Robust Control Theory Research Articles

Wireless stepper motor control and optimization based on robust control theory

<img src="blob:http://ijra.iaescore.com/f3842e5c-715f-4e1e-9ffd-952309f5ccb1" alt="" />Stepper motors are broadly utilized in actual systems, which are marked by non-linear parameters such as internal, external noises and uncertainties from wireless network. As well, a suitable controller is required when the problem is to track the target signal. In this paper, robust controller based on model reference are investigated to wireless control and optimize position and time in stepper motors. The core impression to build a robust controller is to use a model reference control system. Furthermore, simulations are implemented to control stepper motor position and time in two cases: first, when the wireless network without any delay and packet dropout. Second, uncertain equations when the wireless network with time delays and packet dropout. Simulation results demonstrate that proposed controller has achieved and enhanced the performance in tracking and robustness.

Quantum robust control theory for Hamiltonian and control field uncertainty* *Part of this work was carried out while RC was Professor of Chemical Engineering in the Center for Advanced Process Decision Making at Carnegie Mellon University.

Quantum robust control—which can employ fast leading order approximations, slower but more accurate asymptotic methods, or a combination thereof for quantification of robustness—enables control of moments of quantum observables and gates in the presence of Hamiltonian uncertainty or field noise. In this paper, we present a generalized quantum robust control theory that extends the previously described theory of quantum robust control in several important ways. We present robust control theory for control of any moment of arbitrary quantum control objectives, introducing moment-generating functions and transfer functions for quantum robust control that generalize the tools of frequency domain response theory to quantum systems, and extend the Pontryagin maximum principle for quantum control to control optimization in the presence of noise in the manipulated amplitudes or phases used to shape the control field. To provide guidelines as to the types of quantum control systems and control objectives for which asymptotic robustness analysis is important for accuracy, we introduce methods for assessing the Lie algebraic depth of quantum control systems, and illustrate through examples drawn from quantum information processing how such accurate methods for quantification of robustness to noise and uncertainty are more important for control strategies that exploit higher order quantum pathways. In addition, we define the relationship between leading order Taylor expansions and asymptotic estimates for quantum control moments in the presence of Hamiltonian uncertainty and field noise, and apply such leading order approximations to significant pathways analysis and dimensionality reduction of asymptotic quantum robust control calculations, describing numerical methods for implementation of these calculations.

Analysis of a generalised expectation–maximisation algorithm for Gaussian mixture models: a control systems perspective

The expectation–maximisation (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyse a generalised EM (GEM) algorithm in the context of Gaussian mixture models, where the maximisation step in the EM is replaced by an increasing step. We show that this GEM algorithm can be understood as a linear time-invariant (LTI) system with a feedback nonlinearity. Therefore, we explore some of its convergence properties by leveraging tools from robust control theory. Lastly, we explain how the proposed GEM can be designed and present a pedagogical example to understand the advantages of the proposed approach.

Concise Robust Control of the Nonlinear Ship in Course-Keeping Control

Most of the existing nonlinear ship course-keeping control systems are designed with the Nomoto model, which solely considers the yawing of the ship with only one Degree of Freedom (DOF), and it does not consider the coupling between the longitudinal and the lateral velocity of the ship. In this paper, a nonlinear ship course controller design method that can be used in a nonlinear coupled model was proposed. A stable nonlinear ship course controller with anti-wind and anti-wave interference was constructed based on the Lyapunov stability principle and robust control theory, which can be used in the course control of autopilot in the case of wind and waves. In this method, the coupling among the longitudinal and lateral velocity as well as yawing of the ship was considered. The simulation results showed that the method can not only effectively control the ship’s course but also can track the dynamic course effectively. At the same time, compared with the PID control method based on backstepping, the steering angle of the rudder angle of our method is smaller and the wear and tear of steering gear will be smaller.

Inverse Optimal Robust Adaptive Controller for Upper Limb Rehabilitation Exoskeletons With Inertia and Load Uncertainties

We propose a robust adaptive controller for the safe and accurate trajectory tracking control of upper limb rehabilitation exoskeletons. The proposed controller can adapt to the inertia and load uncertainties, and compensate for their effects. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> robustness of the controller in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_2$</tex-math></inline-formula> perturbation/disturbance attenuation is realized by nonlinear robust control theory via inverse optimality. We mathematically prove the asymptotic stability and optimality of the controller by stabilizing a Lyapunov function and minimizing a meaningful cost function, respectively. We then demonstrate the performance of the controller with the simulations of two different exoskeleton control systems. The results show that the controller can identify and compensate for model uncertainties, and realize good tracking performance in the presence of perturbations and disturbances. These qualities are crucial to the reliability and safety of exoskeleton operations. In addition to rehabilitation exoskeletons, the proposed framework can also be applied to the control of other multibody robotic systems.

