Bounded-input Bounded-output Stability Research Articles

An analytical criterion for stability testing of delayed Bode’s transfer function with unity feedback

The unity feedback where delayed Bode’s transfer function is placed in forward path is used as reference transfer function in controller design for fractional time delay systems. In this study, bounded input-bounded output stability of this reference transfer function is investigated. This investigation is based on a theorem for fractional order time delay systems using Hassard’s techniques. Sufficient and necessary conditions are obtained for testing the stability of this reference transfer function. Moreover, an explicit formula is given for calculating the number of unstable roots in case of instability. The illustrative examples show that this stability criterion works efficiently.

Practical one-shot data-driven design of fractional-order PID controller: Fictitious reference signal approach

This study proposes a one-shot data-driven tuning method for a fractional-order proportional-integral-derivative (FOPID) controller. The proposed method tunes the FOPID controller in the model-reference control formulation. A loss function is defined to evaluate the match between a given reference model and the closed-loop response while explicitly considering the closed-loop stability. A loss function value is based on the fictitious reference signal computed using the input/output data. Model matching is achieved via loss function minimization. The proposed method is simple and practical: it needs only one-shot input/output data of a plant (no plant model required), considers the bounded-input bounded-output stability of the closed-loop system from a bounded reference input to a bounded output, and automatically determines the appropriate parameter value via optimization. Numerical simulations show that the proposed approach facilitates good control performance, and destabilization can be avoided even if perfect model matching is unachievable.

Disturbance rejection of offshore drilling platforms: An equivalent-input-disturbance-based dynamic positioning control method

Offshore drilling platforms are exposed to wind, waves, currents, and other unknown disturbances. Accurately estimating and rejecting these disturbances is the key to ensuring reliable station-keeping of the platforms. In this study, a novel dynamic positioning method using an improved equivalent-input-disturbance (EID) approach is proposed for offshore drilling platforms. An improved EID estimator is employed to estimate and suppress unknown disturbances, significantly enhancing the disturbance-rejection performance of the dynamic positioning system. The input channels are decoupled through linear transformation, and the parameter tuning process of the observer and controller is optimized, thus improving system performance. The bounded-input bounded-output stability of the closed-loop system is proved. This study provides insights into the design of dynamic positioning systems for offshore drilling platforms.

On the Relative Stability of Linear Time Invariant Systems

In this paper, state space representation based approach to relative stability of Linear Time Invariant (LTI) systems is discussed. Specifically, given a bound on the output, relative Bounded Input-Bounded Output (BIBO) stability of LTI systems is discussed. The bound on dominant pole is first determined using input-output description of LTI system. Using state space representation of homogeneous (no external input) LTI system, the components of state vector are upper bound. The results are applied to Continuous Time Markov Chains (i.e. homogeneous stochastic linear systems). Finally, using state space representation of arbitrary (with external input) Linear Time Invariant systems, the location of dominant pole is bounded. Using the upper bound, the location of line (parallel to imaginary-axis jω and to the left of it) is utilized for determining relative stability.

Automatic Landing System Design for Unmanned Fixed-Wing Vehicles via Multivariable Active Disturbance Rejection Control

Landing control of unmanned aerial vehicles (UAVs) is challenging because of the strong nonlinear dynamics, multivariable, model uncertainties, wind variations, and sensor noise. Motivated by this fact, this paper investigates an automatic landing system (ALS) that includes trajectory generation and guidance law for the first flight test of a turbine-based combined cycle technology demonstrator. Specifically, the control scheme increases the original model’s order to generate a reasonable monotone-decreasing throttle reference flare trajectory by the pseudospectral method. Subsequently, the guidance law based on innovative multivariable active disturbance rejection control is designed to robustly track the reference altitude and velocity simultaneously with high accuracy. The multivariable extended state observer (ESO) incorporated decoupling algorithm enhances the estimation capability and accuracy of potential problem in cross-coupling dynamics compared to the traditional ESO. It is proven that the closed-loop error dynamic has bounded-input bounded-output stability and an explicit upper bound is given. Numerical simulation verifies that the presented approach has better robustness and higher tracking accuracy for external disturbances and parametric uncertainties than the existing benchmark autolanding controller. Finally, flight tests show that the proposed ALS can land the vehicle effectively and safely under severe wind conditions.

