Robust Feedback Control Research Articles

Particle-Swarm-Optimization-Based 2D Output Feedback Robust Constraint Model Predictive Control for Batch Processes

For the input and output constraints and uncertainties in batch processes, a 2D output feedback robust constrained model predictive control (MPC) method is designed by combining iterative learning control (ILC), MPC and output feedback. Firstly, an equivalent 2D-FM closed-loop prediction model is established by combining with the proposed output feedback controller. Then an optimization performance index function with terminal constraint is constructed to study its control optimization. According to the designed optimization performance index and Lyapunov stability theory, the feasible MPC problem is obtained by solving the linear matrix inequalities (LMIs). At the same time, the gain of the new output feedback control law is given to ensure that the performance index reaches the minimum upper bound under the constraints of input and output. In order to solve the manual adjustment problem of some parameters in the performance index function, the particle swarm optimization (PSO) algorithm is introduced, and a better solution is found near the controller by using the search optimization method. Finally, taking the injection molding process as an example and comparing with the existing method without using PSO algorithms, it is proved that the above method is more feasible.

Robust MPC for Systems With Model Uncertainties and Measurement Outliers

This paper considers the observer-based output feedback robust model predictive control (RMPC) problem for systems with model uncertainties and possible measurement outliers. For the sake of alleviating the effects from possible abnormal measurements, we design a set of observer-based output feedback RMPC controllers with the saturation constraint where the saturation level is adaptive according to the estimation errors. The purpose of the addressed problem is to design a set of desired RMPC controllers so as to guarantee the robustness and the asymptotical stability of the closed-loop system. Sufficient stability conditions are obtained by solving a time-varying terminal constraint set of an auxiliary optimization problem, and the corresponding control law and the upper bound of the quadratic cost function are derived. In addition, an algorithm including both off-line and on-line parts is provided to find a sub-optimal solution. Finally, two simulation examples are employed to illustrate the effectiveness of the proposed RMPC approach.

A switching feedback control approach for persistence of managed resources

<p style='text-indent:20px;'>An adaptive switching feedback control scheme is proposed for classes of discrete-time, positive difference equations, or systems of equations. In overview, the objective is to choose a control strategy which ensures persistence of the state, consequently avoiding zero which corresponds to absence or extinction. A robust feedback control solution is proposed as the effects of different management actions are assumed to be uncertain. Our motivating application is to the conservation of dynamic resources, such as populations, which are naturally positive quantities and where discrete and distinct courses of management actions, or control strategies, are available. The theory is illustrated with examples from population ecology.</p>

Robust Cooperative Attack of Multiple Missiles with External Disturbances and Communication Delay

The problem of cooperative attack of multiple missiles is studied in this paper, and these missiles are supposed to suffer from external disturbances, communication delay. A kinematics model of the multi-missile under the situation of external disturbances and communication delay is firstly developed. And then based on the topology of directed graph, the problem of multi-missile convergence is transformed into the stability analysis of a closed-loop control system. A state feedback robust controller is designed by linear matrix inequality. Finally, a numerical simulation is given to demonstrate the effectiveness of the proposed control strategy.

HIGH GAIN FEEDBACK ROBUST CONTROL FOR FLOCKING OF MULTI-AGENT SYSTEM WITH UNKNOWN PARAMETERS

In this paper, the control that has high gain feedback robust control with un- known parameters is designed. By the boundedness theorem and the Lyapunov stability theory, the velocity error is bounded and no collision occurs between the multi-agent is proved. Flocking of multi-agent system can be formed under the action of the high gain feedback robust control with unknown parameters. In the simulation, the feasibility of high gain feedback robust control for flocking of multi-agent system is verified.

Neural network-based robust integral error sign control for servo motor systems with enhanced disturbance rejection performance

Uncertain dynamics and unknown time-varying disturbances always exist in servo systems and deteriorate tracking accuracy significantly. To tackle the problem, this paper presents a novel adaptive robust control scheme based on neural networks and the robust integral of the sign of the error (RISE) method. In the proposed scheme, a new neural network compensator is developed, where a reference-driven neural network and an error-driven neural network are employed to compensate for uncertain system dynamics and unknown time-varying disturbances, respectively. And an RISE-based robust feedback controller is designed to suppress uncompensated dynamics. Asymptotic tracking control of the servo system with uncertain dynamics and unknown time-varying disturbances is guaranteed by using the Lyapunov theory. Comparative experiments and simulations with different reference signals and various types of external disturbances were conducted based on a linear motor-driven stage. Experimental and simulational results verify the superior tracking performance and powerful disturbance rejection ability of the proposed method.

Sensing Deformation in Vacuum Driven Foam-Based Actuator via Inductive Method.