A Discrete-Time Robust Adaptive PI Controller for Grid-Connected Voltage Source Converter with LCL Filter

In this work, it is presented a new direct discrete-time robust adaptive PI (Proportional Integral) Controller for grid-injected current control loop of a voltage source converter with LCL filter. The mathematical background is based on Robust Model Reference Adaptive Control theory. However, the proposed controller is straightforward, it does not need a reference model and has capability to track directly currents reference. This approach simplifies significantly controller design, resulting in a reformulation of parameters vector used for adaptation of adjustable gains. It turns the controller robust to unmodelled dynamics, while avoid the complexity inherent to the conventional high order adaptive controllers for grid-connected power systems. Besides, it is highlighted that proposed controller does not need resonant controllers for grid disturbance rejection, or require any knowledge of grid parameters, lines impedance or load power demand. Also, due to its simple structure, it is easily implemented and does not require a high processing capacity. Furthermore, the effectiveness of the control strategy in terms of reference tracking, harmonics content and robustness to the grid impedance variation is corroborated through experiments.

Low-Order Passivity-Based Robust Current Control Design for Grid-Tied VSCs

This article presents a systematic robust current control design approach for three-phase voltage-source converters. Robustness is guaranteed by combining intrinsic passive properties of the impedance uncertainty at the point of common coupling together with stability results from a passivity-based control theory. This approach ensures stability against typical uncertainty sources at mid and high frequencies, such as cable resonances or other converters interaction, with significant less conservative performances than the obtained with the traditional robust control theory. The approach uses multiobjective controller synthesis formulation that allows us to logically combine robustness requirements with performance objectives avoiding heuristic iteration over the control structure and parameters. The controller synthesis is performed by means of a nonsmooth <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> optimization technique that tunes all free parameters of a vector-based controller function, which constraints its structure. This results in a synthesized controller with lower order than those obtained with convex optimization definitions of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> control problem. The design methodology is validated in time and frequency domain by means of theoretical analysis and experimental results with three usual grid filters: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL,</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLCL</i> .

Estimating robustness

I estimate and evaluate a model with a representative agent who is concerned that the persistence properties of her baseline model of consumption and inflation are misspecified. Coping with model uncertainty, she discovers a pessimistically biased worst-case model that dictates her behavior. I combine interest rates and aggregate macro series with cross-equation restrictions implied by robust control theory to estimate this worst-case distribution and show that (1) the model's predictions about key features of the yield curve are in line with the data, and (2) the degree of pessimism underlying these findings is plausible. Interpreting the worst-case as the agent's subjective belief, I derive model implied interest rate forecasts and compare them with analogous survey expectations. I find that the model can replicate the dynamics and average level of bias found in the survey.

A performance region‐based approach to the leader‐following consensus of nonlinear multiagent systems

AbstractThe communication network is usually susceptible to effective communication channel capacity variation and transmission imperfections, which renders the connection among networked agents unstable. Motivated by this fact, we assume that the communication graphs are Markovian randomly switching, because the Markovian chain process is commonly employed to describe the network subject to Rayleigh fading channel. Under such a communication connection assumption, this article investigates the globally leader‐following consensus control problem for grouped agents with nonlinear dynamics. Different nonlinear dynamics, including Lur'e and Lorenz‐type chaotic systems, are considered. By using the tools from the robust control theory, the conditions guaranteeing the globally leader‐following consensus are derived. Under such conditions, consensus control protocols can be designed solely based on the relative state information transmitted over the communication network, by solving some linear matrix inequalities. Then, we characterize the robustness of the controlled systems against the variation of the communication graphs with the globally leader‐following consensus performance region. It is theoretically shown that the networked nonlinear systems under the proposed controller yield unbounded and connected robust performance regions. Finally, the theoretical results are verified by conducting numerical simulations on networks consisting of Chua's oscillators and Lü systems.

Methods for adaptive control of objects with variable parameters

The work uses the method of standard characteristic polynomials, based on the Lyapunov theorem on adaptive control systems, the theory of flexible and robust control, methods of the theory of nonlinear systems. When modeling an internal combustion engine, methods of identification theory were additionally involved. When obtaining theoretical results, the method of Lyapunov functions, the method of standard characteristic polynomials, methods of the theory of adaptive and robust control, methods of the theory of nonlinear systems were used. When constructing a model of an internal combustion engine, methods of identification theory were additionally involved. For the synthesis of control systems in conditions of uncertainty, one of the topical directions is adaptive systems. These are control systems that compensate for parametric, signal, functional, or structural uncertainties of the control object by automatically adjusting the controller during the system's working operation, i.e., adaptive systems make up for the lack of a priori information about the control object during operational operation. To solve the problem of managing undefined objects, for example, classical methods are used. In such methods, when state variables are immeasurable, it becomes necessary to use additional dynamic filters. Classical methods are more often used for a limited class of objects. In the case of class extension, the structure of the control algorithm becomes more complicated.

