Minimum-phase Nonlinear Systems Research Articles

Robust output regulation of a class of uncertain nonlinear minimum phase systems perturbed by unknown external disturbances

This paper addresses the problem of robust output regulation for uncertain nonlinear minimum phase systems affected by an unknown external disturbance. We present a novel unknown input observer (UIO)-embedded high-gain stabilizer to completely reconstruct the disturbance in a finite time. A new saturation function is introduced to prevent finite time escape of the closed-loop trajectories. This allows us to achieve a semi-globally exponential regulation of the regulated output. The proposed method features the exact cancellation rather than approximate cancellation, for both structured and/or unstructured external disturbance. The presented controller is finite-dimensional and does not require the nominal model of the plant. Finally, a numerical experiment is conducted to demonstrate the effectiveness of the proposed method.

Robust adaptive leaderless consensus of unknown non-minimum phase linear multi-agent systems subject to disturbances and/or unmodeled dynamics

This article investigates the problem of robust adaptive leaderless consensus for heterogeneous uncertain non-minimum phase linear multi-agent systems over directed communication graphs. Each agent is assumed to be of unknown nominal dynamics and also subject to external disturbances and/or unmodeled dynamics. A novel distributed robust adaptive control strategy is proposed. It is shown that the robust adaptive leaderless consensus problem is solved with the proposed control strategy under some sufficient conditions. Two examples are provided to demonstrate the efficacy of the proposed control strategy.

A Model-Following Control Approach to Peaking Attenuation in High-Gain Partial State Feedback for Nonlinear Systems

We consider the model-following control (MFC) scheme for a class of nonlinear minimumphase systems in Byrnes-Isidori form using the nonlinear model in the model control loop (MCL). For the control design we apply partial state feedback in the process control loop (PCL). In particular we consider a high-gain feedback of the external state in the PCL to stabilise the system globally. For the proposed MFC design the typical peaking phenomenon of the high-gain feedback can be overcome if a sufficiently accurate estimate of the initial process state is available. We further establish that the control effort of the proposed MFC design is guaranteed less than that of a comparable stabilising high-gain design using a single-loop feedback only. We demonstrate the design capability of peaking attenuation by a numerical example.

Global state regulation of time-delay minimum-phase systems by delay-free dynamic compensation

This paper studies the global control problem, in the sense of “almost stabilization” or state regulation, for a class of time-delay minimum-phase nonlinear systems via delay-free dynamic compensation. Both dynamic state and output feedback control schemes are developed. By taking advantage of dynamic rather than static feedback, we design delay-independent dynamic state and output feedback compensators, respectively, to achieve asymptotic state regulation with global stability. In the case of dynamic state feedback, a structural condition is imposed on the inverse dynamics that are nonlinear yet imply linear zero dynamics. In the case of dynamic output feedback, more strict conditions on the nonlinearity are characterized to guarantee the existence of a dynamic output controller. In both cases, it is proved by the Lyapunov–Krasovskii functional method, combined with the Barbalat’s lemma, that all the states of the time-delay minimum-phase systems are regulated to zero and boundedness of the closed-loop system is ensured. Two examples are given to validate the proposed delay-free dynamic compensators.

Drift estimation by timescale transformation

In this study, we consider a model free control technique for a class of minimum phase nonlinear systems with unknown dynamics. We propose a timescale transformation approach that can be used to estimate the drift and the high frequency gain of the output dynamics of nonlinear systems with a well defined relative degree. The proposed controller provides an effective output regulation mechanism that avoids the need for direct disturbance model estimation and high gain output feedback controllers. A simulation study is conducted to demonstrate the effectiveness of the proposed approach.

Nonlinearity compensation based robust tracking control of nonlinear nonminimum phase hypersonic flight vehicles

This paper introduces a nonlinearity compensation based robust tracking controller for hypersonic flight vehicles. The controller focuses on robust control design with respect to the nonminimum phase feature and system uncertainties for the control-oriented model. Firstly, following the principle of decomposing the complex control problem into two simpler problems, the original robust tracking problem for nonlinear nonminimum phase hypersonic flight vehicles is decomposed into a simpler robust tracking problem for a linear nonminimum phase system with disturbances and a stabilization problem for a nonlinear system without disturbances. After the problem decomposition, a proportional–integral tracking controller and a feedback linearization controller are designed for the linear system and the nonlinear system, respectively. Then, the addition of the two designed controllers gives the final controller. By compensating for the system nonlinearity using the secondary system and its controller, the proposed control method can satisfy the robust tracking control requirements for nonlinear nonminimum phase hypersonic flight vehicles. The simulation results show, compared with a feedback linearization control method and a composite neural learning control method, the proposed method has superior tracking accuracy and robustness against system uncertainties and external disturbances.

