Robust multi-variable identification: Optimal experimental design with constraints

Model identification for use in the design of multi-variable controllers should utilize an experimental design that optimizes the resulting robust control stability and performance, irrespective of the eventual controller structure or tuning. Previous research has shown that a key factor is to identify a steady-state gain matrix with minimal mismatch in the multi-variable gain directionality. In particular, for ill-conditioned systems, precise estimation of the weak process directions is essential.This research extends prior work to provide two alternative design formulations for robust multi-variable identification that allow seamless inclusion of any linear inequality constraints in the inputs, outputs or combinations thereof. These designs, based on D-optimality theory, produce highly correlated input sequences, and accommodate the input and output constraints by using highly unbalanced replications at the various input condition support-points.The superior effectiveness of the proposed designs over prior methods in the literature is demonstrated on a two-input, two-output binary distillation case study. In addition, the seamless extension of the method to higher-order systems is exhibited via a four-input, four-output fluid catalytic cracking example.Uncertainty in the prior estimate of the steady-state gain matrix and in design implementation is addressed in both of the proposed formulations. Furthermore, the second formulation provides a single tuning parameter to balance the efficacy of robust identification versus minimizing sensitivity to uncertainty. Finally, guidelines are presented for the extension of these methods to non-square systems.     

Adaptive feedforward compensation algorithms for active vibration control with mechanical coupling

Adaptive feedforward broadband vibration (or noise) compensation is currently used when a correlated measurement with the disturbance (an image of the disturbance) is available. However in most of the systems there is a ”positive” mechanical feedback coupling between the compensator system and the measurement of the image of the disturbance. This may lead to the instability of the system. The paper proposes new algorithms taking into account this coupling effect and provides the corresponding analysis. The algorithms have been applied to an active vibration control (AVC) system and real time results are presented. A theoretical and experimental comparison with some existing algorithms is also provided.     

MPC-based dual control with online experiment design

We present two dual control approaches to the model maintenance problem based on adaptive model predictive control (mpc). The controllers employ systematic self-excitation and design experiments that are performed under normal operation, resulting in improved control performance with smaller output variance and less control effort. Our control formulations offer a novel approach to the question of how to excite the plant input to generate informative data within the context of mpc and adaptive control. One controller actively tries to reduce the parameter-estimate error covariances; the other controller maximizes the information in the signals for enhanced learning. Our approach differs from existing ones in that we let our controllers converge to standard certainty equivalence (ce) mpc when the parameter uncertainty decreases or more information is generated, and as a result we avoid plant excitation when the uncertainty is low or enough information has been generated. We demonstrate that the controllers work well with a large number of tuning configurations and also address the issue of models that are not admissible for control design.     

An integrated approach to active model adaptation and on-line dynamic optimisation of batch processes

In the application of on-line, dynamic process optimisation, adaptive estimation of the system states and parameters is usually needed to minimise the unavoidable model-process mismatch. This work presents an integrated approach to optimal model adaptation and dynamic optimisation, with specific focus on batch processes. An active approach is proposed whereby the input variables are designed so as to maximise the information content of the data for optimal model adaptation. Then, this active adaptation method is combined with the objective of process performance to form a multi-objective optimisation problem. This integrative approach is in contrast to the traditional adaptation method, where only the process performance is considered and adaptation is passively carried out by using the data as is. Two strategies for solving the multi-objective problem are investigated: weighted average and constrained optimisation, and the latter is recommended for the ease in determining the balance between these two objectives. The proposed methodology is demonstrated on a simulated semi-batch fermentation process.     

Composite adaptation and learning for robot control: A survey

Composite adaptation and learning techniques were initially proposed for improving parameter convergence in adaptive control and have generated considerable research interest in the last three decades, inspiring numerous robot control applications. The key idea is that more sources of parametric information are applied to drive parameter estimates aside from trajectory tracking errors. Both composite adaptation and learning can ensure superior stability and performance. However, composite learning possesses a unique feature in that online data memory is fully exploited to extract parametric information such that parameter convergence can be achieved without a stringent condition termed persistent excitation. In this article, we provide the first systematic and comprehensive survey of prevalent composite adaptation and learning approaches for robot control, especially focusing on exponential parameter convergence. Composite adaptation is classified into regressor-filtering composite adaptation and error-filtering composite adaptation, and composite learning is classified into discrete-data regressor extension and continuous-data regressor extension. For the sake of clear presentation and better understanding, a general class of robotic systems is applied as a unifying framework to show the motivation, synthesis, and characteristics of each parameter estimation method for adaptive robot control. The strengths and deficiencies of all these methods are also discussed sufficiently. We have concluded by suggesting possible directions for future research in this area.     