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 the effect of model uncertainty on the Hopf bifurcation of aeroelastic systems

This paper investigates the effect of model uncertainty on the nonlinear dynamics of a generic aeroelastic system. Among the most dangerous phenomena to which these systems are prone, Limit Cycle Oscillations are periodic isolated responses triggered by the nonlinear interactions among elastic deformations, inertial forces, and aerodynamic actions. In a dynamical systems setting, these responses typically emanate from Hopf bifurcation points, and thus a recently proposed framework, which address the problem of robustness from a nonlinear dynamics viewpoint, is employed. Briefly, the notion of robust bifurcation margin extends the concept of mu analysis technique from the robust control theory. The main contribution of this article is a systematic investigation of the numerous scenarios arising in the study of nonlinear flutter when uncertainties in the model are accounted for in the analyses. The advantages of adopting this framework include the possibility to: quantify relevant information for the determination of the nonlinear stability envelope; gain a more in-depth understanding of the physical mechanisms triggering subcritical and supercritical Hopf bifurcations; and reveal properties of the nominal system by identifying isolated branches not straightforward to detect with conventional numerical approaches.

Constrained H∞ Consensus of Second-Order Discrete-Time Multi-Agent Networks With Nonconvex Velocity Constraints

This paper addresses the constrained H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus of second-order discrete-time multi-agent systems with nonconvex velocity constraints and external disturbances over a directed network. A novel nonlinear distributed control law is proposed to enable all agents converge to an agreement cooperatively while their velocities remain in different nonconvex constraint sets. To measure the effect of external disturbances on consensus, a nonlinear H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> output function is introduced via maximum and minimum functions. By a model transformation, the original closed-loop system is changed into an equivalent one. And then, the convergence analysis and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance analysis are completed by utilizing Lyapunov stability theory and robust control theory. In addition, the sufficient constrained H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus conditions are deduced in the form of matrix inequalities under the assumption of strong connectivity of directed network. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Robust Control Theory Based Stability Certificates for Neural Network Approximated Nonlinear Model Predictive Control

Abstract Model predictive control requires the real-time solution of an optimal control problem, which can be challenging on computationally limited systems. Approximating the solution such as by neural networks or series expansions, or deriving an explicit solution, can overcome this challenge. Using neural networks for approximation, a question arises as to how to guarantee closed-loop safety and stability. We use robust control theoretic tools to provide stability guarantees using a neural network trained to approximate a model predictive controller. Notably, the model predictive controller, which might offer desirable closed-loop performance, is not required to provide provable stability properties. To provide stability guarantees for the neural network approximated controller, the closed-loop system is reformulated as a diagonal nonlinear differential form, exploiting that the neural network activation functions are sector bounded and that their slopes are globally bounded. Based on this representation, we establish sufficient closed-loop stability conditions in form of linear matrix inequalities for the nominal and the disturbed system using the neural network approximated model predictive controller.

Robust Divided Differences Gaussian Mixture Non Linear Filtering Applied to INS/GNSS Integrated Navigation System with Impulsive Measurement Noise

In this paper, robust INS/GNSS is designed to solve specific problem of non linear time variant state space estimation with non Gaussian measurement noise based on parallel divided difference filtering. Non linear approximation techniques such as Extended Kalman filter EKF, Interpolation Non Linear Filters called DD1 and DD2 are computed. Great comparisons are conduced and criticized in order to confirm and compare some different robust techniques explored in literature. The most tested noise in robust control and estimation theory has been simulated and disturbed GPS+GLONASS signals. Three parallel modified algorithms are simulated and compared with robust and modified forms of the same algorithms based on Root Mean Square Error RMSE Criteria.

ANALYSIS AND VERIFICATION OF THE OPERATION OF THE STABILIZING ROBUST CONTROLLER'S ELECTRICAL CIRCUIT OF THE ROTOR FLUX-LINKAGE CONTROL SYSTEM

On the basis of the classical theory of robust control, the theory of stability and the theory of continued fractions, the linearized mathematical model, the procedure for calculating and designing an analog electrical circuit of the H∞-suboptimal robust controller of the flux-linkage control system of the rotor of an asynchronous electric drive, protected by Ukrainian Patent no.137157, were built. The circuit contains three operational amplifiers, several resistors and capacitors. The proposed mathematical model, the procedure for calculating and choosing the parameters of the resistors and capacitors of the circuit take into account the random variations of the object and the controller within the specified boundaries. An analytical relationship between the transfer function coefficients and the resistances of the resistors and the capacitances of the capacitors of the controller's electrical circuit was established. On a specific example, by calculation according to the developed algorithm, the limiting values of the tolerances of the circuit's resistances of the resistors and capacitances of the capacitors were identified and these values were selected with a margin from the standard series. Analysis of noise filtering by the electrical circuit of the controller in the Multisim package shows its insensitivity to noise spreads within fairly wide boundaries.

