Estimated Plant Model Research Articles

Indirect Adaptive MPC for Discrete-Time LTI Systems With Parametric Uncertainties

This article addresses the problem of controlling discrete-time linear time-invariant systems with parametric uncertainties in the presence of hard state and input constraints. A suitably designed gradient-descent-based indirect adaptive controller, used to handle parametric uncertainties, is combined with a model predictive control (MPC) algorithm, which guarantees constraint satisfaction. An estimated model of the actual uncertain plant is used for predictions of the future states. The parameters of the estimated model are updated using a gradient-descent-based adaptive update law. The errors arising due to the model mismatch between the estimated plant model and the actual uncertain plant are accounted for using a constraint tightening method in the MPC algorithm. The proposed adaptive MPC strategy is proved to be recursively feasible and the closed-loop system is proved to be bounded at all instants and asymptotically converging to the origin.

Disturbance observer based adaptive model predictive control for uncalibrated visual servoing in constrained environments

This paper presents an adaptive model predictive control (MPC) method based on disturbance observer (DOB) to improve the disturbance rejection performance of the image-based visual servoing (IBVS) system. The proposed control method is developed based on the depth-independent interaction matrix, which can simultaneously handle unknown camera intrinsic and extrinsic parameters, unknown depth parameters, system constraints, as well as external disturbances. The proposed control scheme includes two parts which are the feedback regulation part based on the adaptive MPC and the feedforward compensation part based on the modified DOB. Unlike the traditional DOB that is based on the fixed nominal plant model, the modified DOB here is based on the estimated plant model. The adaptive MPC controller consists of an iterative identification algorithm, which not only can provide the model parameters for both the controller and the modified DOB, but also can be used to control plant dynamics and to minimize the effects of DOB. Simulations for both the eye-in-hand and eye-to-hand camera configurations are conducted to illustrate the effectiveness of the proposed method.

Temperature based spindle speed controller during friction stir welding of aluminium metal matrix composites

PurposeThis paper aims to investigate two control mechanisms on the two parameters, namely, spindle speed and tool pin position, while performing friction stir welding (FSW) for aluminium metal matrix composites (Al-MMC) using the concept of system identification.Design/methodology/approachFSW is a feasible choice for joining of Al-MMC over the fusion welding due to the formation of the narrow heat-affected zone and minimizing the formation of intermetallic compounds at weld interface. The goal in FSW is to generate enough thermal energy by friction between the workpiece and rotating tool. Heat energy is generated due to mechanical interaction because of the difference in velocity between the workpiece and rotating tool. The generated heat is proportional to the tool pin position and the spindle speed. In the present work, a Smith Predictor Control scheme and adaptive control scheme are developed during joining of Al6061/SiC/B4C Al-MMC by FSW. Adaptive controller is developed to control the tool pin position while Smith Predictor control is developed to control the spindle speed. Initially, the Al-MMC plates are prepared at five combinations of SiC and B4C reinforcements and welded at three level parameter settings followed by tensile testing. The experimental data are used in estimating the plant transfer function model using system identification. The control schemes are then developed for the estimated plant model and the same are validated using a standard PID controller. In both the control schemes, PID controller results in a sluggish response. Experimental validations are performed for the developed control schemes followed by microscopic studies of the weldments.FindingsIn both the control schemes, PID controller results in a sluggish response. Experimental validations are performed for the developed control schemes followed by microscopic studies of the weldments.Research limitations/implicationsResults from the study concluded that the developed MRAC and Smith predictor scheme effectively controlled the vibrations and spindle speed effectively.Originality/valueIt is observed that the scanning electron microscopy micrographs of the Al-MMC’s welded using developed control schemes resulted in good boding with homogenous distribution of reinforcement particles.

Model reference adaptive controller for enhancing depth of penetration and bead width during Cold Metal Transfer joining process

Abstract In this paper, an adaptive control scheme is employed for joining Aluminium 6061 alloy sheets by Cold Metal Transfer (CMT) process. The transfer function model of the CMT welding system is derived using empirical equations. The CMT plant transfer function is estimated using system identification technique. For the estimated plant model, a conventional PID controller is initially designed by tuning the controller parameters. The designed control system is tested for its ability to control the welding current when short circuit phase and arcing phase are detected. Following the conventional PID controller, a Model Reference Adaptive Controller is implemented to maintain the welding current at desired range during melting and electrode wire short circuiting. The performance analysis for the proposed adaptive control scheme and the conventional PID controller is compared. The simulation results indicate that the conventional PID controller is unable to retrieve the desired current during short circuit phase and arcing phase. Nevertheless, the proposed MRAC for CMT process successfully maintains the welding current at the setpoint when subjected to arcing phases and short circuit respectively, while ensuring arc stability. The experimental validation is carried out in the CMT welding set up using the designed MRAC. The experimental results emphasize that the MRAC improves the welding performance by yielding good weld joints swiftly and enhanced quality besides minimizing the design complexities.

