Analysis of gain scheduled control for nonlinear plants

Gain scheduling has proven to be a successful design methodology in many engineering applications. In the absence of a sound theoretical analysis, these designs come with no guarantees of the robustness, performance, or even nominal stability of the overall gain-scheduled design. An analysis is presented for two types of nonlinear gain-scheduled control systems: (1) scheduling on a reference trajectory, and (2) scheduling on the plant output. Conditions which guarantee stability, robustness, and performance properties of the global gain schedule designs are given. These conditions confirm and formalize popular notions regarding gain scheduled designs, such as that the scheduling variable should vary slowly, and capture the plant's nonlinearities     

Improved stability analysis and gain-scheduled controller synthesisfor parameter-dependent systems

We present new algorithms for robust stability analysis and gain-scheduled controller synthesis for linear systems affected by time-varying parametric uncertainties. These new techniques can also be applied to parameter-dependent nonlinear systems with real-rational nonlinearities. Sufficient conditions for robust stability, as well as conditions for the existence of a robustly stabilizing gain-scheduled controller, are given in terms of a finite number of linear matrix inequalities (LMIs); explicit formulas for constructing robustly stabilizing gain-scheduled controllers are given in terms of the feasible set of these LMIs. The improvement offered by our approach over existing methods for stability analysis and gain-scheduled controller synthesis for parameter-dependent linear systems are analyzed in theory. Numerical examples demonstrate that our approach can offer significant improvement in practice     

磁悬浮储能飞轮线性变参数鲁棒增益调度控制

针对强陀螺效应的磁悬浮储能飞轮转速快变引起的模型变化而带来的控制问题,设计了线性变参数增益调度鲁棒控制器.根据飞轮的线性变参数模型,设计的鲁棒增益调度控制器,能够保证其全转速范围内的鲁棒稳定性和性能.为降低控制器设计的保守性,在设计控制器时,可缩小转速区间,使控制性能得到提高.与按照非时变模型设计的鲁棒控制器相比,线性变参数鲁棒增益调度控制器可以实现以转速为参数的自适应调节,在全转速范围内,其鲁棒稳定性和性能均具有显著优势.仿真结果验证了此控制器的有效性和先进性.     

Genetic synthesis of production-control systems for unreliable manufacturing systems with variable demands

The control of manufacturing systems with variable demands has attracted much research attention over the years. However, only limited results have been obtained due to the difficulty of this production-control problem. In this paper, genetically optimized short-run hedging points are used to construct gain-scheduled adaptive controllers for unreliable manufacturing systems with variable demands. The performance of such adaptive controllers is illustrated for unreliable systems subjected to piecewise-constant demands. It is demonstrated that the performance of these adaptive controllers is superior, in general, to that of genetically optimized non-adaptive controllers. However, such gain-scheduled adaptive controllers are designed for variable demands that are piecewise-constant. Therefore, in order to deal with more general classes of variable demands, a genetic rule-induction design methodology is used to synthesize robust fuzzy-logic controllers to provide automatic closed-loop control for unreliable manufacturing systems. Such robust fuzzy-logic controllers are shown to provide effective control for unreliable manufacturing systems with various kinds of variable demands.     

Robust tracking of the heating value in an underground coal gasification process using dynamic integral sliding mode control and a gain-scheduled modified Utkin observer

In this paper, a model-based control and state reconstruction of an underground coal gasification (UCG) process is elaborated. In order to deploy model-based control strategies, a sophisticated model of the UCG process based on partial differential equations is approximated with a nonlinear control-oriented model that adequately preserves the fundamental dynamic characteristics of the process. A robust dynamic integral sliding mode control (DISMC) is designed based on the control-oriented model to track the desired heating value, which is one of the key indicators for evaluating the performance of an UCG process. Unknown states required for the model-based control are reconstructed using a gain-scheduled modified Utkin observer (GSMUO). In order to assess the robustness of the nonlinear control and estimation techniques, the water influx phenomenon is considered as an input disturbance. Moreover, the underlying UCG plant model is subjected to parametric variations as well as measurement noise. In order to guarantee the stability of the overall system, the boundedness of the internal dynamics is also proved. To make a fair comparison, the performance of the proposed controller is compared with an integral sliding mode control (ISMC) and a classical proportional-integral (PI) controller. Simulation results highlight the effectiveness of the proposed control scheme in terms of minimum control energy and improved tracking error. Moreover, the simulation study shows that the combination of DISMC and GSMUO exhibit robustness against an input disturbance, parametric uncertainties and measurement noise.     