Fast Real-Time Reinforcement Learning for Partially-Observable Large-Scale Systems

We propose a fast real-time reinforcement learning (RL) control algorithm for large-scale partially-observable linear dynamic systems. We first develop a one-shot RL method for designing model-free optimal controllers based on a finite-time history of the inputs and the outputs. However, when the system dimension is large, this method may suffer from a long learning time. To overcome this problem, in the second half of the paper we introduce a new notion of approximation to the design, where the original set of input-output history is replaced by a much shorter set. We show that this approximation can lead to a nearly optimal controller that is based on a lower-dimensional approximant of the original system in terms of reachability and observability. We provide a guideline for determining an appropriate length of the input-output history to reduce the suboptimality gap. The dimension of the resulting suboptimal controller is far less than that of the optimal controller, thereby speeding up learning time. The learned controller, however may cause instability when implemented in the original high-dimensional system by adversely exciting the approximation error. We theoretically establish the conditions for closed-loop stability using robust control theory, followed by numerical investigations of the trade-offs between learning time, length of input/output history, and closed-loop performance. The effectiveness of the method is illustrated using examples from electric power systems, modeled by partially-observable nonlinear differential-algebraic equations.

Design of a robust controller for a rotary motion control system: disturbance compensation approach

This paper proposes a design of a robust controller for a rotary motion control system that includes a PID controller, a disturbance observer, and a friction compensator. Friction force versus angular velocity has been measured, and viscous, Coulomb friction and stiction components have been identified. With nominal PID (proportional- integral-derivative) controller, we have observed adverse effects due to friction such as excessive steady-state errors, oscillations, and limit-cycles. By adding a friction model as an augmented nonlinear dynamics of a plant, we are able to conduct a simulation study of a motion control system that matches very well with experimental results. The disturbance observer (DOB) based on simple and effective robust control theory has been implemented to make the rotary motion control system “robust” against inertia/load variations, external torque disturbances, and some of friction forces. Further performance enhancement of the DOB-based robust motion control system has been achieved by adding the friction compensator and experimentally verified.

Advanced aeroelastic robust stability analysis with structural uncertainties

Robust flutter analysis described in this paper is based on the robust control theory framework. Therefore, a time-domain linear fractional transformation representation of the perturbed aeroelastic system is modeled. Then, the robust stability is analyzed by means of the structured singular value mu, which is defined as an alternative measure of robustness. Robust flutter analysis deals with aeroelastic (or aeroservoelastic) stability analysis taking structural dynamics, aerodynamics and/or unmodeled system dynamics uncertainties into account. Flutter is a well-known dynamic aeroelastic instability phenomenon caused by an interaction between structural vibrations and unsteady aerodynamic forces, whereby the level of vibration may trigger large amplitudes, eventually leading to catastrophic failure of the structure. The primary motivation of the robust flutter analysis is that this method allows the computation of the worst-case flutter velocity which can support, for example, the flight test program by a valuable robust flutter boundary. This paper addresses the issue of an approach for aeroelastic robust stability analysis with structural uncertainties with respect to physical symmetric and asymmetric stiffness perturbations on the wing structure by means of tuning beams.

Gain‐phase information based robust control theory

SummaryThis article presents new approaches for analyzing and designing the robust control system by using both the gain and phase information. These approaches aim to relax the stability condition and further improve the system performance than the H∞‐robust control theory. The contributions of this article are: (i) to propose a new gain‐phase (GP‐) robust stability theorem which can further relax the stability condition than the small‐gain theorem by using both the gain and phase information of uncertainty, (ii) to propose a new GP‐mixed sensitivity problem which can further improve the system performance than the mixed sensitivity method by using the GP‐robust stability theorem instead of the small‐gain one, (iii) to develop the WΩ‐K iteration algorithm to solve the GP‐mixed sensitivity problem and to verify the effectiveness of the proposed method through the design example of automotive fuel control system, and (iv) to formulate a new Ψ‐control problem with phase optimality criterion and an H∞/Ψ‐mixed control problem with both the gain and phase optimality criteria, to derive their solution for SISO output feedback systems and to show their effectiveness through two design examples.