Robust Controller Design Method Research Articles

Nonlinear Robust Stabilization of Ship Roll by Convex Optimization

For ship roll stabilization, this paper presents a nonlinear robust controller design method using the sum of squares (SOS) technique combined with the dual of Lyapunov's stability theorem. Varying ship speed and initial metacentric height are seen as uncertainties, sea waves are regarded as external disturbance, and then the robust nonlinear controller is also designed based on the suggested method. Simulations are performed by taking container ship model as an example. It is shown that the designed system guarantees robust performance with respect to the uncertainties and disturbance.

Piezoelectric Actuators in Smart Engineering Structures Using Robust Control.

In this study, piezoelectric patches are used as actuators to dampen structural oscillations. Damping oscillations is a significant engineering challenge, and the use of piezoelectric patches in smart structures allows for a reduction in oscillations through sophisticated control methods. This analysis involved H-infinity (H∞) robust analysis. H∞ (H-infinity) control formulation is a robust control design method used to ensure system stability and performance under disturbances. When applied to piezoelectric actuators in smart structures, H∞ control aims to design controllers that are robust to variations in system dynamics, external disturbances, and modeling uncertainties, while meeting specified performance criteria. This study outlines the piezoelectric effects and advanced control strategies. A structural model was created using finite elements, and a smart structural model was analyzed. Subsequently, dynamic loads were applied and oscillation damping was successfully achieved by employing advanced control techniques.

A nonlinear design method of robust PI control by using adaptive backstepping control for web winding system of reversible cold rolling mill

A nonlinear design method of robust PI control by using adaptive backstepping control for web winding system of reversible cold rolling mill

Robust Control of Right Invertible Nonlinear Systems

In a MIMO a nonlinear system having the same number of inputs and outputs, if certain coefficients that characterize its normal form have a special structure, a number of relevant design problems can been successfully addressed. In this paper we consider the more general case of a system having more inputs than outputs, we show that such special structure implies the regularity of the algorithm for construction of a right-inverse, and we show how a recently developed design method for robust control can be implemented on this class of MIMO systems.

Observer-based robust preview tracking control for a class of continuous-time Lipschitz nonlinear systems

<p>In this paper, a novel observer-based robust preview tracking controller design method is proposed for a class of continuous-time Lipschitz nonlinear systems with external disturbances and unknown states. First, a state observer is designed to reconstruct unknown system states. Second, using differentiation, the state lifting technique, the differential mean value theorem, and several ingenious mathematical manipulations, an augmented error system (AES) containing the previewable information of a reference signal is constructed, thereby transforming the tracking control problem into a robust $ H_{\infty} $ control problem. Based on linear parameter-varying (LPV) system theory, a sufficient condition for asymptotic stability of a closed-loop system with a robust $ H_{\infty} $ performance level is established in terms of the linear matrix inequality (LMI). Furthermore, a tracking controller, which includes observer-based feedback control, integral control, and preview feedforward compensation, is established for the original system. In particular, the tracking controller design is simplified by computing the observer and tracking controller gains simultaneously via only a one-step LMI algorithm. Finally, numerical simulation results demonstrate that the proposed controller leads to superior improvement in the output tracking performance compared with the existing methods.</p>

A fast design technique for robust industrial controllers

This paper provides a new fast design method for robust industrial controllers via majorant systems in the frequency domain. The proposed methodology allows to establish several fast design techniques for a broad class of industrial controllers of plants with internal and/or external delays, parametric and/or structural uncertainties, and subject to disturbances, when an analytical model of the plant or data acquired from simple experimental tests are available. The provided design and control techniques are more general with respect to the Ziegler-Nichols ones and their numerous variants, which, in some cases, do not guarantee the control system stability.The used key idea consists in increasing the frequency response of the process to be controlled with the frequency response of a simpler system, also of order greater than one, with external delay, which allows designing, using simple formulas, controllers of PI, PID, PIDR, PI2, PI2D, PI2DR, PI2D2, and PI2D2R types. The designed controllers always guarantee stability margins larger than those of appropriate reference systems. Therefore, good performance of robustness of the stability and tracking precision of smooth references, with respect to parametric and/or structural uncertainties and/or smooth disturbances, are always guaranteed.The stated general methodology and various performance comparisons, also about the tracking precision of references with bounded first or second derivative, are illustrated and validated in several case studies, experimentally too.