Perception in soft robotics is crucial to allow a safe interaction to effectively explore the environment. Despite the inherent capabilities of soft materials, embedding reliable sensing in soft actuators or robots could introduce constraints in the overall design (e.g., loss of deformability, undesired trajectories, etc.) or reduce their compliant characteristics. Consequently, an adequate stiffness for both sensor and actuator becomes a crucial design parameter. In particular, for sensing the deformation related to actuation motion, sensing and actuating strategies must work in full mechanical synergy. In this view, an inductive sensing solution is presented, exploiting open-cell foam and a copper (Cu) wire in an Inductive Foam Sensor (IFS). Due to entangled air cells high deformability is enabled upon vacuum pressure, and proprioceptive information is provided. The IFS is then successfully integrated into the earlier developed Ultralight Hybrid Pneumatic Artificial Muscle (UH-PAM), which encases an elastomeric bellow skin and plastic rings. Such sensorized UH-PAM (SUH-PAM) is capable of a high contraction ratio (54% upon -80kPa), while the inductive sensing shows a high sensitivity of 0.01031/1% and a hysteresis of 5.35%, with an average error of 1.85%, respectively. In order to implement a robust feedback control system, an adaptable proportional sliding mode control is presented. As a result, the SUH-PAM motion can be controlled to the mm-scale, with an RMSE of 0.925 mm, and high robustness against disturbances is demonstrated.

Adaptive Neural Networks Based Robust Output Feedback Control for Nonlinear System

The performance of the control system is reduced by uncertain nonlinearities behaviors, which can be enhanced by implementing an adaptive approach represented by the robust output-feedback control and artificial neural network, which is proposed in this paper and utilized for identification and control of a nonlinear system. The Cart Pole System (CPS) is treated as a multi-body dynamical system, and the nonlinear swing-up problem is handled by designing an adaptive neural network which trained using a modified conventional controller called Linear Quadratic Optimal State Estimator with Integral Control (LQOSEIC). In this paper, the nonlinear system CPS stabilized utilizing robust output feedback control called LQOSEIC, this controller allows a linearized system to act as a model reference for the original nonlinear system, but they are only valid for a limited range of operations and will fail if the plant characteristics are unknown or uncertainty. An adaptable neural network is used to overcome this challenge., in which the adaptive neuro controller is trained offline using LQOSEIC to get the initial weights of neurons for layers network, after finished the training the LQOSEIC will be replaced by adaptive neural control. The real advantage of a neuro-controller is its ability to update online depending on the error signal. The neuro-controller demonstrates that when any disturbance or uncertainty arises in a non-linear system, neural networks characterized by online learning compensate for the effect of unpredictable conditions. The suggested adaptive neural network improves control performance and ensures the closed-loop control system's robust stability. Finally, numerical simulations are used to demonstrate the efficacy of the proposed controllers.

Performance Bounds for Optimal and Robust Feedback Control in Networks

Important complex networks, including critical infrastructure and emerging industrial automation systems, are becoming increasingly intricate webs of interacting feedback control loops. A fundamental concern is to quantify the control properties and performance limitations of the network as a function of the structure of its dynamics and control architecture. We study performance bounds for networks in terms of both optimal and robust feedback control costs as a function of the system dynamics and actuator structure. For unstable network dynamics, we demonstrate a tradeoff between feedback control performance and the number of control inputs, in particular, showing that optimal cost can increase exponentially with the number of unstable nodes in the network. Likewise, we demonstrate a tradeoff between robustness and the numbers of control and adversarial inputs, which shows that either an increase in the number of unstable nodes or the number of adversarial inputs can make optimal cost increase exponentially or become infinite. We also derive a bound on the performance of the worst-case actuator subset for open-loop stable networks, providing insight into dynamics properties that affect the potential efficacy of actuator selection in terms of measures for how close the open-loop dynamics are to instability. However, we show that such a bound is generally not guaranteed even for open-loop stable networks in terms of robustness to adversarial inputs. When the open-loop network dynamics has a finite <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> norm with respect to the adversarial inputs, we find an analogous performance bound of the worst case actuator set. We illustrate our results with numerical experiments that analyze performance in regular and random networks.

Robust static output feedback control for hidden Markov jump linear systems

This paper studies the robust static output feedback control of discrete-time Markov jump systems considering that the mode of operation cannot be directly measured. It is assumed that the only available information concerning the main jump process comes from a detector, so that the jump and detector processes can be modelled as a hidden Markov model. Initially, it is considered that the system's dynamic matrix is subject to parametric uncertainties. By assuming a full row rank condition for the output matrix and employing a clusterisation technique for the state space of the hidden Markov model, it is derived a set of linear matrix inequalities (LMIs) that guarantees robust stability in the mean-square sense of the closed-loop system, as well as a bound on its norm. It is also shown that this design technique is linked to the bounded real lemma, so that a new set of LMIs conditions can be obtained for the ‘pure’ control problem, which can be extended to cover the robust polytopic case. The paper is concluded with an illustrative example.

