Output Tracking Controller Design Research Articles

Output tracking control design with anti-disturbance rejection for modified repetitive nonlinear control systems

ABSTRACTThis paper intends to analyse the disturbance rejection and output tracking control for a class of nonlinear control systems with disturbances. In this connection, we present a method that combines a proportional-integral observer and nonlinear-equivalent-input-disturbance estimator for superior disturbance rejection performance. Specifically, the nonlinear-equivalent-input-disturbance estimator comprises of equivalent-input-disturbance estimator and nonlinear feedback term, which is employed to estimate and reject the disturbances from the nonlinear system. Notably, the proportional-integral loop in the proportional-integral observer reduces the estimation inaccuracy of the nonlinear-equivalent-input-disturbance. Then the estimated disturbance is intertwined into the repetitive control input to compensate it efficiently. In order to obtain the required results, the proposed control system is converted into a two-dimensional modified repetitive control system to describe the learning and control actions. In particular, the proposed controller enables to adjust the gains directly to improve the learning and control performance and as a result, the tracking accuracy increases. Using a general Lyapunov–Krasovskii functional, singular value decomposition technique and linear matrix inequalities approach, a design algorithm for establishing proportional-integral observer and feedback gains is developed for the system under consideration. Finally, simulation results are given to illustrate the developed method's validity and superiority.

Sliding mode control design using generalized relative degree approach: Aerospace application

Relative degree (RD) approach is a powerful tool for obtaining system's input-output dynamics used for output tracking controller designs of minimum phase systems. Designs using the RD alone can fail due both to insufficient control authority in minimum phase systems, and instability of internal/zero dynamics attributed to nonminimum phase systems. A novel definition and a concept of Practical Generalized RD (PGRD) are proposed in this paper and are used in concert with Sliding Mode Control (SMC) to compensate for system perturbations in minimum phase systems. The use of known Generalized Relative Degree (GRD) in nonminimum phase systems allows for the elimination of internal dynamics. However, instability that emerges in the corresponding control dynamic extension is defeating any output tracking controller design. A novel methodology of using GRD for designing continuous SMC in nonminimum phase systems is presented. An algorithm for generating a bounded solution of the unstable dynamic extension is proposed and used in concert with SMC, allowing robust control design for nonminimum phase systems. The efficacy of the proposed GRD-based approaches is demonstrated on a minimum and nonminimum phase rocket attitude control problem both analytically and via simulation.

Boundary Fuzzy Output Tracking Control of Nonlinear Parabolic Infinite-Dimensional Dynamic Systems: Application to Cooling Process in Hot Strip Mills

This paper utilizes a combination of integral control, fuzzy control, and observer-based output feedback control to deal with the issue of nonlinear output tracking control (OTC) design for nonlinear infinite-dimensional dynamic systems. The system dynamics model is represented by a semi-linear parabolic partial differential equation (PDE) with boundary control and non-collocated boundary measurement. Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is constructed to surmount the OTC design difficulty from the infinite-dimensional nonlinear system dynamics. Subsequently, a fuzzy-observer-based OTC law is proposed via the T-S fuzzy PDE model and the integral control approach. Here, the integral control ensures asymptotic output regulation, and the observer-based output feedback control is employed to conquer the stabilizing control design difficulty caused by the non-collocation between control actuation and measurement. It is shown via the Lyapunov technique with variants of vector-valued Poincaré-Wirtinger's inequality that the suggested fuzzy OTC law drives the measurement output to asymptotically track the desired reference signal and ensures the boundedness of the resulting closed-loop system, provided that a sufficient condition given in the form of linear matrix inequalities is fulfilled. Moreover, the proposed fuzzy-model-based OTC design is also revised for the exponential stabilization case. Finally, extensive simulation results for a numerical example and a cooling process in hot strip mills are provided to examine the effectiveness and merit of the proposed fuzzy OTC scheme.