Synthesis of a Calibration-Free Visual Feedback Controller for an Inverted Pendulum Using a Fisheye Lens

This article considers the synthesis of feedback controllers for a class in which strong robust stability is required against sensing errors. The motivation dealing with this class arises from the stabilization problem of a cart-driven inverted pendulum by visual feedback control using a fisheye lens. While fisheye lenses guarantee a wide-angle of view, a large image distortion at off-center area is inevitable. Therefore this study first derives a geometric measurement model of a pendulum angle using a general fisheye lens model. A new design method for robust controllers for our problem is then proposed. Finally, a robust feedback controller that allows lens distortion is designed. The effectiveness of the controller based on the proposed model and the proposed design method is verified through numerical simulations and experiments.

Robust feedback compensation and PID Tuning under actuator rate limit effect based on Bode’s integrals

The actuator rate limit is a common phenomenon in control systems while its underlying mechanism remains elusive. Magnitude reduction and phase delay generated by the rate limiter degrade the control performance, but this adverse effect has always been omitted in practical engineering. This study proposes a robust controller design method and controller update rules for general minimum-phase systems to compensate for the rate limit effect and improve control performance. Firstly, a simplified implementation method of “flat phase” constraint is carried out based on the Bode’s integrals for proportional–integral–derivative (PID) and fractional-order proportional–integral (FOPI) controllers. Secondly, the update rules of the controller design specifications are proposed based on Bode’s integrals to mitigate the actuator rate limit effect. The proposed method maintains the original controller structure without extra compensation filters, thereby can be easily applied to engineering practice. The outperformance of FOPI controllers compared to PID controllers is qualitatively analyzed and has been indicated to have lower probability of infinity loops under actuator rate limit. Illustrative examples and experimental results have demonstrated the effectiveness, robustness under gain variation and disturbance rejection capability of the proposed rate limit compensation strategies.

A generalized proportional integral observer–based robust tracking design approach for quadrotor unmanned aerial vehicle

This article mainly studies the trajectory tracking control for quadrotor unmanned aerial vehicle with unknown time-varying disturbances including parametric uncertainties, model errors, and external disturbances such as wind effects. Conventional backstepping control schemes usually cannot guarantee the performance when it faces the time-varying disturbances. Improved schemes, such as integral backstepping, can only compensate the disturbances in a relatively slow way. By introducing disturbance observer technology into the design of controller, a composite generalized proportional integral observer–based robust control design method is developed. First, by utilizing the generalized proportional integral observer, the lumped time-varying disturbances of unmanned aerial vehicle are estimated. Secondly, combining the value of disturbance estimation and feedforward controller by using backstepping control technology together, a composite controller has been developed, which can be called as backstepping control + generalized proportional integral observer. The proposed control method has a better capability of disturbance rejection and is easy to implement. Simulation and experimental results illustrate the good robustness and tracking performance of the proposed scheme.

Robust boundary of stability and design of robust controller in uncertain polytopic linear systems

Abstract This paper is devoted to design of a robust controller for an uncertain continuous-time linear polytopic system. The design procedure will take place in two steps. In the first step, we calculate the robust stability boundary of a closed loop system. Then on the basis of the result obtained in this way, we select a robust controller design method that accepts the calculated stability boundary. This procedure allows better implementation of the second step of the designed robust controller. Two examples of application of the proposed method follow finally, which illustrate its effectiveness.

Robust LFC of Power Systems With Wind Power Under Packet Losses and Communication Delays

Network-induced packet losses and communication delays, as well as load fluctuations and uncertain wind power have a negative effect on the frequency regulation of power system. This paper is concerned with designing a robust load frequency control (LFC) scheme for a multi-area power system penetrated by wind power via sampled-data control. Firstly, considering the effects of the inertia reduction, packet losses, communication delays and measurement noise, a decentralized aperiodic sampled-data LFC model with time delay is constructed, where the maximum sampling interval is characterized by limiting the maximum count of successive packet losses (MCSPL). Secondly, by applying Lyapunov theory and linear matrix inequality technique, a new exponential stability condition for the modeled LFC system with given controller is proposed based on a combination method of Lyapunov-Krasovskii functional and loop function, which is dependent on delay and MCSPL. It can be used to find the delay margin and allowable MCSPL of the LFC system. Thirdly, based on the <inline-formula> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula>-gain performance condition developed by the stability condition above, a design method of robust PI-type controller is proposed by maximizing an exponential decay rate (EDR). The larger EDR, the faster frequency response speed to cope with the effect of inertia reduction, but the worse robustness to load fluctuations, packet losses and delays, and vice versa. Finally, case studies are carried out by a one-area power system and a three-area power system with wind power. By comparing with the existing LFC schemes, simulation results show that the proposed LFC scheme for the tested system is more effective and has better robustness.