Active suppression of milling chatter with LMI-based robust controller and electromagnetic actuator

Milling chatter occurs as undesired vibration in the cutting process, imposing negative effects on the tool’s life, the quality of surface finishes and the limitation of machining efficiency. In this paper, a discrete output feedback robust controller based on linear matrix inequality (LMI) is developed for the chatter suppression, with an electromagnetic actuator applying the needed active control force. Considering the model of electromagnetic actuator and the actual mounting position in the milling system, active milling chatter control system is modeled and discretized for the controller’s design. In addition, uncertainties of model parameters, such as modal parameters, axial cutting depth, are also considered. Then the LMI-based robust controller is designed, with which the performance of active chatter suppression can be guaranteed even the mentioned uncertainties exist in the actual milling system. Simulation results show that the chatter-free boundary of milling process is significantly enlarged with the designed robust controller. An experimental prototype for active milling chatter suppression is also presented, and milling chatter experiments are also performed with the developed spindle system, and the results show that surface finishes and chatter-free boundary are improved significantly.

Two-time-scale robust output feedback control for aircraft longitudinal dynamics via sliding mode control and high-gain observer

This paper presents output feedback control for longitudinal dynamics of fixed-wing aircraft using singular perturbation techniques. The longitudinal dynamic model is separated into two timescales. A composite feedback control law based on sliding mode control (SMC) is designed for slow and fast subsystems to track the aerodynamic velocity and flight path angle references. Additionally, two separate high-gain observers (HGO) are designed for the slow and fast subsystems to estimate system states. The proposed technique not only simplifies the design but also is computationally efficient. Simulations are performed in MATLAB/Simulink environment with results demonstrating that the proposed output feedback control method robustly achieves trajectory tracking.

Robust DOF control for uncertain polynomial fuzzy systems in finite frequency domain

This study addresses the issue of robust dynamic output feedback control (DOF) for polynomial Takagi–Sugeno (T–S) fuzzy systems in the Finite Frequency (FF) domain. Sufficient conditions for designing the robust DOF control are derived in terms of the sum of squares (SOS). The proposed strategy is built in the FF domain to reduce conservation-generated by the techniques established in the whole frequency domain. In addition, there are no transformation matrices or equality constraints under these conditions, which simplifies the numerical solution. To show the validity of the suggested technique, several numerical examples are presented.

Comprehensive study of charge-based motion control for piezoelectric nanopositioners: Modeling, instrumentation and controller design

High performance motion control of piezoelectric nanopositioners is crucial for a wide range of applications. The primary challenges stem from several aspects, including hysteresis and creep effects, along with the lightly damped mechanical resonance. In view of these issues, this paper proposes a comprehensive charge-based motion control solution, including a generalized electromechanical model, a charge controller with non-resistive DC stabilization and a robust charge control (RCC) strategy. The advantages of charge-based control in system identification and controller design are clearly indicated. Towards this solution, a generalized model of piezoelectric nanopositioner is first proposed, showing the effectiveness of charge control approach in the presence of arbitrarily complicated mechanical dynamics. Furthermore, we present a charge controller with a simple configuration, which eliminates the frequency-dependent performance of classical controller design. This guarantees consistently high control performance over the full operating bandwidth. Finally, to deal with the mechanical resonance and remaining nonlinearities and uncertainties, we propose a control strategy that combines charge control and robust feedback control into a single framework. Superior tracking and damping control performance of the proposed solution is confirmed by extensive experimental validations.

A GEVP formulation for robust predictor feedback controller design of linear systems with uncertain input delay

Predictor feedback controllers are irreplaceable and widely used for systems with long input delays. However, it is also known to be sensitive to mismatch between the nominal input delay and the true unknown one. In this paper, we propose a robust predictor feedback controller design to enlarge the admissible delay mismatch, while keeping the convergence rate within a prescribed level. It is shown that the controller synthesis problem can be cast into a generalised eigenvalue problem (GEVP).

Specification Guided Automated Synthesis of Feedback Controllers

The growing use of complex Cyber-Physical Systems (CPSs) in safety-critical applications has led to the demand for the automatic synthesis of robust feedback controllers that satisfy a given set of formal specifications. Controller synthesis from the high-level specification is an NP-Hard problem. We propose a heuristic-based automated technique that synthesizes feedback controllers guided by Signal Temporal Logic (STL) specifications. Our technique involves rigorous analysis of the traces generated by the closed-loop system, matrix decomposition, and an incremental multi-parameter tuning procedure. In case a controller cannot be found to satisfy all the specifications, we propose a technique for modifying the unsatisfiable specifications so that the controller synthesized for the satisfiable subset of specifications now also satisfies the modified specifications. We demonstrate our technique on eleven controllers used as standard closed-loop control system benchmarks, including complex controllers having multiple independent or nested control loops. Our experimental results establish that the proposed algorithm can automatically solve complex feedback controller synthesis problems within a few minutes.

