基于回路成形的鲁棒增益调度控制器设计

针对目前基于线性变参数系统的增益调度控制设计中存在的控制结构复杂性问题，提出一种基于回路成形的简单且易实现的增益调度控制结构.在此基础上，提出一个鲁棒增益调度控制设计方法.设计过程首先采用补偿器函数使得被控对象奇异值具有期望的形状，以保证被控对象的性能要求，然后利用小增益定理设计一个鲁棒控制器，得到具有良好性能的、结构简单的鲁棒增益调度控制器.最后针对一个化工过程，说明此方法的有效性.     

Robust global stabilization of linear systems with input saturation via gain scheduling

The problem of robust global stabilization of linear systems subject to input saturation and input‐additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation‐based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing ?₂‐type gain scheduling controller, which requires the online solution of a state‐dependent nonlinear optimization problem and a state‐dependent ?₂ algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input‐additive uncertainties, the proposed controller also partially recovers Teel's ?_∞‐type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The ?_∞‐type scheduling approach achieves robustness not only with non‐input‐additive uncertainties but also requires the closed‐form solution to an ?_∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the ?_∞‐type scheduling approach in the absence of non‐input‐additive uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.     

Gain-scheduled controller synthesis for a nonlinear PDE

Linear parameter-varying (LPV) modelling and control of a nonlinear partial differential equation (PDE) is considered in this article. The one-dimensional viscous Burgers' equation is discretised using a finite difference scheme; the boundary conditions are taken as control inputs and the velocities at two grid points are assumed to be measurable. A nonlinear high-order state space model is generated and proper orthogonal decomposition is used for model order reduction. After assessing the accuracy of the reduced model, a low-order functional observer is designed to estimate the reduced states which are linear combinations of the velocities at all grid points. A discrete-time quasi-LPV model that is affine in scheduling parameters is derived based on the reduced model. A polytopic LPV controller is synthesised based on a generalised plant containing the LPV model and the functional observer. More generally, the proposed method can be used to design an LPV controller for a quasi-LPV system with non-measurable scheduling parameters. Simulation results demonstrate the high tracking performance and disturbance and measurement noise rejection capabilities of the designed LPV controller compared with a linear quadratic Gaussian (LQG) controller based on a linearised model.     

Mixed‐Objective Robust Dynamic Output Feedback Controller Synthesis for Continuous‐Time Polytopic Lpv Systems

A robust dynamic output feedback controller synthesis algorithm considering H_∞/H₂ performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.     

Model and robust gain‐scheduled PID control of a bio‐inspired morphing UAV based on LPV method

In this paper, a linear parameter‐varying (LPV)‐based model and robust gain‐scheduled structural proportion integral and derivative (PID) control design solution are proposed and applied on a bio‐inspired morphing wing unmanned aerial vehicle (UAV) for the morphing process. In the LPV model method, the authors propose an improved modeling method for LPV systems. The method combines partial linearization and function substitution. Using the proposed method, we can choose the varying parameters simply, thus creating a model that is more flexible and applicable. Then, a robust gain‐scheduled structural PID control design method is given by introducing a structural matrix to design a structural PID controller, which is more consistent with the structure of the PID controller used in practice and has a simpler structure than representative ones in the existing literature. The simulation results show that the developed LPV morphing UAV model is able to catch the response of the original nonlinear model with a smaller error than the existing Jacobian linearization method and the designed controller can maintain stable flights in practice with satisfactory robustness and performance.     

Linear parameter varying switching attitude control for a near space hypersonic vehicle with parametric uncertainties

This paper deals with the problem of linear parameter varying (LPV) switching attitude control for a near space hypersonic vehicle (NSHV) with parametric uncertainties. First, due to the enormous complexity of the NSHV nonlinear attitude dynamics, a slow–fast loop polytopic LPV attitude model is developed by using Jacobian linearisation and the tensor product model transformation approach. Second, for the purpose of less conservative attitude controller design, the flight envelope is divided into four subregions. For each parameter subregion, slow-loop and fast-loop LPV controllers are designed. By the defined switching character function, these slow–fast loop LPV controllers are then switched in order to guarantee the closed-loop NSHV system to be asymptotically stable and satisfy a specified tracking performance criterion. The condition of LPV switching attitude controller synthesis is given in terms of linear matrix inequalities, which can be readily solved via standard numerical software, and the robust stability analysis of the closed-loop NSHV system is verified based on multiple Lypapunov functions. Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.     

