. Based on the proposed control scheme, the designed system is robustly stable and the desired output tracking performance can be realized simultaneously. Finally, a simulation example about nonlinear plant preceded by backlash is given to show the design procedure of the proposed method.

Vehicle active steering control research based on two-DOF robust internal model control

Because of vehicle’s external disturbances and model uncertainties, robust control algorithms have obtained popularity in vehicle stability control. The robust control usually gives up performance in order to guarantee the robustness of the control algorithm, therefore an improved robust internal model control(IMC) algorithm blending model tracking and internal model control is put forward for active steering system in order to reach high performance of yaw rate tracking with certain robustness. The proposed algorithm inherits the good model tracking ability of the IMC control and guarantees robustness to model uncertainties. In order to separate the design process of model tracking from the robustness design process, the improved 2 degree of freedom(DOF) robust internal model controller structure is given from the standard Youla parameterization. Simulations of double lane change maneuver and those of crosswind disturbances are conducted for evaluating the robust control algorithm, on the basis of a nonlinear vehicle simulation model with a magic tyre model. Results show that the established 2-DOF robust IMC method has better model tracking ability and a guaranteed level of robustness and robust performance, which can enhance the vehicle stability and handling, regardless of variations of the vehicle model parameters and the external crosswind interferences. Contradiction between performance and robustness of active steering control algorithm is solved and higher control performance with certain robustness to model uncertainties is obtained.

Internal Model Control of A Class of Continuous Linear Underactuated Systems

This paper presents an Internal Model Control (IMC) structure designed for a class of continuous linear underactuated systems. The study treats the case of Minimum Phase (MP) systems and those whose zero dynamics are not necessarily stable. The proposed IMC structure is based on a specific controller which is obtained by the realization of an approximate inverse of the model plant. It is shown that, using such IMC structure, it is possible to remedy the problem of system underactuation and Non-Minimum Phase (NMP) behavior. The case of non-zero initial conditions and imperfect modeling are also presented and model parameters effects on the system evolution are discussed. Simulated examples are presented to prove the effectiveness of the proposed control method to ensure set-point tracking, stability and disturbance rejection.

IMC based Smith Predictor Design with PI+CI Structure: Control of Delayed MIMO Systems

In this study a novel structure for time-delay MIMO systems controller design is introduced. In this method decoupled Smith predictor (SP) controller is designed using Internal Model Control structure (IMC). In order to approximate decoupled system, step response model approximation is employed and simulated on MIMO multiple time-delay system. Moreover, to improve system performance from overshoot and rise time perspective, Smith predictor controller is combined with PI+CI structure. Furthermore, to increase system robustness, a low pass filter is designed. Afterwards, the proposed structure is applied to the model of a time-delay MIMO distillation tower system and obtained results are compared to those of a PID controller. Finally, performance of different design methods is evaluated using Integral error criterion (Integral Square Error criterion).

Velocity control of a DC motor based on fractional order PI and IMC-based fractional order controllers

In this paper, two fractional order controllers are employed to control the angular velocity of a permanent magnet DC motor. A fractional order PI controller with isodamping property is appropriately designed to achieve the desired phase margin and gain crossover frequency requirements. Moreover, by selecting a fractional order filter in internal model control (IMC) structure, an IMC-based fractional order controller is designed. These two fractional order controllers are utilised for velocity control of a laboratory DC servomechanism system. The experimental results demonstrate the capability of these fractional order controllers in the desired angular velocity tracking and load disturbance rejection.

Nonlinear internal model controller design for wastegate control of a turbocharged gasoline engine

Internal Model Control (IMC) has a great appeal for automotive powertrain control in reducing the control design and calibration effort. Motivated by its success in several automotive applications, this work investigates the design of nonlinear IMC for wastegate control of a turbocharged gasoline engine. The IMC design for linear time-invariant (LTI) systems is extended to nonlinear systems. To leverage the available tools for LTI IMC design, the quasi-linear parameter-varying (quasi-LPV) models are explored. IMC design through transfer function inverse of the quasi-LPV model is ruled out due to parameter variability. A new approach for nonlinear inversion, referred to as the structured quasi-LPV model inverse, is developed and validated. A fourth-order nonlinear model which sufficiently describes the dynamic behavior of the turbocharged engine is used as the design model in the IMC structure. The controller based on structured quasi-LPV model inverse is designed to achieve boost-pressure tracking. Finally, simulations on a validated high-fidelity model are carried out to show the feasibility of the proposed IMC. Its closed-loop performances are compared with a well-tuned PI controller with extensive feedforward and anti-windup built in. Robustness of the nonlinear IMC design is analyzed using simulations.

Composite Adaptive Internal Model Control and Its Application to Boost Pressure Control of a Turbocharged Gasoline Engine

Internal model control (IMC) explicitly incorporates the plant model and its approximate inverse and offers an intuitive controller structure and calibration procedure. In the presence of plant-model uncertainty, combining the IMC structure with parameter estimation through the certainty equivalence principle leads to adaptive IMC (AIMC), where either the plant model or its inverse is identified. This paper proposes a composite AIMC (CAIMC) that explores the IMC structure and simultaneous plant dynamics and inverse dynamics identification to achieve improved performance of AIMC. A toy plant is used to illustrate the feasibility and potential of CAIMC. The advantages of CAIMC are later demonstrated on the boost-pressure control problem of a turbocharged gasoline engine. The design of the CAIMC assumes that the plant model and its inverse are represented by the first-order linear dynamics. The unmodeled dynamics and uncertainties due to linearization and variations in operating conditions are compensated through adaptation. The resulting CAIMC is first applied to a physics-based high-order and nonlinear proprietary turbocharged gasoline engine model, and then validated on a turbocharged 2-L four-cylinder gasoline engine on a vehicle with vacuum-actuated wastegate. Both the simulation and experimental results show that the CAIMC cannot only effectively compensate for uncertainties but also auto-tune the IMC controller for the best performance.