Closed-loop Control Performance Research Articles

Cooperative Control and Performance Evaluation of a Linear MIMO Parabolic Spatiotemporal Dynamic System on Directed and Switching Topologies.

The current work concerns on cooperative control of exponential stabilization and control performance improvement in the spatial domain for a linear spatiotemporal dynamic system associated with multiple control actuators and multiple collaborative measurement sensors. By assuming that the system dynamics is modeled by a MIMO parabolic partial differential equation (PPDE) and each sensor can share measurement information with its topological neighbors in directed and switching topological networks, a cooperative control protocol is proposed to achieve the control aim of this article. With the help of a combination of multiagent consensus theory, Lyapunov's method, and integral inequality technique, sufficient conditions are presented for the closed-loop exponential stability of the PPDE in the norm |·|2 . Moreover, some performance indexes are defined to evaluate the closed-loop control performance improvement in the spatial domain. Extensive simulation results are finally presented for a simple numerical example and a practical heat treatment process to verify the effectiveness and performance improvement capability of the proposed cooperative control protocol.

FI-NPI: Exploring Optimal Control in Parallel Platform Systems

Typically, the current and speed loop closure of servo motor of the parallel platform is accomplished with incremental PI regulation. The control method has strong robustness, but the parameter tuning process is cumbersome, and it is difficult to achieve the optimal control state. In order to further optimize the performance, this paper proposes a double-loop control structure based on fuzzy integral and neuron proportional integral (FI-NPI). The structure makes full use of the control advantages of the fuzzy controller and integrator to improve the performance of speed closed-loop control. And through the feedforward branch, the speed error is used as the teacher signal for neuron supervised learning, which improves the effect of current closed-loop control. Through comparative simulation experiments, this paper verifies that the FI-NPI controller has a faster dynamic response speed than the traditional PI controller. Finally, in this paper, the FI-NPI controller is implemented in C language in the servo-driven lower computer, and the speed closed-loop test of the BLDC motor is carried out. The experimental results show that the FI-NPI double-loop controller is better than the traditional double-PI controller in performance indicators such as convergence rate and RMSE, which confirms that the FI-NPI double-loop controller is more suitable for BLDC servo control.

Extracorporeal Blood Pump Driven by a Novel Bearingless Split-Tooth Flux-Reversal Motor

This article describes a novel bearingless split-tooth flux-reversal motor with integrated centrifugal blood pump. This motor has a magnet-free rotor and is capable of operating at up to 3000 r/min with up to 100 mN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\cdot$</tex-math></inline-formula> m torque. The motor also has 50 N radial force capability for centering the rotor. The motor rotor is 50 mm diameter, housed in a 170 mm wide stator. The motor has a novel magnetic configuration, wherein the force generation is independent of the rotor angle. This allows simple radial force generation using stator-fixed currents. The motor torque is generated using commutated two-phase currents. The finite-element simulations are used to optimize the design in order to achieve sufficient radial force and motor torque while minimizing cogging torque. The design also achieves an axial passive magnetic stiffness of 5.4 N/mm, which is the constraint on axial motions of the rotor. This article includes mechanical design and fabrication details as well as experimental closed-loop levitation and speed control performance. With an integrated impeller, the rotor and the centrifugal pump are tested by pumping fluid in a closed circuit to obtain experimental pressure–flow curves with impeller-limited performance.

Application of self-improving Q-learning controller for a class of dynamical processes: Implementation aspects

This paper deals with a practical application of the Q-learning algorithm as a general-purpose self-improving controller operating in a class of industrial closed-loop control systems. The proposed approach solves a practical control engineering problem by designing a controller that starts its operation with the predefined closed-loop control performance and then, without unnecessarily disturbing the normally operated closed-loop system, it learns on-line from interactions with the controlled process to ensure the gradual improvement in the closed loop control performance until this performance reaches a desired user-defined level. It is proposed how to ensure its initial performance by an appropriate initialization of the Q-matrix without assuming any knowledge about the process model. The desired target closed-loop performance is defined by the first-order reference trajectory that should be preserved by the closed-loop system, which requires determining the current state of the closed-loop system by the values of the control error and its time derivative. The novelty of the proposed approach results from: (i) preserving the first order reference trajectory with reduced dimensions of the Q-matrix to two, which significantly reduces memory and computational requirements without any loss of generality, (ii) proposing a method for a reduction of the number of states designed directly for the proposed approach, and (iii) proposing a method for a very convenient initialization of the Q-matrix based only on the tunings of the existing PI controller. All these features bring the proposed approach closer towards practical applications. Results of the simulation and experimental validation show that the proposed Q-learning controller can substitute the existing PI controller bumplessly and provides a gradual improvement in the closed loop performance due to its online learning abilities.

