Robust Model-based Control Research Articles

Data-driven analysis and control of continuous-time systems under aperiodic sampling

We investigate stability analysis and controller design of unknown continuous-time systems under state-feedback with aperiodic sampling, using only noisy data but no model knowledge. We first derive a novel data-dependent parametrization of all linear time-invariant continuous-time systems which are consistent with the measured data and the assumed noise bound. Based on this parametrization and by combining tools from robust control theory and the time-delay approach to sampled-data control, we compute lower bounds on the maximum sampling interval (MSI) for closed-loop stability under a given state-feedback gain, and beyond that, we design controllers which exhibit a possibly large MSI. Our methods guarantee the stability properties robustly for all systems consistent with the measured data. As a technical contribution, the proposed approach embeds existing methods for sampled-data control into a general robust control framework, which can be directly extended to model-based robust controller design for uncertain time-delay systems under general uncertainty descriptions.

On data-driven nonlinear uncertainty modeling: Methods and application for control-oriented surface condition prediction in hard turning

Abstract In this article, two data-driven modeling approaches are investigated, which allow an explicit modeling of uncertainty. For this purpose, parametric Takagi-Sugeno multi-models with bounded-error parameter estimation and nonparametric Gaussian process regression are applied and compared. These models can for instance be used for robust model-based control design. As an application, the prediction of residual stresses during hard turning depending on the machining parameters and the initial hardness is considered.

A 2D-FM model-based robust iterative learning model predictive control for batch processes

The work deals with composite iterative learning model predictive control (CILMPC) for uncertain batch processes via a two dimensional Fornasini–Marchesini (2D-FM) model. A novel equivalent error system is first presented which is composed of state error and tracking error. Then an iterative learning predictive updating law is constructed by 2D state feedback control and the ‘worst’ case linear quadratic function is also designed. Besides, the update controller considering the input and output constraint will be optimized using the worst-case objective function along the infinite moving horizon. The solvable conditions that can be optimized online in real time are constructed using linear matrix inequalities (LMIs). The stability of the proposed control scheme can be achieved with the feasibility of the optimization problem. Compared with robust traditional MPC using one-dimensional models, the presented control approach can guarantee more degrees of tuning to achieve faster convergence of tracking error, which is of more significance since uncertainties exist inevitably in industrial batch processes. Finally, an injection molding process and a three-tank are introduced as two cases to demonstrate the feasibility and superiority of the proposed MPC strategy.

Robust μ-synthesis: Towards a unified glucose control in adults, adolescents and children with T1DM

Type 1 Diabetes Mellitus (T1DM) remains as a severe public health problem in a wide range of population, from children to adults. Recently, the number of diabetics worldwide and morbility rates are increasing. Therefore, emerging technologies as the artificial pancreas (AP) are directing their efforts to improve treatments and to reduce long-term complications. In this work, a cross-age control strategy is proposed to tackle the blood glucose regulation problem in people with T1DM. The contribution of this paper is focused on the blood glucose regulation in T1DM patients, at distinct ages, and it can be controlled in face to physiological uncertain parameters. In other words, a robust model-based controller is proposed via μ-synthesis technique by considering structured uncertainties in physiological meaningful parameters. The proposed controller exhibits the feasibility for blood glucose regulation in virtual diabetic children, adolescents and adults. The relevance of these parameters lies in their high sensitivity to the solutions of a physiological mathematical model; that is, a slight parametric variation can lead to a hyperglycemic scenario. Thus, it is innovative to consider this uncertainties scheme in parameters that are directly related to the glucose dynamics. The robust control algorithm was integrated into the well-known Uva/Padova simulator for T1DM to show the technical viability of this methodology in the available three populations. The outcomes of a control variability grid analysis show that 90.9% of virtual adults are in upper B-zone and 9.09% in B-zone. Likewise for virtual adolescents, 90.9% fall in upper B-zone and 9.09% B-zone. Regarding children, 63.63% lie in upper B-zone, 27.27% B-zone and only 9.09% failure to deal with hypoglycemia. Furthermore, the results are compared to the ones obtained from H∞ schemes previously reported which also were implemented in the simulator. Despite being a theoretical approach, the results reveal that the proposed cross-age control scheme could be a useful strategy in the development of real PA systems that lead to future clinical trials in humans.