Data-Driven Robust Control Using Reinforcement Learning

This paper proposes a robust control design method using reinforcement learning for controlling partially-unknown dynamical systems under uncertain conditions. The method extends the optimal reinforcement learning algorithm with a new learning technique based on the robust control theory. By learning from the data, the algorithm proposes actions that guarantee the stability of the closed-loop system within the uncertainties estimated also from the data. Control policies are calculated by solving a set of linear matrix inequalities. The controller was evaluated using simulations on a blood glucose model for patients with Type 1 diabetes. Simulation results show that the proposed methodology is capable of safely regulating the blood glucose within a healthy level under the influence of measurement and process noises. The controller has also significantly reduced the post-meal fluctuation of the blood glucose. A comparison between the proposed algorithm and the existing optimal reinforcement learning algorithm shows the improved robustness of the closed-loop system using our method.

Robust stabilization control for multi-station motion system with network communication constraints

In this article, the robust stabilization control techniques and the time delays compensation method are proposed in a networked multi-station cooperative motion system (MSCMS), where random network-induced communication constraints are presented. First, an uncertain multi-nodes model of MSCMS is established. Moreover, the random network communication delays, station nodes position compensation, two types of topologies of the station nodes, and the mutual position disturbance among the multi-station nodes are considered simultaneously. Second, a discrete-time Markov chain is used to model the random network delays for the MSCMS. A time delay compensation method is applied to compensate the tracking errors among the multi-motor nodes. Moreover, the stability conditions and the robust controller design method for MSCMS are presented by constructing a new Lyapunov functional and combining stability theory and inequality techniques. Finally, the effectiveness of the proposed method for the MSCMS is verified by several comparative experimental results.

Robust gain-scheduling [formula omitted] control of uncertain continuous-time systems having magnitude- and rate-bounded actuators: An application of full block S-procedure

This paper addresses a novel robust gain-scheduling(GS) state-feedback (SF) H∞ (induced L2) control method for uncertain continuous-time(CT) systems having actuators with hard rate and magnitude bounds. The proposed method relies on acceleration form representation of the uncertain CT system. The technique enables the user to represent the control signal and its slew rate as auxiliary outputs along with the main controlled output. Two different norms, namely the induced L∞ and L2 are used to control the system effectively. While the L∞ gain from the exogenous disturbance inputs to the control signal related outputs is used to deal with actuator saturation problem, L2 gain from the disturbance inputs to the performance outputs is utilised in attenuation of the effects of the disturbances. To achieve these goals with minimal conservatism, we develop new forms of dilated Matrix Inequality (MI) conditions for peak-to-peak gain and L2 gain with no additional conservatism. Then, we propose a novel robust GS control methodology to deal with the problem via dilated MIs and a modified full block S-procedure method (MFBSPM). The utilisation of MFBSPM ensures that the robust control design method of this note applies to any uncertain system having rational parameter dependence. Finally, the efficiency of the presented method is portrayed through extensive simulations of the responses of a marine vessel to wave excitations in which the vessel model is assumed to have magnitude and rate limited active fin stabiliser.

Robust adaptive control of uncertain nonlinear systems with unmodeled dynamics using command filter

AbstractThis article proposes a robust adaptive controller design method for strict feedback nonlinear systems with unmodeled dynamics and input saturation. By using command filters, the explosion of complexity is obviated. The influence of filter errors bought in by command filters is eliminated by introducing compensating signals. Moreover, by skillfully constructing annth‐order auxiliary dynamic system, the effect of input saturation is avoided, where the disadvantages of conventional methods based on the hyperbolic tangent function are overcome. To tackle the effect of unmodeled dynamics which can destroy the performance and even destabilize the system, based on input‐to‐state stability theory, a dynamic signal is designed. Finally, the Lyapunov theory‐based stability analysis proves that all the closed‐loop signals are uniformly ultimately bounded. The effectiveness of the proposed controller design scheme is verified in simulation experiments.