Learning for Depth Control of a Robotic Penguin: A Data-Driven Model Predictive Control Approach

For bionic underwater robots, it is a great challenge for depth control due to model uncertainty and strong nonlinearity. To this end, we propose a data-driven model predictive control (MPC) approach using reinforcement learning (RL) for robotic penguin depth control. First, by imitating the underwater mode of the biological penguin, a robotic prototype with a tendon-driven head, two degrees of freedom wings, and a tendon-driven tail was designed. Then, a data-driven MPC framework is proposed considering the structure and motion properties of the robotic penguin. Specially, a data-based learning environment is constructed using a motion capture system, computational fluid dynamics, and a back-propagation neural network. Meanwhile, to maximize the benefits of the controller while ensuring safety and stability, a data-driven MPC using the RL scheme is applied to approximate the optimal policy. Combined with an appropriate reward design and periodic training, the closed-loop controller performance is significantly improved, and the validity of the proposed framework is finally tested by extensive simulations and experiments. Notably, this work will provide valuable insights into the learning-based motion control of bionic underwater robots.

Flexible operation of Post-combustion CO2 capture process enabled by NARX-MPC using neural network

Post-combustion CO2 capture (PCC) process is expected to serve as the role of a bridge solution during the transition from fossil-based to renewable energy, but extensive energy consumption is a significant hurdle to its widespread commercial adoption. Operating a PCC process economically often requires large operating condition changes in response to power plant load changes and time-varying energy prices. The ‘flexible’ operation requires a controller that aids in such a dynamic operating environment of the PCC process. To balance model complexity with prediction accuracy, we adopt NARX-MPC which employs a neural network-based NARX model as a prediction model for MPC. Under various dynamic operation scenarios, the proposed NARX-MPC is evaluated and compared with a linear MPC (LMPC) controller. Our observations indeed reveal that the NARX-MPC delivers significantly superior closed-loop control performance over the LMPC, especially in scenarios involving large changes in the power plant load or inlet flue gas flow rate and simultaneous changes in the flue gas flow rate and the CO2 capture rate.

Nonlinear Functional Observer Design for Robot Manipulators

In this paper, a nonlinear functional observer (NFO) is first proposed for the control design of robot manipulators under model uncertainties, external disturbances, and a lack of joint velocity information. In principle, the proposed NFO can estimate not only lumped disturbances and uncertainties but also unmeasurable joint velocities, which are then fed back into the main controller. Compared to the well-known ESO design, the proposed NFO has a simpler structure, more accurate estimations, and less computational effort, and consequently, it is easier for practical implementation. Moreover, unnecessary observations of joint displacements are avoided when compared to the well-known extended state observer (ESO). Based on the Lyapunov theory, globally uniformly ultimately bounded estimation performance is guaranteed by the proposed NFO. Consequently, it is theoretically proven that the estimation performances of the NFO are better than those of the ESO. Simulations with a two-degree-of-freedom (2-DOF) robot manipulator are conducted to verify the effectiveness of the proposed algorithm in terms of not only the estimation performance but also the closed-loop control performance.

Toward Reducing Undesired Rotation Torque in Maglev Permanent Magnet Synchronous Linear Motor

The dq current transformation method can be used to achieve the drive control of the maglev permanent magnet synchronous linear motor (MPMSLM). Specifically, the control of the suspension force Fz can be achieved by controlling the d-axis current, and the control of the thrust force Fx can be achieved by controlling the q-axis current. However, the direct use of the dq current transformation method on traditional MPMSLM structures produces an additional rotation torque around the y-axis. In order to reduce this additional torque, a new MPMSLM structure is proposed in this work. First, the characteristics of additional torque through finite element analysis are analyzed. Second, the Halbach permanent magnet array and coil size are optimized, and the topology of the MPMSLM coil is designed to reduce the additional torque. The decoupling performance and current of the proposed MPMSLM are experimentally verified through open-loop experiments using finite element simulation software. Finally, the decoupling algorithm of the generalized inverse matrix is used to achieve the decoupling between forces Fx and Fz and torque Ty and the d-axis and q-axis currents in each drive unit. Based on this, a three-degree-of-freedom closed-loop control system of the MPMSLM is designed. The LabVIEW 2018 software is used for the simulation analysis of the three-degree-of-freedom MPMSLM motion control system, and the results show that the proposed motor structure has superior closed-loop control performance.