Observer‐based synthesis of linear parameter‐varying mixed sensitivity controllers

This article presents a computationally efficient way of synthesizing linear parameter‐varying (LPV) controllers. It reviews the possibility of a separate observer and state feedback synthesis with guaranteed performance and shows that a standard mixed sensitivity problem can be solved in this way. The resultant output feedback controller consists of an LPV observer, augmented with dynamic filters to incorporate integral control and roll‐off properties, and an LPV state feedback gain. It is thus highly structured, which is beneficial for implementation. Moreover, it does not depend on scheduling parameter rates regardless of whether parameter‐dependent Lyapunov matrices are used during synthesis. A representative control design for active flutter suppression on an aeroelastic unmanned aircraft demonstrates the benefits of the proposed method in comparison with state‐of‐the‐art LPV output feedback synthesis.     

A robust self-scheduled missile autopilot: design by multi-model eigenstructure assignment

This paper describes the synthesis of a self-scheduled controller robust with respect to parametric uncertainties. Traditionally, scheduling is done a posteriori by interpolation of gains computed for several points within the parameter space. The method proposed here, named (Mu-μ)-iteration, is based on worst-case analysis and multi-model eigenstructure assignment. It permits the designer to synthesize a robust low order controller by considering a priori its dependence of some scheduling parameters. The method is then applied to derive a robust missile autopilot.     

A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance

This paper considers a multi-step output feedback robust model predictive control (OFRMPC) approach for the linear parameter varying (LPV) systems with bounded changes of scheduling parameters and bounded disturbance. Less conservative bounds of future estimation error sets and system parametric uncertain sets are predicted by considering bounded changes of scheduling parameters in LPV systems. In the multi-step OFRMPC approach, an optimization problem is solved to obtain a sequence of controller gains, which considers predictions of future bounds of estimation error sets and system parametric uncertain sets. The optimized sequence of controller gains corresponding to a sequence of Lyaponov matrices have less constraint conditions and also introduce more degree of freedom for the optimization. The proposed multi-step OFRMPC guarantees robust uniform ultimately bounded of the estimation error and robust stability of the observer system. A numerical example is given to demonstrate the effectiveness of the approach.     

A synthesis framework for robust gain-scheduling controllers

We present a general framework for the systematic synthesis of robust gain-scheduling controllers by convex optimization techniques and for uncertain dynamical systems described by standard linear fractional representations. We distinguish between linear time-varying parameters, which are assumed to be available online as scheduling parameters for the controller, and genuine uncertainties, not necessarily time-varying, parametric or linear, that are not available online. Under the rough hypothesis that the control channel is not affected by the unmeasurable uncertainties and that the properties of the uncertainties and scheduling variables are captured by suitable families of integral quadratic constraints, this paper reveals how controller synthesis can be turned into a genuine semi-definite program. The design framework is shown to encompass a rich class of concrete scenarios.     

Probabilistic Robust Linear Parameter-varying Control of a Small Helicopter Using Iterative Scenario Approach

In this paper, we present an iterative scenario approach (ISA) to design robust controllers for complex linear parameter-varying (LPV) systems with uncertainties. The robust controller synthesis problem is transformed to a scenario design problem, with the scenarios generated by identically extracting random samples on both uncertainty parameters and scheduling parameters. An iterative scheme based on the maximum volume ellipsoid cutting-plane method is used to solve the problem. Heuristic logic based on relevance ratio ranking is used to prune the redundant constraints, and thus, to improve the numerical stability of the algorithm. And further, a batching technique is presented to remarkably enhance the computational efficiency. The proposed method is applied to design an output-feedback controller for a small helicopter. Multiple uncertain physical parameters are considered, and simulation studies show that the closed-loop performance is quite good in both aspects of model tracking and dynamic decoupling. For robust LPV control problems, the proposed method is more computationally efficient than the popular stochastic ellipsoid methods.      

Controller reduction for linear parameter-varying systems with a priori bounds

In this paper we develop a controller reduction procedure for linear parameter-varying (LPV) systems. The method uses synthesis Riccati inequalities for the normalized robust stabilization problem as a basis for the approximation. The technique provides a priori error bounds which are used to obtain closed-loop stability conditions and performance degradation level. We also generalize the relative model reduction method to LPV systems and give an energy interpretation to the controller reduction procedure. To illustrate the method, a reduced order controller is synthesized and tested on a nonlinear missile model.     

Output feedback control of linear fractional transformation systems subject to actuator saturation

In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.     

Missile autopilot design via a multi‐channel LFT/LPV control method

In this paper, the missile pitch‐axis autopilot design is revisited using a new and recently available linear parameter‐varying (LPV) control technique. The missile plant model is characterized by a linear fractional transformation (LFT) representation. The synthesis task is conducted by exploiting new capabilities of the LPV method: firstly, a set of H₂/H_∞ criteria defined channel‐wise is considered; secondly, different Lyapunov and scaling variables are used for each channel/specification which is known to reduce conserva tism; and finally, the controller gain‐scheduling function is constructed as affine matrix‐valued function in the polytopic co‐ordinates of the scheduled parameter. All these features are examined and evaluated in turn for the missile control problem. The method is shown to provide additional flexibility to tradeoff conflicting and demanding performance and robustness specifications for the missile while preserving the practical advantage of previous single‐objective LPV methods. Finally, the method is shown to perform very satisfactorily for the missile autopilot design over a wide range of operating conditions. Copyright © 2001 John Wiley & Sons, Ltd.     