Robust Secondary Frequency Control for Virtual Synchronous Machine-Based Microgrid Cluster Using Equivalent Modeling

The technology of virtual synchronous machine (VSM) is attracting interest of researchers as it controls converters mimicking the synchronous machine's response so as to provide inertial support for power electronics dominated smart grids. For the VSM-based microgrid, its slow dynamics are dominated by synchronous generators (SGs) and the VSM control loops, which makes it possible to model this microgrid into an equivalent SG (EqSG) model. This paper proposes a robust secondary frequency control design method for the VSM-based low voltage (LV) microgrid cluster (MGC) using equivalent modeling. The EqSG model is used to construct the MGC model so as to reduce the model order and the complexity of controller synthesis. Modeling errors caused by the EqSG model and different operating conditions are integrated into the MGC model as unstructured uncertainties. The proposed secondary frequency control strategy is based on the distributed-centralized hybrid control structure to coordinate frequency restoration among LV microgrids. Structured μ-synthesis is applied for tuning control parameters realizing H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust performance against unstructured uncertainties. To reduce the communication resource consumption, an event-triggered mechanism considering communication delay is introduced in the robust secondary frequency control strategy. The triggering condition is analyzed using a Lyapunov function to guarantee H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust stability. Simulation and real-time experiment results on a MGC composed of four CIGRÉ benchmark LV microgrids are presented to demonstrate the effectiveness of the proposed control strategy.

Asynchronous dissipative control design for semi-Markovian jump systems with uncertain probability distribution functions of sojourn-time

This paper is concerned with the problem of asynchronous mode-dependent dissipative control for continuous-time semi-Markovian jump systems (S-MJSs), where the probability distribution functions of sojourn-time are established in a generic form to cover uncertainties that occur due to experimental limitations and errors. Further, based on a control-mode-dependent Lyapunov function, this paper proposes a robust control design method developed such that 1) the control system performance can be further improved compared to using system-mode-dependent Lyapunov functions, 2) the block size of stabilization conditions can be reduced, and 3) the non-convex terms combined with either positive or negative transition rates can be explicitly addressed. Finally, three illustrative examples are given to show the effectiveness of the proposed method.

A Systematic Optimization Design of New Constrained Robust Model Predictive Fault-Tolerant Control for Industrial Processes

A comprehensive optimization design method of new constrained robust model predictive fault-tolerant control is proposed for industrial processes with partial actuator failures and unknown disturbances. A new state space model which is composed of differential state variables, output tracking errors, and new state variables related to output tracking errors is first constructed according to the multiple single-input single-output (SISO) models. Considering the uncertainties existing in the system, the reproduced model is represented by a discrete switched model with polytopic uncertainties. Subsequently, the model predictive controller with min-max optimization is designed to ensure the performance improvement and solve the drawback that the controller gain is not adjustable. To further enhance the system performance, the designed controller is optimized in two steps based on the switching strategy. In addition, the corresponding switching strategy is designed to realize the mutual switching between different models of the system. Finally, taking continuous stirred tank and injection molding processes as examples, the effectiveness of the proposed method is verified by comparing with the traditional control method.

이산시간 불확실 특이시스템의 새로운 강인 유한시간 상태궤환 제어

In this paper, we consider the problem of robust finite-time singular stability(RFSS) and state feedback controller design method for discrete–time linear singular systems with norm-bounded parameter uncertainties. First, the FSS sufficient condition is derived by equivalently transformed closed-loop system. Second, a state feedback controller design method satisfying regular, causal, and RFSS is proposed by LMI(linear matrix inequality) technique on the basis of the obtained FSS condition and equivalent properties of the considering system. The presented conditions are strict LMI conditions in terms of finding all variables compared with previous results. Finally, a numerical example is given to illustrate the validity of the proposed method.

Implementation and design non-linear controller for stand-alone generator

This article describes the implementation and design of a non-linear controller for a stand-alone generator which has a DC motor as a prime mover based on input-output feedback linearization (FL) technique. While in the grids-connected synchronous generator the attention is focused on the load angle as stability assessment, the speed and terminal voltage is the main effective state in stand-alone generators. Therefore, the FL robust control design method is utilized to truck the desired speed and terminal voltage. First, a non-linear mathematical model is derived for the synchronous generator with a dc motor as a prime mover then input-output FL is applied to this non-linear model to make it linear. The tracking control low of the linearized model is designed using a pole placement technique. For verifying the efficiency and performance of the system, several tests were conducted in the Matlab simulation with some experimental results. These results showed a high dynamic response to a large and fast load difference and zero steady-condition error.