Gain-scheduled L-one control for linear parameter-varying systems with parameter-dependent delays

This paper deals with the problem of gain-scheduled L-one control for linear parameter-varying (LPV) systems with parameter-dependent delays. The attention is focused on the design of a gain-scheduled L-one controller that guarantees being an asymptotically stable closed-loop system and satisfying peak-to-peak performance constraints for LPV systems with respect to all amplitude-bounded input signals. In particular, concentrating on the delay-dependent case, we utilize parameter-dependent Lyapunov functions (PDLF) to establish peak-to-peak performance criteria for the first time where there exists a coupling between a Lyapunov function matrix and system matrices. By introducing a slack matrix, the decoupling for the parameter-dependent time-delay LPV system is realized. In this way, the sufficient conditions for the existence of a gain-scheduled L-one controller are proposed in terms of the Lyapunov stability theory and the linear matrix inequality (LMI) method. Based on approximate basis function and the gridding technique, the corresponding controller design is cast into a feasible solution problem of the finite parameter linear matrix inequalities. A numerical example is given to show the effectiveness of the proposed approach.     

Reducing conservatism in the design of a robust gain-scheduled controller for non-linear chemical processes

A robust control approach has been used to design gain-scheduled controllers, which guarantee closed-loop stability and performance. The inherent conservatism of robust control results in smaller ranges of parameters that satisfy the design criteria and consequently in degraded performance. The main focus of this paper is to reduce the conservatism to enhance the efficiency of the robust design method. Two approaches, the use of parameter-dependent Lyapunov condition and calculation of saturation factor bounds, are proposed to reduce the conservatism of the controller design.     

Robust optimal trajectory design by integrating genetic algorithm with min-max method

A robust optimal trajectory design method is proposed in this paper. Genetic Algorithm (GA) is employed to optimize the whole trajectory to improve the terminal attack performance. To enhance the robustness of the trajectory to disturbances, the min-max method is integrated into the GA optimization process. The proposed approach is carefully illustrated with the robust optimization design of the trajectory for a portable short-range top-attack (PSRTA) missile. The H _∞ robust gain-scheduled technique is used to design the attitude tracking autopilot to facilitate the trajectory design. The damp feedback loop of the weakly-damped missile body is innovatively treated as the Linear Parameter Varying system (the controlled plant), which is good for practical use. The proposed robust optimal trajectory design method and the H _∞ robust gain-scheduled attitude tracking autopilot are demonstrated to be effective from the whole trajectory simulation results of the PSRTA missile, which also exhibit high applicability for practical engineering problems.     

Model reference robust control of a class of SISO systems

A new control design technique, model reference robust control (MRRC), is introduced for a class of SISO systems which contain unknown parameters, possible nonlinear uncertainties, and additive bounded disturbances. The design methodology is a natural, nontrivial extension of model reference adaptive control (MRAC) which is essential to achieving robust stability and performance for linear time-invariant systems. The methodology also represents an important step toward achieving robust stability for time-varying and nonlinear systems. MRRC requires only input and output measurements of the system, rather than the full state feedback and structural conditions on uncertainties required by existing robust control results. MRRC is developed from existing model reference control (MRC) in a manner similar to MRAC. An intermediate result gives conditions under which MRRC yields exponentially asymptotic stability. The general result yielding uniformly ultimately bounded stability is then developed. A scalar example provides intuition into why the control works against a wide class of uncertainties and reveals the implicit learning capability of MRRC     