A Tool for Control Research Using Evolutionary Algorithm That Generates Controllers with a Pre-Specified Morphology

In control research and design it is frequently necessary to explore, evaluate, tune and compare many control strategies. These activities are assisted by software tools of increasing complexity; however, even with the existing high performance tools these activities are very time consuming due to they imply hundred if not thousand of simulations. If the process of doing such simulations is not automated it can be a very time consuming task. There has been proposed evolutionary algorithms (EA) that in the search for an optimal control automatically generate many control structures. However, the space of possible controllers for any dynamical system is huge. Hence it is mandatory to restrict the search space. The best way to restrict the controller search space is to let the designer influence the search direction. In this paper we propose a software tool for control research that has as its main part an EA that produce only controllers having a pre-specified morphology. By specifying a controller morphology the designer can influence the search direction without losing the exploration capability of evolutionary algorithms. The EA is endowed with a cost function tailored for fast evaluation of closed-loop controller performance. The use of the tool is illustrated by searching an sliding mode and similar controllers for an unstable linear and two nonlinear systems.

Rigid-Body Noncertainty Equivalence Adaptive Control on the Tangent Bundle of SE(3)

This paper addresses an adaptive rigid-body pose-tracking control problem with unknown system parameters. The proposed control is based on a noncertainty equivalence (NCE) adaptive principle applied to the configuration manifold of rigid-body motion, i.e., special Euclidean group SE(3), and its tangent bundle TSE(3). The controller drives the system to follow an arbitrary reference trajectory with bounded time derivatives. The system states are composed of the elements of SE(3), consisting of rotations and translations, and the six-dimensional vector of angular and translational velocities in Euclidean space. Almost-global-asymptotic stability of the system is demonstrated using a Morse–Lyapunov stability analysis. Then, the performance of the proposed controller is verified and is compared to the results obtained by a certainty-equivalence (CE) adaptive control applied to exponential coordinates associated with the linear space of the Lie algebra . It is shown that the TSE(3)-based NCE adaptive control design can eliminate the performance degradation due to the cancellation of uncertain parameter effects that would otherwise appear when the CE adaptive controller is used. As a result, the proposed NCE-based adaptive pose-tracking controller recovers the closed-loop pose-tracking controller performance with the system parameters fully known to the controller.

Ultrasound Imaging-Based Closed-Loop Control of Functional Electrical Stimulation for Drop Foot Correction

Open-or closed-loop functional electrical stimulation (FES) has been widely investigated to treat drop foot syndrome, which is typically caused by weakness or paralysis of ankle dorsiflexors. However, conventional closed-loop FES control mainly uses kinematic feedback, which does not directly capture time-varying changes in muscle activation. In this study, we explored the use of ultrasound (US) echogenicity as an indicator of FES-evoked muscle activation and hypothesized that including US-derived muscle activation, in addition to kinematic feedback, would improve the closed-loop FES control performance compared to the closed-loop control that relies only on the kinematic feedback. A sampled-data observer (SDO) was derived to continuously estimate FES-evoked muscle activations from low-sampled US echogenicity signals. In addition, a dynamic surface controller (DSC) and a delay compensation (DC) term were incorporated with the SDO, denoted as the US-based DSC-DC, to drive the actual ankle dorsiflexion trajectory to the desired profile. The trajectory tracking error convergence of the closed-loop system was proven to be uniformly ultimately bounded based on the Lyapunov–Krasovskii stability analysis. The US-based DSC-DC controller was validated on five participants with no disabilities to control their ankle dorsiflexion during walking on a treadmill. The US-based DSC-DC controller significantly reduced the root-mean-square error of the ankle joint trajectory tracking by 46.52% <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 7.99% ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p&lt;0.001$</tex-math> </inline-formula> ) compared to the traditional DSC-DC controller with only kinematic feedback but no US measurements. The results also verified the disturbance rejection performance of the US-based DSC-DC controller when a plantarflexion disturbance was added. Our control design, for the first time, provides a methodology to integrate US in an FES control framework, which will likely benefit persons with drop foot and those with other mobility disorders.

Predictive control of networked control system with event-triggering in two channels

Event-triggered communication is often desired in a networked control system to reduce the high-rate of data transfer through the network. This work employs event-triggering in both the feedback and forward channels yet retaining the closed-loop control performances through predictive control. The predictive controller not only takes care of the information loss due to the event-triggering but also the delays and packet dropouts caused by the communication network. A comparison of the effect of using event-triggering in the feedback channel alone and using event-triggering in both the feedback and forward channels is presented that shows to yield comparable performances even though event-triggering is used in both the channels.