Suboptimal output consensus of a group of discrete-time heterogeneous linear non-minimum phase systems

This paper formulates the suboptimal output consensus problem for a discrete-time heterogeneous linear multi-agent system with unstable zero dynamics, where each agent possesses its own objective function and the sum of all these private objective functions, called the overall objective function, is to be minimized. Mild assumptions on the communication topology and the agent dynamics are made under which a parameterized distributed consensus protocol based on low gain feedback is proposed for each agent. The multi-agent system is shown to achieve suboptimal output consensus under the proposed protocols in the sense that the states of all agents remain bounded while their outputs converge to a pre-specified arbitrarily small neighborhood of the optimal point as long as the design parameter is chosen small enough. Simulation results are presented that demonstrate the proposed design.

Finite Quantized-Output Feedback Tracking Control of Possibly Non-Minimum Phase Linear Systems

This paper proposes a finite quantized-output feedback tracking control method for a general class of continuous-time linear time-invariant systems. Firstly, an analytical pole placement-based control law is constructed using a finite quantized-output signal and an external reference output signal. Then, it is proven that the proposed control law can ensure all closed-loop signals are bounded, and the output tracking error converges to a residual set of the origin exponentially. Moreover, we show that the residual set can be made arbitrarily small if the magnitude of the quantizer satisfies a specified condition. This method combines the advantages of the classical pole placement control technique and the quantized control technique. Compared with the existing tracking control methods, it not only reduces the feedback information requirement, but also has full capability to deal with unstable poles and zeros in the controlled plant for output tracking. A numerical example is presented to verify the validity and new features of the proposed method.

Repetitive control design based on forwarding for nonlinear minimum-phase systems

We propose a new design for a repetitive control scheme for nonlinear minimum-phase systems with arbitrary relative degree and globally Lipschitz nonlinearities. We represent the delay of the repetitive control scheme as a transport equation and we propose a new forwarding-based (partial) state-feedback design that uses not only the boundary information of the delay, but the entire state of the transport equation representing the delay. Through a rigorous mathematical analysis, we show that, from a theoretical point of view, asymptotic convergence of the desired regulated output can be achieved with the proposed control design.

Online Time Delay and Disturbance Compensation for Linear Non-Minimum Phase Systems

Online Time Delay and Disturbance Compensation for Linear Non-Minimum Phase Systems

Output tracking for a non-minimum phase robotic manipulator

We exploit a recently developed funnel control methodology for linear non-minimum phase systems to design an output error feedback controller for a nonlinear robotic manipulator, which is not minimum phase. We illustrate the novel control design by a numerical case study where we simulate end-effector output tracking of the robotic manipulator.

Output-feedback repetitive control for minimum-phase nonlinear systems with arbitrarily relative degree

Abstract A new design of output-feedback repetitive control scheme for nonlinear minimum-phase systems with arbitrary relative degree and globally Lipschitz nonlinearities is proposed. This work extends the recent results in Astolfi et al. [2021]. The delay of the repetitive control scheme is represented by a transport equation. A high-gain observer and a forwarding-based feedback law are employed to steer the desired output to zero in presence of periodic signals (references and/or perturbations) and model uncertainties.

Quantitative robustness analysis of model following control for nonlinear systems subject to model uncertainties

Abstract We investigate a model following control (MFC) design for nonlinear minimumphase systems subject to model uncertainties. The model following control architecture is a two degrees-of-freedom structure consisting of two control loops. The model control loop (MCL) includes a nominal model of the process. The design of the process control loop (PCL) is based on the error system resulting from the nominal design and the actual process. Both control loops are designed using (partial) feedback linearisation. We analyse the robustness in view of the norm of the uncertainty and the region of attraction compared to a single-loop (partial) feedback linearisation control. It turns out that the proposed approach is able to stabilize significantly larger uncertainties, shows better tracking performance, and exhibits a larger region of attraction (based on a quadratic Lyapunov function).

Asymptotic Tracking for Nonminimum Phase Linear Systems via Steady-State Compensation

The problem of output tracking is addressed in this article by a reformulation in terms of a two-point boundary value problem for the plant's zero dynamics, which is allowed to be unstable. On this basis, a hybrid feedback regulator ensuring output tracking is then designed. The robustness properties of the proposed regulator as well as connections with periodic (cheap) optimal control, output regulation, and possible extensions to the nonlinear setting are also discussed.