Inverse system design for LPV systems using parameter-dependent Lyapunov functions

This paper addresses the design problem of gain-scheduled inverse systems (GSISs) for linear parameter-varying (LPV) systems, whose state-space matrices are represented as parametrically affine matrices, using parameter-dependent Lyapunov functions (PDLFs), and proposes a method for them via parametrically affine linear matrix inequalities (LMIs). Our method includes robust inverse system (RIS) design as a special case. For RIS design, our method theoretically encompasses the method using constant Lyapunov functions. A design example is included to illustrate our conclusions.     

Robust state feedback synthesis for control of non-square multivariable nonlinear systems

In this paper, a robust nonlinear controller is designed in the Input/Output (I/O) linearization framework, for non-square multivariable nonlinear systems that have more inputs than outputs and are subject to parametric uncertainty. A nonlinear state feedback is synthesized that approximately linearizes the system in an I/O sense by solving a convex optimization problem online. A robust controller is designed for the linear uncertain subsystem using a multi-model H₂/H_∞ synthesis approach to ensure robust stability and performance of non-square multivariable, nonlinear systems. This methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor.     

Nonlinear observers for a class of continuous-time uncertain state delayed systems

This paper is concerned with the problem of observer design for a class of time-delay nonlinear systems with parameter uncertainties. The purpose of this problem is to design the gain-scheduled state observers such that, for the addressed nonlinearities as well as all admissible parameter uncertainties in state and output equations, the observation process remains globally exponentially stable, independently of the time delay. The nonlinearities are assumed to satisfy the global L ipschitz conditions, and the parameter uncertainties are allowed to be time varying, unstructured and norm bounded. An effective matrix inequality methodology is developed to solve the proposed problem. W e derive the conditions for the existence of the desired robust nonlinear observers, and then characterize the analytical expression of these observers. Two numerical examples demonstrate the validity and applicability of the present approach.     

Robust approximation-free prescribed performance control for nonlinear systems and its application

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.     

Dynamic Balance Control Based on an Adaptive Gain-scheduled Backstepping Scheme for Power-line Inspection Robots

This paper presents an adaptive gain-scheduled backstepping control (AGSBC) scheme for the balance control of an underactuated mechanical power-line inspection (PLI) robotic system with two degrees of freedom and a single control input. First, a nonlinear dynamic model of the balance adjustment process of the PLI robot is constructed, and then the model is linearized at a nominal equilibrium point to overcome the computational infeasibility of the conventional backstepping technique. Second, to solve generalized stabilization control issue for underactuated systems with multiple equilibrium points, an equilibrium manifold linearized model is developed using a scheduling variable, and then a gain-scheduled backstepping control (GSBC) scheme for expanding the operational area of the controlled system is constructed. Finally, an adaptive mechanism is proposed to counteract the impact of external disturbances. The robust stability of the closed-loop system is ensured by Lyapunov theorem. Simulation results demonstrate the effectiveness and high performance of the proposed scheme compared with other control schemes.      

A class of nonlinear observers for discrete-time systems with parametric uncertainty

In this paper the problem of observer design is considered for a class of nonlinear discrete-time systems with parametric uncertainty. The problem addressed aims at designing the gain-scheduled state observers such that, for all admissible nonlinearities and time-varying parameter uncertainties in the state equation, the observation process is asymptotically stable. An effective, purely algebraic methodology is developed to solve the proposed problem for discrete-time systems. It is shown that the solution is related to a generalized Riccati-like matrix equation. Specifically, by using the generalized inverse theory and singular value decomposition technique, we obtain the conditions for the existence of desired robust nonlinear observers and then characterize the explicit expression of these observers. Two numerical examples are used to demonstrate the applicability and flexibility of the present approach.     