Active Suspension Robust Preview Control by Considering Actuator Delay

Active suspension systems (ASSs) are crucial for realizing the improvement demand of ride comfort in autonomous vehicles (AVs). This paper presents a novel integrated robust preview control (PC) algorithm to further improve the ride comfort by effectively handling actuator delay. An augmented ASS model is first established to consider actuator delay. Then, to obtain the time-domain feedforward disturbance, updating the local spatial road dataset from sensing systems by low-pass filtering and introducing speed for conversion. A predictive control framework that utilizes preview road disturbances is developed to achieve better ride comfort. And assuming parameterized disturbances, it is transformed into a consistent quadratic programming (QP) problem for real-time application in ASS. Furthermore, an innovative design of combined observer provides accurate and robust observations under multiple uncertainties, with which the algorithm can effectively compensate for actuator delay under different road conditions. Finally, the bounded-input bounded-output (BIBO) stability of the algorithm is well demonstrated. Simulation and bench test results indicate that the proposed algorithm can not only significantly improve road holding and ride comfort, but also realize a robust observation of the augmented ASS state. In addition, the solving time of the bench test satisfies the real-time requirements of the algorithm.

A Synthesized Sliding-Mode Control for Attitude Trajectory Tracking of Quadrotor UAV Systems

This article presents a practical synthesized sliding-mode control (SSMC) scheme and, then, applies it to quadrotor unmanned aerial vehicle (UAV) systems. A new adaptive law is developed to be suitable for real applications with small moment of inertia such as quadrotor UAV systems that become more sensitive to abrupt and external disturbances. Since it is designed to respond to both sliding variables and time-delayed estimation errors, it makes the switching gains provide remarkably fast convergence rate and high robustness while compensating for abrupt and external disturbances. Besides, the proposed SSMC scheme works together with the pole-placement control to enhance the system stability while yielding the desirable closed-loop dominant poles. Also, the proposed control scheme employs one-sample delayed information to cancel out the system uncertainties and disturbances so that it makes a simple and compact structure. It is shown that attitude trajectory tracking errors of the proposed SSMC scheme are guaranteed to be bounded by the bounded-input bounded-output stability theory. The practical effectiveness and feasibility of the proposed control scheme are illustrated in real implementation with a quadrotor UAV system, which are compared with those of the existing control schemes.

Data-Driven Bipartite Formation for a Class of Nonlinear MIMO Multiagent Systems.

The bipartite formation control for the nonlinear discrete-time multiagent systems with signed digraph is considered in this article, in which the dynamics of the agents are completely unknown and multi-input multi-output (MIMO). First, the unknown nonlinear dynamic is converted into the compact-form dynamic linearization (CFDL) data model with a pseudo-Jacobian matrix (PJM). Based on the structurally balanced signed graph, a distance-based formation term is constructed and a bipartite formation model-free adaptive control (MFAC) protocol is designed. By employing the measured input and output data of the agents, the theoretical analysis is developed to prove the bounded-input bounded-output stability and the asymptotic convergence of the formation tracking error. Finally, the effectiveness of the proposed protocol is verified by two numerical examples.

