Robust observer-based controller design for nonlinear parameter-varying systems with uncertainty and external disturbances

International audience

Robust velocity and height control problem is dealt with for hypersonic vehicles subject to highly nonlinearity and uncertainties. The linear robust controller design for nonlinear systems suffers from the conservation problem, because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve the dynamic decoupling of the velocity and height channels. Then, robust controllers are designed for each channel to restrain the effects of the parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be counteracted accurately by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system, while the conservation of the robust controller design can be reduced because the nonlinear information of dynamic system is used. Simulation comparisons are given to show the advantages of the proposed robust nonlinear control method.

The problem of robust velocity and height control is dealt with for hypersonic vehicles subject to high nonlinearity and uncertainties. Robust linear controller design for nonlinear systems suffers from the problem of conservation because the nonlinear dynamics are considered as uncertainties. In this paper, a feedback linearization controller is firstly applied to achieve dynamic decoupling of the velocity and height channels. Robust controllers are then designed for each channel to achieve the desired tracking and restrain the effects of parametric uncertainties, external disturbances, and nonlinear dynamics, which cannot be accurately counteracted by the feedback linearization technique. This method can guarantee the robust stability and robust tracking properties of the closed-loop control system. Moreover, the conservation of the robust controller design can be reduced because the nonlinear information of the dynamic system is used. Simulation results are given to show the advantages of the proposed robust nonlinear control method compared with its linear counterpart.

A nervous system consists of a large number of highly interconnected nerve cells. Nerve cells communicate by generation and transmission of short electrical pulses (action potential). In addition, membrane voltage is the only measurable state in nervous systems. A robust observer-based model reference tracking control is proposed for Hodgkin-Huxley (HH) neuron systems to generate a desired reference response in spite of environmental noises, uncertain initial values, and diffusion currents from other interconnected nerve cells. In order to simplify the robust tracking control design of nonlinear stochastic HH neuron systems, a fuzzy interpolation method is employed to interpolate several linear stochastic systems to approximate a nonlinear stochastic HH neuron system so that the nonlinear robust tracking control problem can be solved by the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. The proposed robust observer-based tracking control scheme can provide new methods for desired action potential generation, suppression of oscillations, and blockage of action potential transmission under environmental noise and diffusion currents. These new methods are useful for patients with different neuron system dysfunctions. Finally, three simulation examples of tracking control of nervous systems are given to illustrate the design procedure and confirm the tracking performance of the proposed method.

Robust control for nonlinear systems with structured [formula omitted]2-gain bounded uncertainty

Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming

<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>

In this article, a novel robust observer-based nonlinear control approach is proposed for quadrotors with unmodeled dynamics and external disturbances, wherein the tracking errors are restricted effectively. Two nonlinear disturbance observers are proposed to deal with uncertainties in the inner and outer loops, respectively. On this basis, a robust observer-based nonlinear control approach is put forward for quadrotor systems. Specifically, in the outer loop subsystem, a robust observer-based control scheme is proposed, which can reduce unexpected tracking errors for quadrotors effectively. Subsequently, based upon the geometric methods, the coordinate-free attitude controller and the nonlinear disturbance observer are integrated as a robust controller in the inner loop subsystem. Based upon full nonlinear dynamics, the solutions of the closed-loop system are proven to be uniformly ultimately bounded by means of rigorous Lyapunov analysis. A series of comparative experiments consisting of the implementation of a nonlinear proportional-integral-derivative (PID)-type controller, an observer-based sliding mode controller, and the proposed controller are conducted to demonstrate the remarkable performance of the proposed method in terms of higher tracking accuracy and stronger robustness.

This paper is devoted to robust output feedback tracking control design for a class of switched nonlinear cascade systems. The main goal is to ensure the global input-to-state stable (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. First, a nonlinear observer is constructed through state transformation to reconstruct the unavailable states, where only one parameter should be determined. Then, by virtue of the nonlinear sliding mode control (SMC), a discontinuous nonlinear output feedback controller is designed using a backstepping like design procedure to ensure the ISS property. Finally, an example is provided to show the effectiveness of the proposed approach.

Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

This article focuses on establishing a general robust actor‐critic online learning control structure for disturbed nonlinear continuous systems with input constraints. It enriches the existing studies for the robustness of input constraint systems. First, the problem of robust controller design is successfully transformed into optimal controller design, and this process is proven, in which a particular nonquadratic discount cost function is defined. Then, build two neural networks (NNs) to estimate the cost function together and update each other. In the update process of actor NN, a robust term related to the state is introduced, which can guarantee the system's stability during the online learning process, and the state information is more fully utilized. Furthermore, using Lyapunov's direct method, it is proved that the estimated weights of the closed‐loop optimal control system and the actor‐critic NNs are uniformly ultimately bounded (UUB). It also provides extended discussions and a simulation example to demonstrate the robustness verification results of the novel algorithm.

This paper presents a new design algorithm for the decentralized output feedback control problem of large- scale interconnected systems. A decentralized estimated state feedback controller and a decentralized observer are designed for each subsystem, based on linear matrix inequalities (LMIs). Sufficient conditions for the synthesis of feedback action are provided, under which the proposed controllers and observers can achieve robust stabilization of the overall large-scale system. An attractive feature of the proposed scheme is that it guarantees connective stability of the overall system, and requires no in- tersub system communication. The controller design is evaluated on a natural circulation drum boiler, where the nonlinear model describes the key dynamical properties of the drum, the risers, the downcomers and the turbine-generator unit. The linearized system has two poles at origin, one associated with water dynamics and the other with generator dynamics. Simulation results show the effectiveness of the proposed control against instabilities following sudden load variations. The control is also effective for steady state operation.

Detailed in this paper is a SISO non-linear modelling and robust controller design methodology experimentally verified on an internal combustion engine. The methodology begins with the identification of a NARMAX model that captures the non-linear dynamics relating the input to the output of a system. This model is converted to a describing function representation for the purpose of robust feedback controller design. The ideology for the describing function recovery is developed in the form of an algorithm which can be extended to other NARMAX model structures not considered here. The controller design is executed in the frequency domain where the output performance specification is |y(t)|≤β∀t>0 and the actuator saturation constraint is |u(t)|≤K∀t>0. For the engine idle speed control application of this study, a SISO NARMAX model of the engine is developed between the by-pass idle air valve (BPAV) and engine speed. The performance objective for the controller design is the time domain tolerance of |Δ rpm| ≤ 100 rpm on idle speed perturbations despite a non-measurable 20 N m external torque disturbance. The controller is validated through numerical simulations as well as experimental verification.

This paper addresses the problem of robust output feedback controller design with guaranteed cost and multiple quadratic Lyapunov function for linear switched systems in the continuous-time domain. The approach followed in this paper looks at the existence of switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration. Two different linear matrix inequality based conditions allow checking the existence of a family of quadratic Lyapunov functions. Then, a switched robust output feedback design method is established. The proposed method is illustrated on numerical example.

The problem of synthesizing robust pole placement controllers for interval linear time-invariant plants is addressed in the context of the concepts and methods of interval analysis. The robust pole placement design problem is associated with the solution of an interval Diophantine equation, whose basic properties axe analyzed. Robust pole placement controllers axe viewed as inner solutions of the interval Diophantine equation. Simple and computationally efficient characterizations of the set of all robust pole placement controllers are then obtained and some of its geometric properties, discussed. Several aspects of the design of robust controllers by interval analysis are integrated into a linear goal programming formulation, which can also incorporate additional constraints on the controller parameters. Robust pole placement design problems are easily modeled and solved through the approach proposed. Numerical examples illustrate its main characteristics.