An augmented subcutaneous type 1 diabetic patient modelling and design of adaptive glucose control

In the present work, an augmented subcutaneous (SC) model of type 1 diabetic patients (T1DP) is proposed first by estimating the model parameters with the aid of nonlinear least square method using the physiological data. Next, a nonlinear adaptive controller is proposed to tackle two important issues of intra-patient variability (IPV) and uncertain meal disturbance (MD). The proposed patient model agrees quite well with the responses of one of the most popular existing nonlinear model used in the research of artificial pancreas. Further, the developed adaptive control is shown to be capable of providing desired glycemic control without feed-forward action for meal compensation or safety algorithms to avoid hypoglycemia. Due to the simple structure and capability of handling intra-patient variability of the adaptive controller, it can find immediate applicability in the development of the in-silico artificial pancreas.     

A novel robust adaptive control algorithm with finite-time online parameter estimation of a humanoid robot arm

A novel robust adaptive control algorithm is proposed and implemented in real-time on two degrees-of-freedom (DOF) of the humanoid Bristol-Elumotion-Robotic-Torso II (BERT II) arm in joint-space. In addition to having a significant robustness property for the tracking, the algorithm also features a sliding-mode term based adaptive law that captures directly the parameter estimation error. An auxiliary filtered regression vector and filtered computed torque is introduced. This allows the definition of another auxiliary matrix, a filtered regression matrix, which facilitates the introduction of a sliding mode term into the adaptation law. Parameter error convergence to zero can be guaranteed within finite-time with a Persistent-Excitation (PE) condition or Sufficient Richness condition for the demand. The proposed scheme also exhibits robustness both in the tracking and parameter estimation errors to any bounded additive disturbance. This theoretical result is then exemplified for the BERT II robot arm in simulation and for experiments.     

Identification of a rice drying model with an improved sequential optimal design of experiments

Getting relevant parameter estimation of a non-linear model is often a hard task from both an experimental and numerical point of view. The objective of optimally designed experiments procedure is to diminish the experimental effort needed such that the identification is within acceptable confidence ranges. After each experiment, the next experiment is optimally designed, taking into account all past experimental results. It allows quality information to be extracted from the experimental data with less experimental time and resource consumption.In this paper, we present an original approach and implementation of the classical A-, D- and E-optimality on the estimation of 5 unknown (transfer related) coefficients in a compartmental model used to describe the convective drying of rice. The originality of our method is that it uses reparameterization of both parameter and protocol vectors which permits to avoid using a global optimization algorithm. The presented method is implemented in Matlab as a Toolbox and fully tested on a pilot plant. The case study (drying of rice) is typical in the field of process engineering: the dynamic model is strongly non-linear in its parameters and cannot be analytically solved. In addition, the specific technical constrains (inertias, limits, etc.) on the pilot are explicitly taken into account for improved experimental feasibility.In this drying application, three experiments with non-constant drying conditions are shown to be quite as effective as a two-factor three-level grid of nine experiments at constant conditions, with only one third of the experimental effort.     

A tuner that accelerates parameters

We propose a tuner, suitable for adaptive control and (in its discrete-time version) adaptive filtering applications, that sets the second derivative of the parameter estimates rather than the first derivative as is done in the overwhelming majority of the literature.     

Integrated direct/indirect adaptive robust contouring control of a biaxial gantry with accurate parameter estimations

This paper presents an integrated direct/indirect adaptive robust contouring controller (DIARC) for an industrial biaxial high-speed gantry that achieves not only excellent contouring performance but also accurate parameter estimations for secondary purposes such as machine health monitoring and prognosis. Contouring control problem is first formulated in a task coordinate frame. A physical model-based indirect-type parameter estimation algorithm is then developed to obtain accurate on-line estimates of unknown model parameters. A DIARC controller possessing dynamic-compensation-like fast adaptation is subsequently constructed to preserve the excellent transient and steady-state contouring performance of the direct adaptive robust controller (DARC) designs. The proposed DIARC along with previously developed DARC contouring controllers are implemented on a high-speed industrial biaxial gantry to test their achievable performance in practice. Comparative experimental results verify the improved contouring performance and the accurate physical parameter estimates of the proposed DIARC algorithm.     