An adaptive algorithm for nonstationary active sound-profiling

The use of active sound profiling (ASP) in the automobile industry has been under investigation for several years, and the applications have taken advantage of such techniques, balancing amplitudes instead of simply minimizing the sound pressure level (SPL). This paper presents a novel adaptive algorithm to profile nonstationary disturbances such as the noise generated by a gasoline engine. The new algorithm provides profiling capabilities for nonstationary disturbances and stability properties of the system, whilst expending minimum control effort. Mainly assisted through the use of a reshaping signal, necessary phase information is extracted from nonstationary disturbance signals. To deal with changes in sound as the operating conditions of the engine change, the short-time Fourier transform (STFT) filtered-x least mean square (FXLMS) scheme is introduced to improve the convergence rate. The stability properties are based on the command FXLMS approach, which prevents instabilities caused by magnitude errors in the estimated plant model. Moreover, modification of the STFT-FXLMS scheme improves stability and performance when phase error does exist. In this paper, the performance of the proposed algorithm is demonstrated through a series of simulations configured with either simulated noises or noises from a real engine. The results revealed the effectiveness of the proposed algorithm in profiling nonstationary harmonic noise, and enhancement of stability and performance due to the modification of the STFT-FXLMS scheme.

Asymptotic Properties of MOESP-type Methods

Abstract Precision of the estimated plant model is often the main interest of system identification. In order to take the predictable part of the noise into account, the noise model is estimated together with the plant model by using ARMAX model. In that case, a model reduction procedure will be required in order to obtain the plant model. On the other hand, the plant model can be estimated directly by using output error (OE) model. In this paper, PI-MOESP method and PO-MOESP method are compared by analysing the signal and noise components of the estimated plant model under the assumption that there are no common poles in the plant and the noise models. The magnitude of the noise component in each method is discussed when the past or future horizon varies and it is shown that there is a possibility that PI-MOESP method gives better performance than PO-MOESP method.

Combined control strategy using internal model control and adaptive inverse control for electro-hydraulic shaking table

An electro-hydraulic shaking table is a useful experimental apparatus to real-time replicate the desired acceleration signal for evaluating the performance of the tested structural systems. The article proposes a combined control strategy to improve the tracking accuracy of the electro-hydraulic shaking table. First, the combined control strategy utilizes an adaptive inverse control as a feedforward controller for extending the acceleration frequency bandwidth of the electro-hydraulic shaking table when the estimated plant model may be a nonminimum phase system and its inverse model is an unstable system. The adaptive inverse control feedforward compensator guarantees the stability of the estimated inverse transfer function. Then, the combined control strategy employs an improved internal model control for obtaining high fidelity tracking accuracy after the modeling error between the estimated inverse transfer function using adaptive inverse control and the electro-hydraulic shaking table actual inverse system is improved by the improved internal model control. So, the proposed control strategy combines the merits of adaptive inverse control feedforward compensator and improved internal model control. The combined strategy is programmed in MATLAB/Simulink, and then is compiled to a real-time PC system with xPC target technology for implementation. The experimental results demonstrate that a better tracking performance with the proposed combined control strategy is achieved in an electro-hydraulic shaking table than with a conventional controller.

Adaptive Control of Systems with Actuator Failures Using an Adaptive Reference Model

This paper considers model reference adaptive control of uncertain plants under actuator failures when the plant model matching conditions are violated due to abnormal changes in the plant or incorrect knowledge of the plant’s mathematical structure. The approach consists of direct adaptation of state feedback gains for state tracking to compensate for model errors and actuator failures and simultaneous estimation of the plant model mismatch. Because of mismatch resulting from large changes in the plant, the original reference model may no longer be appropriate, and it may be desirable to track the state of a modified reference model that still provides satisfactory performance. The reference model is redesigned if the estimated plant model mismatch exceeds a bound that is determined via robust stability and/or performance criteria. The proposed controller is a hybrid direct–indirect adaptive controller that offers asymptotic state tracking in the presence of plant model mismatch, parameter deviations, and actuator failures.