Data-driven docking control of autonomous double-ended ferries based on iterative learning model predictive control

In large cities with harbors or rivers, ferry services have been a crucial part of public transport. Docking refers to the process of maneuvering a ferry to the designated mooring position by the quayside. To facilitate the transition towards increased autonomy in ferries, this paper proposes an iterative learning-based model predictive control (IL-MPC) strategy for the automatic docking of over-actuated double-ended ferries, in situations in which the hydrodynamic coefficients of a ferry are unknown. It uses the collected data from actual ferry docking operations or reliable simulations to build ferry states prediction model in a linear state-space form based on kernel regression, which reduces the model-solving complexity in MPC. Moreover, it improves its closed-loop control performance and modeling accuracy via an iterative learning scheme. The excitation control input signals have been optimized to create suitable initial data sets. Simulations are carried out considering three docking position types and results show that the open-loop prediction accuracy has been improved with the optimized excitation input signal and that closed-loop control performance has been enhanced with the increase of iterations.

Dynamic Operability Analysis for Process Design and Control of Modular Natural Gas Utilization Systems.

Process modularization is an alternative process design and construction framework, in which modular units are independent and replaceable blocks of a process system. While modular plants have higher efficiency and are safer to construct than conventional stick-built plants (Roy, S. Chem. Eng. Prog. 2017, 113, 28-31), they are significantly more challenging to operate because of the loss in the control degrees of freedom that comes with process integration and intensification (Bishop, B. A.; Lima, F. V. Processes 2021, 9, 2165). To address this challenge, in this work, operability analyses are performed to consider the design and operation of modular units. Initially, a steady-state operability analysis is employed to find a set of feasible modular designs that are able to operate considering different modular plant conditions. A dynamic operability analysis is then applied to the feasible designs to identify the operable designs that are capable of rejecting the operational disturbances. Lastly, a closed-loop control measure is introduced to compare the performances of the different operable designs. The proposed approach is implemented in a modular membrane reactor to find a set of operable designs considering different natural gas wells, and the respective closed-loop nonlinear model predictive control performance of these units is evaluated.

Modeling and Control of Electromagnetic Coil System Using Model Order Reduction-Based LSSVM Method*

Magnetic micro/nanorobot (MM) is promising for in-body therapy due to its advantage of untethered controllability. Since the motion of MMs can be directly manipulated by the magnetic field (MF) created by electromagnetic coil systems, it is essential to study the MF generation control methods. In this study, iron core-based solenoids are employed in an electromagnetic coil system that can produce a stronger MF than regular coil systems. However, the coil system presents hysteretic nonlinearity due to the iron core's coercivity, which degrades closed-loop control performances. To tackle this challenge, an effective hysteresis compensation method is developed to linearize the solenoid system. Specifically, the least squares support vector machine (LSSVM) is adopted to model the hysteretic behavior of the solenoid system, and the discrete empirical interpolation method (DEIM) is applied to reduce the complexity of the model for improving the calculation efficiency. Based on the LSSVM and DEIM approaches, a highly efficient LSSVM-DEIM hysteresis compensator is developed. In order to generate precise dynamic MF effectively, the LSSVM-DEIM hysteresis compensator is combined with prevalent feedback controllers to form composite control schemes. Experiments show that the control system with the LSSVM-DEIM hysteresis compensator can produce a more accurate MF compared with that of the benchmark control methods.

CONFIG: Constrained Efficient Global Optimization for Closed-Loop Control System Optimization with Unmodeled Constraints

In this paper, the CONFIG algorithm, a simple and provably efficient constrained global optimization algorithm, is applied to optimize the closed-loop control performance of an unknown system with unmodeled constraints. Existing Gaussian process based closed-loop optimization methods, either can only guarantee local convergence (e.g., SafeOPT), or have no known optimality guarantee (e.g., constrained expected improvement) at all, whereas the recently introduced CONFIG algorithm has been proven to enjoy a theoretical global optimality guarantee. In this study, we demonstrate the effectiveness of CONFIG algorithm in the applications. The algorithm is first applied to an artificial numerical benchmark problem to corroborate its effectiveness. It is then applied to a classical constrained steady-state optimization problem of a continuous stirred-tank reactor. Simulation results show that our CONFIG algorithm can achieve performance competitive with the popular CEI (Constrained Expected Improvement) algorithm, which has no known optimality guarantee. As such, the CONFIG algorithm offers a new tool, with both a provable global optimality guarantee and competitive empirical performance, to optimize the closed-loop control performance for a system with soft unmodeled constraints. Last, but not least, the open-source code is available as a python package to facilitate future applications.