Nonlinear generalized predictive control with virtual unmodeled dynamics decomposition compensation and data driven

In this study, a novel nonlinear generalized predictive control (NGPC) method is proposed to tackle the tracking control problem which considers a mathematical model in conjunction with the virtual unmodeled dynamics decomposition compensation technology. First, data-modeling technology is adopted to take advantage of the input and output data information from the process to decompose the virtual unmodeled dynamics into the form of posterior measurement unmodeled dynamics and an unknown increment. Then, feedforward compensator is designed. The essential difference between the proposed data modeling algorithm and existing methods is that the effect of the measurement unmodeled dynamics is eliminated by the feedforward compensator. For the increment of the virtual unmodeled dynamics, a novel estimation algorithm is established through a data driven approach; A nonlinear compensator for the unknown increment of the virtual unmodeled dynamics is designed to suppress the effect of the increment of the virtual unmodeled dynamics on the closed-loop system. Second, the developed compensator is combined with the GPC algorithm to construct a nonlinear generalized predictive controller. Theoretical analysis proves that the proposed modeling and control algorithm have bounded-input bounded-output (BIBO) stability. Finally, an experimental study is conducted, which indicates the effectiveness of the proposed algorithm.

Data-driven prescribed performance control for satellite with large rotational component

In this paper, the high precision attitude control for satellite with large misaligned rotational component is investigated, proposing a novel model-free prescribed performance adaptive control (MF-PPAC) method. Based on the model-free adaptive control (MFAC) strategy, high-precision attitude control is achieved depending on the system measurement rather than the spacecraft mathematical model, which demonstrates the superiority in handling nonlinearity and uncertainty of the spacecraft system, especially for those with unbalance of the rotational component. Furthermore, the transient and the stable-state behavior of the tracking error using MFAC is constrained in the prescribed performance bounds and converges to zero gradually with the utilization of prescribed performance function (PPF) and error transformation method. Finally, the convergence and boundedness of the system error, the bounded-input bounded-output (BIBO) stability of the proposed MF-PPAC is demonstrated by the contraction mapping theory. Simulation and comparison with disturbance-observer-based PD control and MFAC illustrate the effectiveness of the proposed method.

Model-Free Adaptive Sliding Mode Control-Based Active Chatter Suppression by Spindle Speed Variation

Abstract This paper presents a novel model-free adaptive sliding mode control (MFA-SMC) algorithm, which is employed to actively adjust the amplitude and frequency of spindle speed variation (SSV) for chatter suppression in turning. The SSV technique is effective for mitigating regenerative chatter, which however is not widely applied due to its poor adaptability to time-varying characteristics of machining dynamics and cutting conditions. The online adjustment of SSV parameters has been reported in previous works, whereas the proportional integral differential (PID)-type controller used cannot compensate for the interactions when abruptly changing the reference input and the parameter tuning procedure consumes much time. The proposed method integrates the model-free adaptive control (MFAC) with the global sliding mode control (GSMC). The method is data-driven and only dependent on the measured input/output data of the cutting process in this paper, which are the normalized wavelet packet entropy and SSV parameters, respectively. The bounded-input bounded-output stability and the tracking error convergence of the proposed control algorithm are guaranteed by theoretical analysis. The effectiveness of the proposed chatter suppression method is investigated with numerical simulations. Finally, experimental results demonstrate that chatter vibration under different cutting conditions can be effectively mitigated by the proposed method.

Funnel control by induced contraction

This note explores a property of the internal dynamics that is essential for the functioning of classical funnel control. We relax the property of internal dynamics bounded-input bounded-output (BIBO) stability by concentrating on a narrower class of output reference trajectories. Our ideas have a connection with the recently introduced concept of induced contraction, which is motivated by the phenomenon of noise-induced synchronization in neuronal oscillators. We remark that, contrary to previous works, we only have to modify the class of admissible output reference trajectories to handle non-minimum phase systems. We also propose a way (specific to nonlinear systems) to choose an output reference trajectory (possibly under output constraints) for classical funnel control to work for a certain class of unknown systems.