Systematic Gain‐Scheduling Control Design: A Missile Autopilot Example

The missile autopilot was designed using linear parameter‐varying (LPV) control techniques. The controller provides exponential stability guarantee and performance bound in terms of induced L₂ norm for the missile plant. The systematic gain‐scheduling approach is motivated by the recent development in LPV control theory and provides a well founded and systematic procedure for high performance missile autopilot design problem.     

Robust global stabilization of spacecraft rendezvous system via gain scheduling

The problem of robust global stabilization of a spacecraft circular orbit rendezvous system with input saturation and inputadditive uncertainties is studied in this paper. The relative models with saturation nonlinearity are established based on Clohessey-Wiltshire equation. Considering the advantages of the recently developed parametric Lyapunov equation-based low gain feedback design method and an existing high gain scheduling technique, a new robust gain scheduling controller is proposed to solve the robust global stabilization problem. To apply the proposed gain scheduling approaches, only a scalar nonlinear equation is required to be solved. Different from the controller design, simulations have been carried out directly on the nonlinear model of the spacecraft rendezvous operation instead of a linearized one. The effectiveness of the proposed approach is shown.     

Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints

A method is presented for synthesizing output estimators and disturbance feedforward controllers for continuous‐time, uncertain, gridded, linear parameter‐varying (LPV) systems. Integral quadratic constraints are used to describe the uncertainty. Since the gridded LPV systems do not have a valid frequency‐domain interpretation, the time domain, dissipation inequality approach is followed. There are 2 main contributions. The first contribution is that a notion of duality is developed for the worst‐case gain analysis of uncertain, gridded LPV systems. This includes notions of dual LPV systems and dual integral quadratic constraints. Furthermore, several technical results are developed to demonstrate that the sufficient conditions for bounding the worst‐case gain of the primal and dual uncertain LPV systems are equivalent. The second contribution is that the convex conditions are derived for the synthesis of robust output estimators for uncertain LPV systems. The estimator synthesis conditions, together with the duality results, enable the convex synthesis of robust disturbance feedforward controllers. The effectiveness of the proposed method is demonstrated using a numerical example.     

Synthesis of a linearly interpolated gain scheduling controller for large flexible spacecraft ETS-VIII

This paper illustrates a design procedure for a linearly interpolated gain scheduling controller for Engineering Test Satellite VIII (ETS-VIII) using its linear parameter-varying (LPV) model. The LPV model here consists of piecewise-linear functions of the paddle rotation angle and a norm-bounded perturbation. The main purpose of this research is to derive a simple structured scheduling law that can be easily implemented in a satellite onboard computer. The derived gain has only two grid points and is scheduled simply by linear interpolation, which is desirable from the standpoint of implementability. Moreover, since the synthesis condition is based on parameter-dependent Lyapunov functions, it gives less conservative results than existing methods. Simulation results are presented to show the effectiveness of the proposed synthesis.     

Stabilization of perturbed system via IMC: An application to load frequency control

This paper proposes a robust controller for a parametric uncertain system of order three. The scheme conceptualizes the approach of selecting the worst-case plant and then the controller is designed using the internal model control principle which constitutes the reduced model of worst-case plant. The beauty of the proposed approach is that even though the plant is uncertain, the complete robust stability analysis and controller design is carried out by a single linear model. As an illustrative example, a load frequency control (LFC) problem is considered for single- and multi-area power systems in presence of unexpected disturbances, parametric uncertainties and physical constraints. The proposed controller is also applied to the network topology similar to standard IEEE 39 bus system (New England 10 machine test system) to validate the more realistic LFC application. Simulation studies show that the proposed controller brings robust and fast disturbance rejection attributes.     

Switching signal design for asymptotic stability of uncertain multiple equilibrium switched systems with actuator saturation

This paper addresses the problem of robust control for a class of multiple equilibrium switched systems with actuator saturation and parameter uncertainties. The parameter uncertainties are described in norm‐bounded form. By combining the parametric Lyapunov equation approach and the gain‐scheduling technique, stabilization conditions are established in terms of linear matrix inequalities. State‐feedback controllers can be designed to guarantee the robust stability and performance of the closed‐loop system in the presence of parameter uncertainties and actuator saturation. The proposed method is to increase the convergence rate during the convergence of the states. Numerical examples and simulations are worked out to illustrate the feasibility of the proposed results. Copyright © 2015 John Wiley & Sons, Ltd.