Robust model-based switching MIMO air handling control of turbocharged lean-burn SI natural gas variable speed engines

This paper demonstrates a multiple-input multiple-output (MIMO) controller design framework and a controller switching algorithm for MIMO controllers in their state-space form, which together achieve robust, efficient control of turbocharged lean-burn engines over a wide operating space. The controller design framework requires a linearized plant model, and uses the [Formula: see text]-synthesis and DK-iteration algorithms while considering state and output uncertainties and actuator bandwidths to synthesize a robust [Formula: see text] controller. A controller switching methodology using slow-fast controller decomposition and also incorporating hysteresis at switching points is utilized to smoothly transfer control authority between several MIMO controllers. The approach is applied to a high-fidelity truth-reference GT-Power engine model for a lean-burn natural gas-fueled engine to evaluate the closed-loop controller performance. The multi-tracking control problem targets engine speed, differential pressure across throttle as well as air-to-fuel ratio to achieve satisfactory engine performance and emissions without compressor surge. The engine response obtained using the robust MIMO controller is compared with that obtained using a state-of-the-art benchmark controller to evaluate the additional benefits of the MIMO controller.

Using stochastic programming to train neural network approximation of nonlinear MPC laws

To facilitate the real-time implementation of nonlinear model predictive control (NMPC), this paper proposes a deep learning-based NMPC scheme, in which the NMPC law is approximated via a deep neural network (DNN). To optimize the DNN controller, a novel “optimize and train” architecture is designed, where the processes of data generation and neural network training are combined together to result in a single large-scale stochastic optimization problem. Unlike the conventional “optimize then train” approach, our proposed one directly optimizes the closed-loop performance of the DNN controller over a finite horizon for a number of initial states. The important features of our proposed scheme are that it can deal with set-valued optimal MPC input, and a probabilistic guarantee of constraint satisfaction can be concluded for the closed-loop system without simulating the DNN controller. With our proposed scheme, an increased number of training scenarios leads to improved constraint satisfaction of the derived DNN controller, which is not necessarily true for the “optimize then train” approach. Statistical approaches for validating closed-loop control performance are also discussed. Furthermore, computational methods are introduced to efficiently solve the resulting stochastic optimization problem. The effectiveness of the proposed scheme is extensively illustrated with several numerical simulations. Compared with the conventional “optimize then train” approach, our proposed approach exhibits better closed-loop constraint satisfaction for all considered case studies.

An algorithm for the selection of linearisation points in non-linear systems: a diesel air-path case study

One typical approach to implement model predictive control in relatively fast sample rate applications utilises linearised plant models to simplify the online optimisation problem in the presence of limited computation budget. A number of linearisation points may be used to account for the variation in the non-linear plant over the entire operating domain, leading to potential switched linear time-invariant (LTI) or linear time-variant (LTV) implementations. The choice of these linearisation points, and the regions over which they are considered valid, can have a significant impact on the closed loop performance of the overall controller. In this work, in the presence of a high-fidelity digital twin of a non-linear plant, a numerical algorithm for the selection of linearisation points is proposed. The approach makes use of the concept of disturbance sets to determine both the linearisation points and the domain to which each linearisation point applies. The use of disturbance sets provides an implicit connection to closed-loop controller performance if robust model predictive control algorithms are implemented. The proposed approach is implemented for the challenging problem of diesel air-path control, with simulation results on a high-fidelity mean value engine model used to demonstrate the efficacy of the approach.

Adaptive sliding mode fault-tolerant control for satellite attitude tracking system

In this paper, an adaptive modified sliding mode control approach is developed for attitude tracking of a nano-satellite with three magnetorquers and one reaction wheel. A sliding variable is chosen based on finite-time convergence of the nano-satellite attitude tracking error and avoiding the singularity of the control signal. The control gain of the proposed method is developed adaptively to reduce the tracking error and improve the closed-loop control performance. The sliding variable and adaptive parameter are also employed in the reaching phase of the control law to decrease the chattering phenomenon. In addition, the finite-time convergence of attitude variables in the presence of actuator faults, inertia uncertainty, and external disturbances is proved using the extended Lyapunov theorem. The simulations are conducted to evaluate the performance of the proposed method according to different evaluation criteria. Monte Carlo simulations are also used to survey the reliability of the system in the presence of the mentioned condition.