Suboptimal output consensus for a group of weakly nonminimum phase linear systems

This paper studies the suboptimal output consensus problem for a multi-agent system, where each agent is described by a weakly nonminimum phase linear system and endowed with an objective function. For each agent, a low gain feedback based protocol consisting of a local term and a distributed term and parameterized with a low gain parameter is constructed. Under the assumption that the communication topology is strongly connected and weight-balanced, these protocols achieve suboptimal output consensus for the multi-agent system, that is, for a small enough value of the low gain parameter, the outputs of all agents reaching consensus at a value in an a priori specified arbitrarily small neighborhood of the optimal value of the overall objective function, which is the sum of the individual objective functions of all agents. The theoretical results are verified by numerical examples.

Tracking with prescribed performance for linear non-minimum phase systems

We consider tracking control for uncertain linear systems with known relative degree which are possibly non-minimum phase, i.e., their zero dynamics may have an unstable part. For a given sufficiently smooth reference signal we design a low-complexity controller which achieves that the tracking error evolves within a prescribed performance funnel. We present a novel approach where a new output is constructed, with respect to which the system has a higher relative degree, but the unstable part of the zero dynamics is eliminated. Using recent results in funnel control, we then design a controller with respect to this new output, which also incorporates a new reference signal. We prove that the original output stays within a prescribed performance funnel around the original reference trajectory and all signals in the closed-loop system are bounded. The results are illustrated by some simulations.

Repetitive control for nonlinear systems: an actuator-focussed design method

There exist at least two viewpoints on the internal model principle (IMP), namely the cancelation viewpoint and the geometrical viewpoint. However, neither of them is applicable to repetitive control (RC, or repetitive controller, also designated RC) of nonlinear systems directly. Because of this, error dynamics are often derived to transform a periodic signal tracking problem into a rejection problem. This not only fails to represent the special feature of periodic signals but also restricts the applications of RC. In view of this, this paper proposes a new viewpoint on IMP, namely the actuator-focussed viewpoint. With this, the periodic signal tracking problem can be converted into a stability problem without deriving error dynamics for linear periodic systems and nonlinear systems. In order to demonstrate its effectiveness, the proposed design approach is applied to RC problems for a linear periodic system, a minimum-phase nonlinear system and a nonminimum-phase nonlinear system.

Consensus Control of a Class of Uncertain Nonlinear Multiagent Systems via Gradient-Based Algorithms.

This paper is concerned with the distributed optimization problem for a class of minimum-phase nonlinear multiagent systems with second relative degree. The target is to minimize a cost function composed of a group of convex local functions of the outputs in a cooperative manner. Novel state feedback control laws are first proposed and the consensus subject to the optimization constraint is achieved when the communication graph is directed. By replacing the derivatives of the outputs in the state feedback control laws with their estimations, the output feedback control laws are constructed and proved to achieve exponential consensus under the undirected graph. The effectiveness of the proposed control laws is validated by some simulations.

Advances on adaptive learning control: The case of non-minimum phase linear systems

The adaptive learning control theory is extended to include the case of non-minimum phase (time-invariant) linear systems with uncertain parameters. The existence of two approximate solutions to the related output tracking problem is proved. Exponential tracking of periodic output reference signals is guaranteed, along with the exponential estimation of the constant system parameters and of the constant coefficients characterizing the truncated Fourier series expansion for the periodic input reference signal.

Switching Control of Acceleration and Safety Protection for Turbo Fan Aero‐Engines Based on Equilibrium Manifold Expansion Model

AbstractThis paper presents a switching control strategy to solve the acceleration problem with safety constraints for aero‐engines. The proposed strategy is based on an equilibrium manifold expansion (EME) model. That brings a more precise description for the dynamic behavior of the aero‐engine during the acceleration procedure. The acceleration controller, the safety protection controller, and the set‐point controller are designed separately for the respective objectives with more degree of freedom and less conservatism. Based on Lyapunov function, the switching law is properly designed to ensure asymptotic stability with acceleration constraint and the high pressure turbine outlet temperature safety constraint for the nonlinear EME model. It is not necessary to construct a minimum phase nonlinear system using the proposed strategy. The effectiveness of the proposed strategy is verified through a case study where the controller designed based on the EME model is used for a nonlinear component‐level (NCL) model. Simulation also indicates better performance from using the proposed strategy than the existing method.