Quad-rotor adaptive sliding mode control using only position and yaw sensors: Generalized relative degree approach

An output tracking controller design is proposed for perturbed Quad-Rotor Unmanned Aerial Vehicles (QR-UAV) using a generalized relative degree approach that allows employing only four measurements of the QR-UAV states, position (x,y,z) and yaw angle (ψ), instead of the traditional six variables. Adaptive Super-Twisting (ASTW) control is applied for controlling the yaw angle (ψ) in the presence of perturbations with bounded derivatives and unknown bounds. The relative degree approach allows the application of Adaptive Continuous High Order Sliding Mode (ACHOSM) control for controlling the position states (x,y,z), in a single loop, in the presence of smooth perturbations with bounded derivatives and unknown bounds. The proposed single loop ASTW and the ACHOSM controllers, with non-overestimated control gains, drive the position trajectory and yaw tracking errors to zero asymptotically in the absence of dynamics of actuators and sensors. Finite convergent time Filtering HOSM differentiators are used to facilitate the ACHOSM controllers in the presence of the noisy measurements. The proposed single loop sliding mode controllers have been validated via simulations.

Output Tracking and Feedback Controller Design for Nonlinear Stochastic Time-Delay System

This paper considers the design of output tracking and feedback controllers for nonlinear stochastic systems. The system status cannot be measured. The studied system contains nonlinear state functions, noise disturbances and time delays. We use the free weight matrix method to avoid the conservatism caused by the use of model transformation or cross-term bounded techniques. Based on the Lyapunov-Krasovskii functional method, we propose an output tracking and feedback controller design method based on linear matrix inequality (LMI). Numerical examples show the validity of the obtained results.

Output Tracking Control Design of Switched Boolean Control Networks

In this letter, the output tracking control design of switched Boolean control networks (SBCNs) is investigated via state feedback and output feedback control. The algebraic state-space representation method which resorts to the semi-tensor product (STP) of matrices is utilized; necessary and sufficient conditions for the solvability of the output tracking control problem are presented. A constructive procedure is given to obtain all possible switching signal-dependent state feedback and output feedback controllers under arbitrary switching signals such that the output of SBCNs tracks a time-varying reference trajectory. Finally, a SBCN model of the lactose regulation in the Escherichia Coli bacteria is considered to illustrate the effectiveness of the proposed results.

HUMAN-INSPIRED ALGEBRAIC CURVES FOR WEARABLE ROBOT CONTROL.

Having unified representations of human walking gait data is of paramount importance for wearable robot control. In the rehabilitation robotics literature, control approaches that unify the gait cycle of wearable robots are more appealing than the conventional approaches that rely on dividing the gait cycle into several periods, each with their own distinct controllers. In this article we propose employing algebraic curves to represent human walking data for wearable robot controller design. In order to generate algebraic curves from human walking data, we employ the 3L fitting algorithm, a tool developed in the pattern recognition literature for fitting implicit polynomial curves to given datasets. For an impedance model of the knee joint motion driven by the hip angle signal, we provide conditions by which the generated algebraic curves satisfy a robust relative degree condition throughout the entire walking gait cycle. The robust relative degree property makes the algebraic curve representation of walking gaits amenable to various nonlinear output tracking controller design techniques.

Output tracking control of switched nonlinear systems with multiple time-varying delays

ABSTRACTIn this paper, the output tracking control problem for a class of switched nonlinear systems with multiple time-varying delays is studied based on equivalent-input-disturbance (EID) approach. More precisely, with the use of suitable Lyapunov-Krasovskii functional together with average dwell-time technique, an output feedback tracking controller is designed which makes that the states of resulting system can asymptotically track the desired trajectory. Further, the EID estimator is implemented to reject both matched and unmatched disturbances effectively without requiring any prior knowledge of the disturbances. Simulation results are presented to illustrate the effectiveness and potential of the developed EID-based output tracking control design technique. The results reveal the fact that the tracking controller based on EID provides a better tracking performance than the feedback controller based on sliding mode technique.