A practical robust yaw servo architecture of ROVs by multi-vector propulsion and nonlinear controller

Multi-vector arrangement is a novel propulsion architecture for remotely operated vehicles (ROV) because of its high manoeuvrability and efficiency, but the influence on the ROV dynamics and attitude servo control has not yet been clearly evaluated. This study fully investigated the kinematic behaviours of a hexagonal multi-vector propulsion ROV with communication delay constraint and reduced the complex model for precision control system design. An enhanced model-based PI robust controller (EMPRC) based on the nominal model is proposed to solve the nonlinear hydrodynamics and communication problems with high performance yaw control, whose stability is also analysed. The conventional proportional-integral-derivative (PID) and integral separation PID are used in the experiments for comparison. The results indicate that the proposed EMPRC can effectively track the desired attitude and reject the external disturbances, while the conventional ones are limited by the nonlinear dynamics and communication delays. The improvement is 3x on average in terms of overshoot, settling time and anti-disturbance recovery time compared to conventional algorithms and proves this proposed novel EMPRC is a practical solution for multi-vector propulsion ROVs.

Design of a robust controller for DC/DC converter–electrolyzer systems supplied by [formula omitted]WECSs subject to highly fluctuating wind speed

A buck-based, isolated, high-voltage-ratio DC/DC converter that allows supplying a proton exchange membrane (PEM) electrolyzer from a micro-wind energy conversion system (μWECS) has been recently presented. It exhibits low ripple at the switching frequency on the output voltage and current and represents an attractive solution for low-cost hydrogen production. In this paper, a more accurate mathematical model of such a converter is derived and discussed. Then, a model-based robust controller is designed in the frequency domain using the Internal Model Control structure and in the context of H2∕H∞ optimal control. The controller satisfies the condition of robust stability and behavior, i.e., it guarantees stability and the desired behavior in the presence of parametric variations and unmodeled dynamics. In particular, the robustness in the presence of variations of DC-link voltage and buck input inductance is verified from the theoretical point of view. The validation of the controller is performed by integrating it into a detailed switching model of the DC/DC converter, which is implemented on a widely used circuit-oriented simulator. Good results are obtained in terms of dynamic and steady-state behavior, even in the presence of the above variations. A comparison is also carried out with the results obtained using an integral controller designed on the basis of the above mathematical model. Such a comparison shows the superiority of the robust controller over the integral controller in all the operating conditions, especially when the DC-link voltage is subject to significant variations and is affected by a non-negligible low-frequency ripple due to the presence of the diode rectifier at the output of the μWECS.

A Novel Model-Based Robust Control for Position Tracking of Permanent Magnet Linear Motor

The main objective of this article is to address the position tracking control problem for permanent magnet linear motor by using a novel model-based robust control method. Specifically, based on the assumed upper bound of the lumped model uncertainties and external disturbances, we design a novel nonlinear control algorithm, which is characterized by error-based and model-based inheriting from traditional proportional-integral-derivative (PID) control and robust control. The proposed control can be considered as an improved PID control or a redesigned robust control, with simple implementation and practical effectiveness. Theoretical analysis is provided to demonstrate that the controller can guarantee the uniform boundedness and uniform ultimate boundedness of the system. Moreover, on the experimental platform, rapid controller prototyping cSPACE is designed to avoid long time programming and debugging, and provides great convenience for practical operation. Numerical simulations and real-time experimental results are finally presented to illustrate the effectiveness and the achievable control performance of the control design.