Stabilization of Nonnecessarily Inversely Stable First-Order Adaptive Systems under Saturated Input

This paper presents an indirect adaptive stabilization scheme for first-order continuous-time systems under saturated input which is described by a sigmoidal function. The singularities are avoided through a modification scheme for the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be non-singular and then the estimated plant model is controllable. The modification mechanism involves the use of a hysteresis switching function. An alternative hybrid scheme, whose estimated parameters are updated at sampling instants is also given to solve a similar adaptive stabilization problem. Such a scheme also uses hysteresis switching for modification of the parameter estimates so as to ensure the controllability of the estimated plant model.

Front-end low-frequency switched-mode rectifier and its control for permanent-magnet synchronous-motor drive

The low-frequency switching-mode rectifier (LF-SMR) possesses the advantages of lower switching frequency, higher conversion efficiency and simpler control, and thus it is extensively utilised in domestic appliances. However, most of the existing LF-SMRs still lack robust operating performance owing to their open-loop control configuration. The development of an AC-switch based LF-SMR and its closed-loop control for PMSM drives are presented. First, the analysis, design and implementation of the power circuit are carried out. The power-circuit components are properly designed considering the compromise between some key performance parameters. Voltage-control aspects of the uncertain effects of double-frequency voltage ripple on the stable closed-loop control behaviour are first studied. On this basis, the voltage-feedback controller type is determined, and its parameters are designed according to the estimated plant model, the properly specified tracking-response requirements and the limitations of LF-SMR. Independently, to improve further the voltage-regulation conrol, an equivalent load-power disturbance is observed and used to perform the disturbance-feedforward-cancellation control. After the effectiveness of the designed LF-SMR has been confirmed, it is applied to serve as a front-end convertor for two types of permanent-magnet synchronous motor (PMSM) drives further to test its validity experimentally.

Stabilization of Continuous-Time Adaptive Control Systems with Possible Input Saturation through a Controllable Modified Estimation Model

This paper presents an indirect adaptive control scheme for linear continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. An alternative modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also proposed. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the estimation model without modification fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the controllability of the modified estimated model. Both schemes ensure that chattering due to switches associated with the modification is not present. The results are extended to the first-order case when the input is subject to saturation being modeled as a sigmoid function. In this case, a hysteresis-type switching law is used to implement the estimates modification.

Adaptive stabilization of continuous‐time systems through a controllable modified estimation model

This paper presents an indirect adaptive control scheme of continuous‐time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. Such singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. An alternative modification scheme based on the achievement of a modifieddiagonally dominant Sylvester matrix of the parameter estimates is also proposed. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the estimation model without modification fails. In both schemes, the use of an explicit hysteresis switching function for the modification of the estimates is not required to ensure the controllability of the modified estimated model. Both schemes ensure that chattering due to switches associated with the modification is not present.

Robust and adaptive control: fidelity or an open relationship?

Robust and adaptive control are essentially meant to solve the same control problem. Given an uncertain LTI model set with the assumption that the controlled plant slowly drifts or occasionally jumps in the allowed model set, find a controller that satisfies the given servo and disturbance rejection specifications. Specifications on the transient response to a sudden plant change or “plant jump” are easily incorporated into the robust control problem, and if a solution is found, the robust control system does indeed exhibit satisfactory transients to plant jumps. The reason to use adaptive control is its ability, when the plant does not jump, to maintain the given specifications with a lower-gain control action (or to achieve tighter specifications), and also to solve the control problem for a larger uncertainty set than a robust controller. Certainly equivalence-based adaptive controllers, however, often exhibit insufficient robustness and unsatisfactory transients to plant jumps. It is therefore suggested in this paper that adaptive control always be built on top of a robust controller in order to marry the advantages of robust and adaptive control. The concept is called adaptive robust control. It may be compared with gain scheduling, two-time scale adaptive control, intermittent adaptive control, repeated auto-tuning, or switched adaptive control, with the important difference that the control is switched between robust controllers that are based on plant uncertainty sets that take into account not only the currently estimated plant model set but also the possible jumps and drifts that may occur until the earliest next time the controller can be updated.

Adaptive stabilization of non-necessarily inversely stable first-order systems by using estimates modification based on testing the Sylvester determinant

This paper presents an adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the a priori estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be non-singular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. In addition, the use of a hysteresis switching function is not required for a modification of the estimates. The global asymptotic stability of the closed-loop scheme is ensured. It is also proved that the problem is well-posed even if chattering motion exists due to the modification process. The results are also extended to the case of presence of uncertainties consisting of bounded noise and a class of unmodelled dynamics so that global stability of the scheme is ensured. In this last case, relative adaptation zones are used on the a priori estimates for robust stabilization purposes so that the estimation process is frozen when the size of the prediction error is small compared to the contribution of the unmodelled dynamics to the plant output.