An off-line approach for output feedback robust model predictive control

For constrained linear parameter varying systems subject to bounded disturbances and noises, this article investigates an off-line output feedback robust model predictive control approach. The sub-observer gains with robust positively invariant sets, and sub-controller gains with robust control invariant sets are simultaneously off-line optimized and stored in a look-up table. According to real-time estimation error bounds and estimated states, the time-varying sub-observer gains and sub-controller gains are on-line searched. The proposed off-line output feedback robust model predictive control approach with the guarantee of nested robust positively invariant sets and robust control invariant sets in theory reduces the on-line computational burden.

State feedback control for stabilization of PMSM ‐based servo‐drive with parametric uncertainty using interval analysis

For a class of multivariable uncertain dynamic systems, the parametric uncertainties are belonging to a closed interval with lower and upper boundaries a priori known. Thereby, these systems can be analyzed based on interval structures and interval matrices. In this article, a fully interval analysis–based method is developed and applied to the state feedback control of permanent magnet synchronous motor (PMSM) in order to design a stabilized servo-drive. Indeed, the parametric uncertainties are investigated in state space representation, which represents a simplified and effective way to analyze the robust stability for the interval system. Firstly, a robust state feedback control technique, dedicated to an uncertain system is introduced. For that, the robust controllability test is performed for the interval system by using the linear independency condition of column interval vectors. It is proven that there is a direct correlation between the controllability test and the existence of a robust modal P-regulator for the correction of the uncertain system. It is also shown that it invariably relies on each input's controllability indices and thus their effect on the uncertain system's state variables. In order to ensure stability in a closed loop, the modal P-regulator is designed with possibility of incorporation of an integral action. The modified modal PI regulator has the ability to reject disturbance and guarantee zero-steady-state error for step inputs. In fact, the stability is achieved by placing all coefficients of the system characteristic polynomial within assigned intervals based on Kharitonov's Theorem. The technique provides a matrix gain with interval coefficients for the stabilizing regulator. Finally, the developed approach is applied to position control of linearized model of the PMSM-based servo-drive, presenting parametrical uncertainties. To demonstrate the efficiency of the proposed method, a numerical and graphical comparison of conventional LQR and pole placement, state feedback controllers for the PMSM servo-drive with the robust interval controller is provided. In order to verify the feasibility of the whole proposed technique, calculations and simulations are performed by using Matlab/Intlab toolbox. Real-time simulation is also investigated using Lab-View Compact-RIO.

Robust finite frequency static output feedback control for uncertain fuzzy systems via a sum‐of‐squares approach

AbstractThis article deals with the problem of robust static output feedback control in finite frequency (FF) domain for polynomial Takagi–Sugeno fuzzy systems. By using generalized Kalman–Yakubovich–Popov lemma and polynomial Lyapunov functions, sufficient conditions are proposed for controllers design in terms of sum of squares. These conditions include neither transformation matrices nor equality constraints, which simplifies the numerical solution. The proposed method is designed in the FF domain to reduce the conservativeness generated by those designed in the full frequency domain. Some numerical examples are provided to demonstrate the applicability of the proposed approach.

High dynamic output feedback robust control of hydraulic flight motion simulator using a novel cascaded extended state observer

High dynamic tracking performance is a key technical index of hydraulic flight motion simulator (HFMS). However, the strong nonlinearities, various model uncertainties and measurement noise in hydraulic actuation systems limit the high dynamic performance improvement. In this paper, the outer axis frame of a HFMS is taken as a case study and its nonlinear dynamic model with consideration of strong nonlinearities, matched and mismatched uncertainties is established. A novel cascaded extended state observer (ESO) is proposed to estimate the unavailable system states to avoid the adverse effect of measurement noise on control performance. Meanwhile, the designed cascaded ESO also produces estimates of matched and mismatched uncertainties. Then, an output feedback robust controller (OFRC) is proposed by integrating the cascaded ESO with a robust integral of the sign of the error (RISE) feedback based on the backstepping framework. The proposed controller achieves compensation of both matched and mismatched model uncertainties in an output feedback form. Theoretical analysis indicates that the proposed OFRC ensures the boundedness of all closed-loop system signals in the presence of matched and mismatched time-varying model uncertainties. Excellent asymptotic tracking performance can also be obtained when the model uncertainties are time-invariant. Comparative experimental results show that the proposed OFRC achieves significant performance improvement compared with the extensively employed PI control with velocity feedforward (VFPI).