Adaptive Fuzzy Robust Tracking Control Using Human Electromyogram Signals for Elastic Joint Robots

Sliding mode control is often used for systems with parametric uncertainties due to its desirable robustness and stability, but this approach carries undesirable chattering. Similarly, joint elasticity is a common phenomenon induced by transmission systems in robots, but it presents additional complexity in robot dynamics that could lead to robot vibrations or even instability. Coupling these two phenomena presents further compounded challenges, particularly when faced with the human interface's added uncertainties. Here, a stable voltage-based adaptive fuzzy strategy to sliding mode control is proposed for an elastic joint robot arm that uses a human's upper limb electromyogram (EMG) signals to direct its movement. The concurrent use of EMG with the elastic joint arm provides a suitable framework for human-robot interaction. EMG signals represent human's ‘intention’ on motion, i.e., they move between 50–100 ms before the mechanical motion begins. Hence this strategy potentially builds better synchronization between the robot and human intention. Furthermore, the adaptive fuzzy strategy eliminates the system chattering while also providing robustness against parametric uncertainties and time delay. Lyapunov analysis also shows bounded-input bounded-output stability of the closed-loop system. Finally, the proposed approach is experimentally implemented in the Sport Science Research Institute. Comparisons with a competing strategy, as well as a torque mode controller, shows that the proposed approach leads to a computationally faster and more accurate controller.

Intelligent Control for Pressurizer System in Nuclear Power Plants

Fine control of output power for nuclear power plants is the essential goal for safe operation. In this work, a Fuzzy analytical proportional-integral-derivative (FPID) controller with different configurations is designed to adjust and control the pressure of the PZR system. The stability analysis of the FPID controller with variable gains is established, and conditions for bounded-input bounded-output stability conditions (BIBO) are derived using the small gain theory. Two scenarios are applied for evaluating the dynamic response of applied controllers. In addition, performance indices are compared between the PZR model and data measured from the PCtran VVER-1200 simulator. Finally, a simulation platform is developed for MATLAB / Simulink to implement the three-region nonlinear non-equilibrium PZR model and the designed pressure controllers. The analysis and evaluation results showed good durability of the designed controllers and satisfactory performance of the control. These results further show that the nonlinear PZR model is accurate, feasible, and valuable for dynamic simulation and control unit design.

Bounded-Input Bounded-Output Stability Tests for Two-Dimensional Continuous-Time Systems

This paper presents two efficient algorithms to determine whether a bivariate polynomial, possibly with complex coefficients, does not vanish in the cross product of two closed right-half planes (is “2-C stable”). A 2-C stable polynomial in the denominator of a two-dimensional analog filter has been proved (not long ago) to imply bounded-input bounded-output (BIBO) stability. The two algorithms are entirely different but both rely on a recently proposed fraction-free (FF) Routh test for complex polynomials in this transaction. The first algorithm tests the 2-C stability of a bivariate polynomial of degree (n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) in order n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> of elementary operations (when n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> =n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> =n). It is a “tabular type” two-dimensional stability test that can be regarded as a “Routh table” whose scalar entries were replaced by univariate polynomials. The second 2-C stability test is obtained from the first by its telepolation. It carries out the 2-C stability test by a finite collection of FF Routh tests and requires only order n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> elementary operations. Both algorithms possess an integer-preserving property that enhances them with additional merits including numerical error-free decision on 2-C stability.

Direct tuning of the data-driven controller considering closed-loop stability based on a fictitious reference signal

The direct tuning of controller parameters, which is based on data-driven control, has been attracting considerable attention because of the ease of its control system design. In practical use, it is important to consider the stability of the closed-loop system and model matching with few design parameters. In this study, we propose a direct tuning method based on a fictitious reference signal that considers the bounded-input bounded-output (BIBO) and model matching without repeating experiments. The proposed method includes two steps. In the first step, the BIBO stability is satisfied. The pole information is lost in the cost function of the conventional method using a fictitious reference signal. Then, we derive a new cost function that can prevent the loss of the pole information. This provides controller parameters that can stabilize the closed-loop system. The model matching between the reference model and the closed-loop system is considered in the second step. When model matching is achieved, the characteristics of the reference model almost match those of the closed-loop system, including the gain and phase margins. The parameters of the reference model are automatically tuned to realize model matching. Using the two-step method, we can obtain parameters considering BIBO stability and the model matching. In addition, there are no design parameters apart from the dealing noise. Two simulations and an experiment were performed on a system with dead time to verify the effectiveness of the proposed two-step method. The results showed that the proposed method provides BIBO stability and model-matched control parameters from the measured data through a one-time experiment without trial and error.