Active disturbance rejection control: some recent experimental and industrial case studies

This paper presents a summary of some recent experimental and industrial case studies of active disturbance rejection control (ADRC). ADRC is a novel disturbance estimation and rejection concept, leading to a new technology with a distinct advantage where, unlike most existing methods, disturbances, internal and external, are actively estimated and rejected. Applications of the new approach in solving industry wide bench mark problems have led to a slew of innovative solutions. The scope of the applications shown in this paper includes motion control, robotic enhanced limb rehabilitation trainings, fuel cell systems, and the two mass spring benchmark problem. Recent production line validation results obtained are also included.     

Optimal experimental design for combinatorial problems

We discuss two experimental designs and show how to use them to evaluate difficult empirical combinatorial problems. We restrict our analysis here to the knapsack problem but comment more generally on the use of computational testing to analyze the performances of algorithms.Corresponding author. Part of this work was carried out while the author was visiting the IOE Department at University of Michigan and the CS department at Columbia University.     

Cycle to cycle adaptive control of simulated moving bed chromatographic separation processes

The simulated moving bed (SMB) technology is increasingly applied in various fields, ranging from the food to the pharmaceutical sectors, for the chromatographic separation of fine (bio)chemicals. In this study, an adaptive controller acting on the fluid flow rates and commutation period is used to regulate the spatial location of the adsorption and desorption waves, and in turn the purity and productivity of the raffinate and extract effluents. This controller is based on a simple discrete-time model of the concentration fronts movement, derived from wave theory. A simple parameter adaptation scheme makes this controller robust to parameter uncertainties and drifts, and allows process start-up with minimum a priori knowledge of the separation parameters. In this study, the performance of the controller is demonstrated for two different applications: the separation of fructo-oligosaccharides (linear isotherms) and cyclopentanone–cycloheptanone (competitive Langmuir isotherms). Different plant/sensor configurations are also examined, indicating the potential of the control strategy even with reduced measurement information.     

Nonlinear control design for excitation controller and power system stabilizer

The paper focuses on the design of excitation controller and power system stabilizer (PSS) control schemes to enhance voltage regulation and transient stability. To design the excitation controller, the nonlinear models of the synchronous generator and electrical system are suitably arranged to give an input-output nonlinear model, which is subsequently made linear by a compensating law. The PSS control scheme is designed according to a new approach, based on the inverse system theory, which guarantees satisfactory swing damping by reducing the mutual influence between transient stability and voltage regulation. The results obtained by numerical simulations in different operating conditions confirm the effectiveness of the proposed design, also in the presence of model parameter inaccuracy.     

A universality advantage of stochastic excitation signals for adaptive control

Adaptive control schemes usually depend on estimation of system parameters, which in turn depends excitation of modes associated with these parameters. Such excitation is supplied by plant noise, the adaptive control signal itself, and any external excitation such as a reference signal. In this note, it is shown that there is a universality advantage for any externally applied signal to be stochastic rather than deterministic. The crucial property of a stochastic signal exploited in this note is its unpredictability by any causal system, such as an adaptive control scheme. When such unpredictable signals excite an adaptive control scheme, there is no need to deliberately constrain the adaptation to be ‘slow’ or ‘excitation maintaining’ to ensure adequate identification.     

Some comments on the use of normalization in robust adaptive control

This paper discusses the role of normalization with respect to robust parameter estimation for discrete-time adaptive control in the presence of unmodeled dynamics. It is pointed out that the normalizing signal may be brought into the adaptive law in two distinct ways; (i) via normalization of the regressor and the error signal in the standard parameter update law, and (ii) by replacement of the error signal with a function of the normalizing signal and the error. The convergence properties for both approaches are derived and shown to be similar.     

Identification test design for multivariable model-based control: An industrial perspective

The design of plant tests to generate data for identification of dynamic models is critically important for development of model-based process control systems. Multivariable process identification tests in industry continue to rely on uncorrelated input signals, even though investigations have shown the benefits of other input designs which lead to correlated, higher-amplitude input signals. This is partly due to difficulties in formulating and solving computationally tractable problems for identification test design. In this work, related results are summarized and extended. Connections between different designs that target D-optimality or integral controllability are established. Related concepts are illustrated through simulation case studies.     

Optimal control for chatter mitigation in milling—Part 1: Modeling and control design

Active structural methods constitute a promising way to mitigate chatter vibrations in milling. This paper presents an active system integrated into a spindle unit. Two different optimal control strategies are investigated. The first one only considers the dynamics of the machine structure in the controller design and minimizes the influence of cutting forces on tool tip deviations. The second one takes explicitly the process interaction into account and attempts to guarantee the stability of the overall closed-loop system for specific machining conditions. The modeling and formulation used for both strategies are presented in this first part. A simulation allows the comparison of their respective working principle. The validation of the proposed concept in experimental conditions is described in the second part.