Gain-scheduled ℓ-optimal control for boiler-turbine dynamics with actuator saturation

This paper presents a gain-scheduled approach for boiler-turbine controller design. The objective of this controller design is to achieve tracking performance in the power output and drum pressure while regulating water level deviation. Also, the controller needs to take into account the magnitude and rate saturation constraints on actuators. The nonlinear boiler-turbine dynamics is brought into a linear parameter varying (LPV) form which is a parameter-dependent state-space realization. The LPV form of the boiler-turbine dynamics is characterized by nonlinear dependence on drum pressure, which is naturally the scheduling variable. The controller is designed by utilizing the set-valued method for l¹- optimization, which explicitly addresses state constraints and controller saturations in the design process. The overall gain-scheduled design is augmented by a reference governor to avoid performance degradation in the presence of large tracking commands.     

Low-complexity linear parameter-varying modeling and control of a robotic manipulator

In this paper, a practical procedure for linear parameter-varying (LPV) modeling and identification of a robotic manipulator is presented, which leads to a successful experimental implementation of an LPV gain-scheduled controller. A nonlinear dynamic model of a two-degrees-of-freedom manipulator containing all important terms is obtained and unknown parameters which are required to construct an LPV model are identified. An important tool for obtaining a model of complexity low enough to be suitable for controller synthesis is the principle-component-analysis-based technique of parameter set mapping. Since the resulting quasi-LPV model has a large number of affine scheduling parameters and a large overbounding, parameter set mapping is used to reduce conservatism and complexity in controller design by finding tighter parameter regions with fewer scheduling parameters. A sufficient a posteriori condition is derived to assess the stability of the resulting closed-loop system. To evaluate the applicability and efficiency of the approximated model, a polytopic LPV gain-scheduled controller is synthesized and implemented experimentally on an industrial robot for a trajectory tracking task. The experimental results illustrate that the designed LPV controller outperforms an independent joint PD controller in terms of tracking performance and achieves a slightly better accuracy than a model-based inverse dynamics controller, while having a simpler structure. Moreover, it is shown that the LPV controller is more robust against dynamic parameter uncertainty.     

Design of fuzzy controllers for uncertain nonlinear systems using stability and robustness analyses

This paper analyzes the stability and robustness of uncertain nonlinear systems and shows that the analysis results provide an efficient technique for the design of fuzzy controllers. Based on a fuzzy plant model describing an uncertain nonlinear plant, this design involves the derivation of a stability criterion and a robust area in the uncertain parameter space in terms of some measures of the closed-loop control system matrices. An application example on balancing an inverted pendulum is given to illustrate the simple design methodology, the stability and the robustness of the feedback system incorporated with the proposed fuzzy controller.     

Model reference tracking control of an aircraft: a robust adaptive approach

This work presents the design and the corresponding analysis of a nonlinear robust adaptive controller for model reference tracking of an aircraft that has parametric uncertainties in its system matrices and additive state- and/or time-dependent nonlinear disturbance-like terms in its dynamics. Specifically, robust integral of the sign of the error feedback term and an adaptive term is fused with a proportional integral controller. Lyapunov-based stability analysis techniques are utilised to prove global asymptotic convergence of the output tracking error. Extensive numerical simulations are presented to illustrate the performance of the proposed robust adaptive controller.     

Neural-network-based robust adaptive control for a class of nonlinear systems

In this study, a robust adaptive control (RAC) system is developed for a class of nonlinear systems. The RAC system is comprised of a computation controller and a robust compensator. The computation controller containing a radial basis function (RBF) neural network is the principal controller, and the robust compensator can provide the smooth and chattering-free stability compensation. The RBF neural network is used to approximate the system dynamics, and the adaptive laws are derived to on-line tune the parameters of the neural network so as to achieve favorable estimation performance. From the Lyapunov stability analysis, it is shown that all signals in the closed-loop RBAC system are uniformly ultimately bounded. To investigate the effectiveness of the RAC system, the design methodology is applied to control two nonlinear systems: a wing rock motion system and a Chua’s chaotic circuit system. Simulation results demonstrate that the proposed RAC system can achieve favorable tracking performance with unknown of the system dynamics.