Near-optimal output tracking controller design for nonlinear systems using an event-driven ADP approach

Abstract In this paper, a novel output tracking control scheme for a class of continuous-time nonlinear system is proposed by using an event-driven adaptive dynamic programming (ADP) approach. Based on the controlled system and the desired reference trajectory, an augmented system is constructed for the optimal tracking control problem (OTCP), where the control law is composed of the steady-state part and the feedback part. According to the standard solution of the OTCP, the feedback part associated to the cost function is to be solved and the steady-state part of the control can be obtained directly. Thus the event-driven near-optimal control method is proposed to solve feedback control of the OTCP, where a single network ADP approach is developed to approximate the optimal cost function. The output tracking error dynamic get converged to zero and the parameters of critic neural network (NN) get converged to the optimal ones by using the designed weight tuning law and event-triggering condition. The stability of the augmented system under the novel control scheme is guaranteed based on Lyapunov theory and two simulation examples are presented to demonstrate the effectiveness of the proposed method.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays.

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

Design of Robust Controller for a Class of Uncertain Discrete-Time Systems Subject to Actuator Saturation

This technical note studies the robust output tracking controller design for a class of uncertain discrete-time systems subject to actuator saturation. To achieve this capability, a new controller is proposed by robustifying the discrete-time composite nonlinear feedback (DCNF) control law. Since, the proposed controller may be saturated; a precise analysis is done to show its robust performance in spite of presence of actuator saturation and time-varying external disturbances. Additionally, a theorem is given and proved which guarantees the disturbance attenuation via the proposed control law for three different cases of the saturation function and it is shown that even if the control signal is saturated, the proposed controller achieves steady-state error of order $O(T)$ for state regulation. Finally, computer simulations are performed for a practical system and the applicability of the proposed controller is shown.

Robust control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

SummaryThe output tracking controller design problem is dealt with for a class of nonlinear semi‐strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.

Delay‐ and Packet‐Disordering‐Dependent H∞ Output Tracking Control for Networked Control Systems

AbstractThis paper is concerned with the problem of H∞ output tracking control for networked control systems (NCSs) with network‐induced delay and packet disordering. Different from the results in existing literature, the controller design in this paper is both delay‐ and packet‐disordering‐dependent. Based on the different cases of consecutive predictions, the networked output tracking system is modeled into a switched system. Moreover, by the corresponding switching‐based Lyapunov functional approach, a linear matrix inequality (LMI)‐based procedure is proposed for designing state‐feedback controllers, which guarantees that the output of the closed‐loop NCSs tracks the output of a given reference model well in the H∞ sense. In addition, the proposed method can be applied variously due to all kinds of prediction numbers of the consecutive disordering packet have been considered, and the designed controller is based on the prediction case in the last transmission interval, which brings about less conservatism. Finally numerical examples and simulations are used to illustrate the effectiveness and validity of the proposed switching‐based method and the delay‐ and packet‐disordering‐dependent H∞ output tracking controller design.

Stability Analysis andH∞Output Tracking Control for Linear Systems with Time-Varying Delays

The problem of stability analysis andH∞output tracking control for linear systems with time-varying delays is studied. First, by construction of a newly augmented Lyapunov-Krasovskii functional, a delay-dependent stability criterion for nominal systems with time-varying delays is established in terms of linear matrix inequalities (LMIs). Second, based on theH∞sense, the proposed method is extended to solve the problem of designing anH∞output tracking controller to track the output of a given reference model. Finally, three examples are included to show the validity and effectiveness of the presented delay-dependent stability and theH∞output tracking controller design.

Robust H ∞ Output Tracking Control for a Class of Nonlinear Systems with Time-Varying Delays

This paper addresses the H ? output tracking problem for a class of nonlinear systems subjected to model uncertainties and with interval time-varying delay. The stability of the nonlinear time-delay system is analyzed with a novel delay-interval-dependent Lyapunov---Krasovskii functional. Compared to state-of-the-art criteria for linear and nonlinear time-delay systems, less conservative stability conditions are derived with the introduction of new delay-interval-dependent terms and the exploitation of the delay subintervals size. The proposed analysis considers that the delay derivative is either upper and lower bounded, bounded above only, or unbounded, i.e., no restrictions are cast upon the derivative. Numerical examples are provided to enlighten the importance and advantages of the present criterion which outperforms previous criteria in time-delay systems literature. Also, an additional example is provided to highlight the effectiveness of the proposed H ? output tracking control design technique for complex nonlinear systems with time-varying delay.