Controller tuning freedom under plant identification uncertainty: double Youla beats gap in robust stability

In iterative schemes of identification and control one of the particular and important choices to make is the choice for a model uncertainty structure, capturing the uncertainty concerning the estimated plant model. Structures that are used in the recent literature encompass e.g. gap metric uncertainty, coprime factor uncertainty, and the Vinnicombe gap metric uncertainty. In this paper, we study the effect of these choices by comparing the sets of controllers that guarantee robust stability for the different model uncertainty bounds. In general these controller sets intersect. However in particular cases the controller sets are embedded, leading to uncertainty structures that are favourable over others. In particular, when restricting the controller set to be constructed as metric-bounded perturbations around the present controller, the so-called double Youla parametrization provides a set of robustly stabilizing controllers that is larger than corresponding sets that are achieved by using any of the other uncertainty structures. This is particularly of interest in controller tuning problems.

Some peculiarities of identification in the presence of model errors

Modelling errors are often the limiting factor in identification problems. Therefore, it is important to qualify their impact on the estimated plant model parameters θ̂(Z), where Z stands for the data. This paper qualifies the influence of model errors and disturbing noise level on: (i) the asymptotic value θ∗ (estimate for an infinite amount of data) of θ̂(Z), and (ii) the asymptotic (amount of data going to infinity) covariance matrix Cov(θ̂(Z)) of θ̂(Z). The theory is elaborated on a time- and frequency-domain estimator.

CONTROLLER TUNING FREEDOM UNDER PLANT IDENTIFICATION UNCERTAINTY: DOUBLE YOULA BEATS GAP IN ROBUST STABILITY

In iterative schemes of identification and control one of the particular and important choices to make is the choice for a model uncertainty structure, capturing the uncertainty concerning the estimated plant model. This is typically done in some norm-bounded form, in order to guarantee robust stability and/or robust performance when redesigning the controller. Structures that are used in the recent literature encompass e.g. gap metric uncertainty, coprime factor uncertainty, and the Vinnicombe gap metric uncertainty. In this paper we study the effect of these choices when our aim is to maximize the (re)tuning freedom for a present controller (in terms of a norm-bounded perturbation) under conditions of robust stability. Particular attention will be given to the representation of plant uncertainty and controller tuning freedom in terms of Youla parameters. In the problem formulation considered here the so-called double Youla parametrization provides a norm-bounded set of robustly stabilizing controllers that is larger than corresponding sets that are achieved by using any of the other uncertainty structures. Copyright & 2002 IFAC

Adaptive Stabilization of Nonnecessarily Inversely Stable First-Order Continuous-Time Systems under Saturated Input

This paper presents an indirect adaptive stabilization scheme forfirst-order continuous-time systems under saturated input which isdescribed by a sigmoidal function. The singularities are avoided througha modification scheme for the estimated plant parameter vector so thatits associated Sylvester matrix is guaranteed to be nonsingular andthen the estimated plant model is controllable. The modificationmechanism involves the use of a hysteresis switching function. Analternative hybrid scheme, whose estimated parameters are updated atsampling instants is also given to solve a similar adaptivestabilization problem. Such a scheme also uses hysteresis switching formodification of the parameter estimates so as to ensure thecontrollability of the estimated plant model.

SOME PECULIARITIES OF IDENTIFICATION IN THE PRESENCE OF MODEL ERRORS

Modelling errors are often the limiting factor in identification problems. Therefore, it is important to qualify their impact on the estimated plant model parameters θˆ. This paper qualifies the influence of model errors and disturbing noise level on (i) the asymptotic value θ* (estimate for an infinite amount of data) of θˆ, and (ii) the asymptotic (amount of data going to infinity) covariance matrix Cov( θˆ) of θˆ. The theory is elaborated on a time domain and a frequency domain estimator.

Recursive identification algorithms for continuous-time nonlinear plants operating in closed loop

A family of algorithms for the identification of continuous-time nonlinear plants operating in closed loop is presented. An adjustable closed-loop output error-type predictor parameterized in terms of the existing controller and the estimated plant model is used. The algorithms are derived from stability considerations in the absence of noise and assuming that the plant model is in the model set. Some convergence results based on passivity concepts are presented. Subsequently, the algorithms are analyzed in the presence of noise and when the plant model is not in the model set.