A New Sufficient Criterion for the Stability of 2-D Discrete Systems

During the past few decades, two and higher dimensional systems have been extensively applied in many areas of research. The representation of the 2-D systems in the frequency domain is usually given by its transfer function. The bounded-input bounded-output (BIBO) stability of the two dimensional discrete systems depends on the zeros of the characteristic polynomial which is the denominator of this transfer function. In this paper, a new sufficient criterion for the stability of two-dimensional linear shift-invariant discrete systems is presented. The new criterion is based on the sufficient condition for stable polynomials with complex coefficients and the stability criterion for 2-D discrete systems proposed by Murray and Delsarte et al. . The new criterion is non-conservative for the stability testing of 2-D discrete systems. It is shown that the proposed sufficient criterion is simple enough to be applied for the stability checking of the 2-D discrete systems. The utility of the proposed criterion is demonstrated by examples.

Application of quasi-f -power increasing sequence in absolute ph - |C, a, b; d; l| of infinite series

An increasing quasi-f-power sequence of a wider class has been used to establish a universal theorem on a least set of conditions, which is sufficient for an infinite series to be generalized ph-|C, a, b; d; l| k summable. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. Considering suitable conditions a previous result has been obtained, which validates the current findings. In this way, Bounded Input Bounded Output(BIBO) stability of impulse has been improved by finding a minimal set of sufficient condition for absolute summability because absolute summable is the necessary and sufficient conditions for BIBO stability.

Model-Free Adaptive Control for Unknown MIMO Nonaffine Nonlinear Discrete-Time Systems With Experimental Validation.

In this article, a model-free adaptive control (MFAC) algorithm based on full form dynamic linearization (FFDL) data model is presented for a class of unknown multi-input multi-output (MIMO) nonaffine nonlinear discrete-time learning systems. A virtual equivalent data model in the input-output sense to the considered plant is established first by using the FFDL technology. Then, using the obtained data model, a data-driven MFAC algorithm is designed merely using the inputs and outputs data of the closed-loop learning system. The theoretical analysis of the monotonic convergence of the tracking error dynamics, the bounded-input bounded-output (BIBO) stability, and the internal stability of the closed-loop learning system is rigorously proved by the contraction mapping principle. The effectiveness of the proposed control algorithm is verified by a simulation and a quad-rotor aircraft experimental system.

Interpretable PID parameter tuning for control engineering using general dynamic neural networks: An extensive comparison.

Modern automation systems largely rely on closed loop control, wherein a controller interacts with a controlled process via actions, based on observations. These systems are increasingly complex, yet most deployed controllers are linear Proportional-Integral-Derivative (PID) controllers. PID controllers perform well on linear and near-linear systems but their simplicity is at odds with the robustness required to reliably control complex processes. Modern machine learning techniques offer a way to extend PID controllers beyond their linear control capabilities by using neural networks. However, such an extension comes at the cost of losing stability guarantees and controller interpretability. In this paper, we examine the utility of extending PID controllers with recurrent neural networks—–namely, General Dynamic Neural Networks (GDNN); we show that GDNN (neural) PID controllers perform well on a range of complex control systems and highlight how they can be a scalable and interpretable option for modern control systems. To do so, we provide an extensive study using four benchmark systems that represent the most common control engineering benchmarks. All control environments are evaluated with and without noise as well as with and without disturbances. The neural PID controller performs better than standard PID control in 15 of 16 tasks and better than model-based control in 13 of 16 tasks. As a second contribution, we address the lack of interpretability that prevents neural networks from being used in real-world control processes. We use bounded-input bounded-output stability analysis to evaluate the parameters suggested by the neural network, making them understandable for engineers. This combination of rigorous evaluation paired with better interpretability is an important step towards the acceptance of neural-network-based control approaches for real-world systems. It is furthermore an important step towards interpretable and safely applied artificial intelligence.