Disturbance-Observer-Based Control for Air Management of PEM Fuel Cell Systems via Sliding Mode Technique

In this paper, a model-based robust control is proposed for the polymer electrolyte membrane fuel cell air-feed system, based on the second-order sliding mode algorithm. The control objective is to maximize the fuel cell net power and avoid the oxygen starvation by regulating the oxygen excess ratio to its desired value during fast load variations. The oxygen excess ratio is estimated via an extended state observer (ESO) from the measurements of the compressor flow rate, the load current, and the supply manifold pressure. A hardware-in-loop test bench, which consists of a commercial twin screw air compressor and a real-time fuel cell emulation system, is used to validate the performance of the proposed ESO-based controller. The experimental results show that the controller is robust and has a good transient performance in the presence of load variations and parametric uncertainties.

Fuzzy-Set Theory Based Optimal Robust Design for Position Tracking Control of Permanent Magnet Linear Motor

In this paper, we design an optimal robust control to address the problem of position tracking control for permanent magnet linear motor (PMLM). The uncertainties in PMLM system, including parameters uncertainty and external disturbance, are nonlinear and time-varying. The uncertainties are assumed to be bounded, and the bounds are described via fuzzy sets. Then, a model-based robust control in deterministic form is proposed. Furthermore, an optimal robust control for PMLM system is formulated as a fuzzy performance index optimization problem, which associated with both the fuzzy system performance and the control cost. The resulting optimal control can guarantee the uniform boundedness and uniform ultimate boundedness. Moreover, on the experimental platform, rapid controller prototyping cSPACE is designed to avoid long time programming and debugging, and provides great convenience for practical operation. Numerical simulations and real-time experimental results are finally presented to illustrate the effectiveness of the optimal robust control for PMLM.

Robust model-based control of multistage manufacturing processes

This paper presents a novel method that utilizes in-process measurements of product quality and models that relate those measurements with the underlying manufacturing process parameters to drive down the product quality errors via strategic adjustments of the controllable process parameters. Uniqueness of the new method is its robustness to inevitable inaccuracies in the underlying models, as well as the absence of traditional, but restrictive assumptions of Gaussianity and independence of measurement and process noise terms. The new approach was demonstrated using models and data from an automotive cylinder head machining process and an industrial-scale semiconductor lithography overlay process.

An improved generalized predictive control algorithm based on the difference equation CARIMA model for the SISO system with known strong interference

ABSTRACT The single input single output (SISO) system with known strong interference is widely used in various occasions. Due to its strong interference, the control accuracy is hard to guarantee. To solve this problem, an improved generalized predictive control (IGPC) algorithm is developed. The IGPC firstly builds the difference equation CARIMA (Controlled Auto-Regressive Integrated Moving-Average) model of the SISO system and then treats the system as a two input single output (TISO) system and calculates its predictive vector, then transforms it into a SISO system and uses the TISO system predictive vector to calculate the SISO system control increment. A new parameter called phase coefficient is added to inhibit the control lag. Simulations are performed to make the comparison among the traditional GPC, PID control, velocity synchronization control (VSC), fuzzy adaptive PID control (FAPID), model-based robust PID control (BPID) and the IGPC. Results show that IGPC has best performance compared to the others. Finally, experiments are developed which proved that the IGPC algorithm has a higher accuracy in the SISO system with known strong interference than that of VSC.

Robust Fuzzy Control with Transient and Steady-State Performance Constraints for Ship Fin Stabilizing Systems

This paper studies the robust fuzzy controller design problem for the nonlinear ship fin stabilizing systems. By considering the perturbations, the nonlinear ship fin stabilizing system is represented by the perturbed Takagi–Sugeno fuzzy model. According to the perturbed Takagi–Sugeno fuzzy model, the parallel distributed compensation technique is used to design a model-based robust fuzzy controller. The purpose of the parallel distributed compensation fuzzy controller is to derive linear controllers such that each fuzzy rule of the Takagi–Sugeno fuzzy model can be compensated. In addition to the robust stability performance, the variance constraint and transient performance constraint are also considered in this paper. According to these performance constraints, the linear matrix inequality technique is employed to solve the sufficient conditions developed in this paper. At last, some simulations for the control of nonlinear ship fin stabilizing systems are made to show the usefulness and effectiveness of the proposed design method.