Step Output Tracking Controller Design for Networked Control Systems

This paper is concerned with the step output tracking controller design problem for networked discretetime linear systems. The communication constraints such as network-induced delay, packet disorder, and packet dropout are considered, which are treated as the round-trip time (RTT) delay with an upper bound. An event-driven networked predictive control scheme is proposed to actively compensate for the RTT delay, which avoids the requirement of synchronization between the controller side and the plant side. The stability of the closed-loop system and the design procedure of the observer-based controller are discussed. A numerical example is employed to illustrate the effectiveness of the proposed methods.

Sampled-data switched control for flexible air-breathing hypersonic vehicles

The nonstandard dynamic characteristics of flexible air-breathing hypersonic vehicles along with the aerodynamic effects of hypersonic flight cause the flight control of such vehicles highly challenging. Additionally, the wide range of speed and the varied parameters make the problem more difficult. In this article, the problem of sampled-data switched output tracking control design is addressed for flexible air-breathing hypersonic vehicles. First, the nonlinear longitudinal model of flexible air-breathing hypersonic vehicles is linearized with respect to different regions, and the switched sampled-data guaranteed cost controller design problem is discussed. Using an input delay approach, the switched system with sampling measurements is transformed into a continuous time-delay system. Then, by a Lyapunov approach, the existence condition of such a controller is developed in the form of linear matrix inequalities. A smooth switching condition is also designed simultaneously, and the sampled-data smooth switching controller design problem is cast into a convex optimization problem. The simulation results are reported to show the effectiveness of the proposed control method.

Fuzzy guaranteed cost tracking control for a flexible air-breathing hypersonic vehicle

This study is concerned with the fuzzy guaranteed cost output tracking control design problem for a flexible air-breathing hypersonic vehicle (FAHV), which can be modelled in a Takagi-Sugeno (T–S) model form. Owing to the enormous complexity of the vehicle dynamics, only the longitudinal model is adopted for control design in the present paper. A T–S fuzzy model is first proposed to represent the non-linear dynamics of FAHV. Then, a new augmented system is developed and a fuzzy guaranteed cost output tracking control problem is studied by considering output tracking and performance cost simultaneously. A fuzzy guaranteed cost state feedback controller is designed for the obtained augmented system to guarantee that the closed-loop system is asymptotically stable and the proposed performance index has an upper bound. By utilising Lyapunov functional approach, sufficient solvability conditions for such a controller are also established in terms of linear matrix inequalities, which can be easily solved via standard numerical softwares. Numerical simulations are performed to show the excellent reference altitude and velocity tracking performance.

Semiglobal robust backstepping output tracking for strict-feedback form systems with nonlinear uncertainty

Output tracking controller design problem is dealt with for a class of nonlinear systems in strict-feedback form in the presence of time-varying nonlinear uncertainties and unmodeled dynamics with multi-operation points. A new method based on signal compensation is proposed to design a robust controller, which consists of a nominal controller and a robust compensator. It is shown that semiglobal robust tracking property can be achieved. A new feature of our results is that the controller is a linear and time-invariant one and “explosion of complexity” problem is avoided.

Delay-Dependent Robust H∞ Output Tracking Control for Uncertain Networked Control Systems

AbstractIn this paper, the H∞ output tracking problem for networked control systems (NCSs) liable to model uncertainties and with delays varying within intervals is investigated. A new method is proposed to the robust H∞ output tracking analysis and control design for NCSs. The results presented here are an improvement over previous ones, for the analysis incorporates state-of-the-art stability techniques for systems with time-varying delays such as convex optimization technique, piecewise analysis method, and a new delay fractioning approach with the introduction of a novel auxiliary delayed state. The analysis is enriched with a numerical example that illustrates the advantages of our criteria which outperform previous criteria in the literature. Moreover, an illustrative example shows the effectiveness of the proposed H∞ output tracking control design.