Aerodynamic model-based robust adaptive control for close formation flight

This paper presents an aerodynamic model-based robust adaptive control algorithm for close formation flight. The leader aircraft is assumed to be at level and straight flight which characterizes the most common scenario for close formation flight. The formation aerodynamic effects are assumed to be unknown, but an online formation aerodynamic model is available to predict those effects. In light of the online formation aerodynamic model, a robust adaptive control algorithm is thereafter developed on the follower aircraft to counteract the unknown formation aerodynamic effects and obtain highly accurate formation tracking performance. The proposed control algorithm is composed of a baseline controller and an integrator-augmented robust adaptive controller, which can efficiently deal with both matched and mismatched formation aerodynamic effects and external disturbances. The major advantage of the proposed design is that it can achieve at least ultimate bounded tracking control with certain transient performance guaranty. The efficiency and robustness of the proposed control design are eventually validated via numerical simulations of close formation flight at two different scenarios.

Design, modeling, and robust control of the flexible rotor to pass the first bending critical speed with active magnetic bearing

Recently, magnetic bearings have been applied to many rotating machines such as turbo-molecular pumps, cooling gas compressor, flywheel energy storage systems. And high-power density is the future development trend of these machines, which demands that the rotor characterizes slender and high rotating speed and operates above the critical speeds. However, it is a big challenge for a flexible rotor to pass the bending critical speeds and operate above the critical speeds steadily and reliably. Based on above reasons, this article presented the design, modeling, and analysis framework of a flexible rotor test rig with active magnetic bearing (AMB). Special attention was paid to the flexible rotor dynamic model development, dynamic analysis, and model-based robust control design. First, the main structure features were illustrated in detail, including the key dimensions and parameters of the AMB components and rotor. Then models of components including power amplifier and displacement sensor were developed. The finite element method based on Timoshenko beam theory was applied to the rotor dynamics model. The dynamic analysis of the rotor is the foundation of the controller design. Hence, modal analysis had been done, obtaining rotor dynamic properties via synthesis of natural frequency, mode shapes, and Campbell plots. Reduced order model was obtained for controller design convenience. A robust H∞ controller was designed based on the system model and controller performance was validated with numerical simulation. The results indicate that the controller has good vibration suppression performance and makes the flexible rotor pass the first bending critical speed.

Robust Cascade Control for Chemical Reactors: An Approach based on Modelling Error Compensation

Abstract In this work, a robust model-based cascade control scheme for composition regulation in chemical reactors is proposed. The controller is based on a two loop control in a composition-temperature configuration. State-observers are introduced to provide robustness to the controller via the estimation of lumped model uncertainties. The second loop is introduced with a favorable choice of the Arrhenius equation as a virtual control input. The control design is illustrated based on two cases studies, a tubular reactor exhibiting two temperature dynamics (quasi-linear and hot-spot) and a CSTR presenting multiple steady-states. Numerical results indicate that proposed controller is robust in the face of external disturbances, operation changes, and model uncertainties.

RBF-ARX model-based robust MPC for nonlinear systems with unknown and bounded disturbance

Considering the unknown and bounded disturbance, a RBF-ARX model-based Robust Predictive Control (RBF-ARX-RPC) algorithm for output tracking control without relying on steady state knowledge is proposed for a class of smooth nonlinear systems. From the identified RBF-ARX model, a local linearization state-space model that considers the modeling error and bounded uncertain disturbance is obtained to represent the current behavior of the nonlinear system, and a polytopic uncertain linear parameter varying (LPV) state-space model is built to represent the future system's nonlinear behavior between the output deviation and input increment. Based on the two state-space models, a quasi-min–max robust MPC algorithm is designed for output tracking control of the nonlinear system under the unknown and bounded disturbance, which does not rely on steady state knowledge. Optimization problem of the RBF-ARX-RPC algorithm is finally converted to a convex linear matrix inequalities (LMIs) optimization problem, and the stability is guaranteed by the use of parameter-dependent Lyapunov function and feasibility of the LMIs. The comparative experiments demonstrate the effectiveness of the proposed RBF-ARX-RPC strategy on a continuously stirred tank reactor (CSTR) simulator.

Uncertain T-S model-based robust controller design with [formula omitted]-stability constraints—A simulation study of quadrotor attitude stabilization

The problem of the attitude stabilization of a quadrotor unmanned aerial vehicle is considered in simulation. An uncertain-like Takagi–Sugeno model of the quadrotor, where the nonlinear entries which depend on the input motor voltages are reported in uncertainties, is proposed to avoid closed-loop algebraic loops. The design of a Parallel Distributed Compensation (PDC) control law is considered with D-stability constraints in order to improve the closed-loop transient response. In this context, new generic and relaxed Linear Matrix Inequality (LMI) conditions are proposed. These new PDC controller design conditions constitute an alternative to previously proposed D-stabilizing non-PDC controller ones. Indeed, non-PDC controllers require online inversions of time-varying matrices, which is a major drawback for embedded applications with low computational capabilities. The conservatism of the proposed LMI conditions with respect to previous results is illustrated through an academic example. Then, simulations of the quadrotor with usual prescribed LMI regions are proposed to show the effectiveness of the proposed conditions.

Bilinear Approximate Model-Based Robust Lyapunov Control for Parabolic Distributed Collectors

This brief addresses the control problem of distributed parabolic solar collectors in order to maintain the field outlet temperature around a desired level. The objective is to design an efficient controller to force the outlet fluid temperature to track a set reference despite the unpredictable varying working conditions. In this brief, a bilinear model-based robust Lyapunov control is proposed to achieve the control objectives with robustness to the environmental changes. The bilinear model is a reduced order approximate representation of the solar collector, which is derived from the hyperbolic distributed equation describing the heat transport dynamics by means of a dynamical Gaussian interpolation. Using the bilinear approximate model, a robust control strategy is designed applying Lyapunov stability theory combined with a phenomenological representation of the system in order to stabilize the tracking error. On the basis of the error analysis, simulation results show good performance of the proposed controller, in terms of tracking accuracy and convergence time, with limited measurement even under unfavorable working conditions. Furthermore, the presented work is of interest for a large category of dynamical systems knowing that the solar collector is representative of physical systems involving transport phenomena constrained by unknown external disturbances.

TS fuzzy robust L1 control for nonlinear systems with persistent bounded disturbances

In this paper, a novel technique for Takagi–Sugeno (TS) model-based robust L1 controller design of nonlinear systems is proposed. Two synthesis methods based on quadratic and non-quadratic Lyapunov functions are considered. To design the robust stabilizing controller, a new approach for deriving sufficient conditions associated with the L1 performance criterion in terms of strict linear matrix inequality is proposed. This novel technique results in less pre-chosen scalar design variables and calculation burden. Furthermore, deriving the controller synthesis conditions via a non-quadratic Lyapunov function (NQLF) relaxes the obtained conditions. Therefore, the proposed approaches not only efficiently minimize the effect of persistent bounded disturbance, but also are applicable for wider classes of TS systems. Furthermore, some new lemmas are proposed to facilitate strict LMI formulation and to provide more degrees of freedom. Finally, several numerical and practical examples are presented to show the merits of this paper.

Model-based Robust Adaptive Control for Power-generating Systems in the Presence of Long Time Delay

This paper proposes a model-based robust adaptive control (MB-RAC) which is derived from the L1 robust adaptive control (L1-RAC). By inheriting excellent control performance from the L1-RAC for systems with nonlinearity and uncertain conditions, the MB-RAC offers its own feature for dealing with a long time delay by using dual-feedback adaptive law from the built-in model and the plant. A nonlinear boiler-turbine-generator unit augmented with time delays is adopted as the plant for verifying the MB-RAC. Simulation results present good control performances of the MB-RAC in a wide-range load-following process with long time delays and show its strong robustness to inner model mismatches from the plant on both dynamics and time delays. The MB-RAC is shown to be reliable and easy to implement for industrial processes.