A Systematic Analysis Approach to Discrete-time Indirect Model Reference Adaptive Control

This paper presents the design and analysis of indirect model reference adaptive control （MRAC） with normalized adaptive law for a class of discrete-time systems. The main work includes three parts. Firstly, the constructed plant parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms but also avoids the possibility of division by zero. Secondly, by finding the relationship between the plant parameter estimate and controller parameter estimate and using the properties of plant parameter estimate, the similar properties of controller parameter estimate are also established. Thirdly, based on the relationship properties between the normalizing signal and all the signals in the closed-loop system and on some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and convergence analysis approach to the discrete indirect MRAC scheme is developed rigorously.     

Direct model reference adaptive control using Kp = LDU factorization for multivariable discrete-time plants

For a large class of discrete-time multivariable plants with arbitrary relative degrees, the design and analysis of the direct model reference adaptive control scheme are investigated under less restrictive assumptions. The algorithm is based on a new parametrization derived from the high frequency gain matrix factorization Kp=LDU under the condition that the signs of the leading principal minors of/fp are known. By reproving the discrete-time Lp and L2σ norm relationship between inputs and outputs, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all signals in the closed-loop system, the stability and convergence of the discrete-time multivariable model reference adaptive control scheme are analyzed rigorously in a systematic fashion as in the continuous-time case.     

A new adaptive backstepping method for nonlinear control of turbine main steam valve

A new approach for nonlinear adaptive control of turbine main steam valve is developed. In comparison with the existing controller based on ＂classical＂ adaptive backstepping, this method does not follow the classical certaintyequivalence principle in the design of adaptive control law. We introduce this approach, for the first time, to power systems and present a novel parameter estimator and dynamic feedback controller for a single machine infinite bus （SMIB） system with steam valve control. This system contains unknown parameters such as reactance of transmission lines. Besides preserving useful nonlinearities and the real-time estimation of uncertain parameters, the proposed approach possesses better performances with respect to the response of the system and the speed of adaptation. The simulation results demonstrate that the proposed approach is better than the design based on ＂classical＂ adaptive backstepping in terms of properties of stability and parameter estimation, and recovers the performance of the ＂full-information＂ controller. Hence, the proposed method provides an alternative for engineers in applications.     

Motion synchronization of dual-cylinder pneumatic servo systems with integration of adaptive robust control and cross-coupling approach

We investigate motion synchronization of dual-cylinder pneumatic servo systems and develop an adaptive robust synchronization controller. The proposed controller incorporates the cross-coupling technology into the integrated direct/indirect adaptive robust control （DIARC） architecture by feeding back the coupled position errors, which are formed by the trajectory tracking errors of two cylinders and the synchronization error between them. The controller employs an online recursive least squares estimation algorithm to obtain accurate estimates of model parameters for reducing the extent of parametric uncertainties, and uses a robust control law to attenuate the effects of parameter estimation errors, unmodeled dynamics, and disturbances. Therefore, asymptotic convergence to zero of both trajectory tracking and synchronization errors can be guaranteed. Experimental results verify the effectiveness of the proposed controller.     

Robust fault diagnosis for a class of nonlinear systems

Robust fault diagnosis based on adaptive observer is studied for a class of nonlinear systems up to output injection. Adaptive fault updating laws are designed to guarantee the stability of the diagnosis system. The upper bounds of the state estimation error and fault estimation error of the adaptive observer are given respectively and the effects of parameter in the adaptive updating laws on fault estimation accuracy are also discussed. Simulation example demonstrates the effectiveness of the proposed methods and the analysis results.     

Robust H-infinity filtering on uncertain systems under sampled measurements

1 Introduction Sampled measurements systems consist of a continuous- time plant and discrete-time plant. The systems contain sig- nals that evolve in continuous time as well as signals that evolve in discrete time. It is rather difficult to apply the stan- dard analysis results for linear continuous-time systems and discrete-time systems to the analysis of sampled measure- ments systems [1]. This fact has motivated much of the re- search on the analysis and synthesis of sampled measure- ments …     

Fault-tolerant control systems design via subdivision of parameter region

This paper presents a linear matrix inequality （LMI） approach to solve the fault-tolerant control （FTC） problem of actuator faults. The range of actuator faults is considered as a parameter region and subdivided into several subregions to achieve a certain desired performance specification. Based on the integral quadratic constraint （IQC） approach, a passive fault-tolerant controller for the whole fault region and multiple fault-tolerant controllers for each fault subregion are designed for guaranteeing stability and improving performance of the FTC system, respectively. According to the estimation of parameters by FDI process, the corresponding subregion controller is chosen for the stability and optimal performance of closed-loop systems when the fault occurs. The case of incorrect estimation is also considered by comparing the performance index between the switched controller and the passive fault-tolerant controller. The proposed design technique is finally evaluated in the light of a simulation example.     

State tracking model reference adaptive control for switched nonlinear systems with linear uncertain parameters

Model reference adaptive control(MRAC)is considered for a class of switched nonlinear systems in which the unknown parameters appear linearly.The linear uncertain parameters in each subsystem can be expressed as a vector and the uncertain vectors in different subsystems are estimated individually by different vector variables.Update laws are designed such that the parameter estimation will ’freeze’ until its corresponding subsystem is active.Controllers for subsystems are given to ensure asymptotic states tracking under arbitrary switchings.Two examples are presented to validate the proposed method.     

An adaptive control with optimal disturbances rejection

This paper provides a way to optimize the overall disturbances rejection performance of the adaptive control system in the presence of unknown external disturbances.Especially,the updatable non-empty admissible model set,which is consistent to the a priori knowledge of the plant parameter and the online measurements,is computed.With the overall system performance as the criteria,the nominal model is optimally chosen within the admissible model set.The optimal nominal model is subsequently used to synthesize the optimal closed-loop controller based on the 1 design methodology.Combining the above two aspects,an optimal adaptive control scheme is proposed.Because of the consistency of the identification criteria and control object,the adaptive control scheme proposed in this paper can achieve the overall optimal disturbances rejection performance,and the effect of the interplay between the identification and control of the adaptive system can be handled effectively.In addition,the computable optimal performance is also provided.     

A modified direct adaptive robust motion trajectory tracking controller of a pneumatic system

In this study, we developed and tested a high-precision motion trajectory tracking controller of a pneumatic cylinder driven by four costless on/off solenoid valves rather than by a proportional directional control valve. The relationship between the pulse width modulation （PWM） of a signal＇s duty cycle and control law was determined experimentally, and a mathematical model of the whole system established. Owing to unknown disturbances and unmodeled dynamics, there are considerable uncertain nonlinearities and parametric uncertainties in this pneumatic system. A modified direct adaptive robust controller （DARC） was constructed to cope with these issues. The controller employs a gradient type adaptation law based on discontinuous projection mapping to guarantee that estimated unknown model parameters stay within a known bounded region, and uses a deterministic robust control strategy to weaken the effects of unmodeled dynamics, disturbances, and parameter estimation errors. By using discontinuous projection mapping, the parameter adaptation law and the robust control law can be synthesized separately. A recursive backstepping technology is applied to account for unmatched model uncertainties. Kalman filters were designed sepa- rately to estimate the motion states and the derivative of the intermediate control law in synthesizing the deterministic robust control law. Experimental results illustrate the effectiveness of the proposed controller.     

Robustness analysis of discrete-time indirect model reference adaptive control with normalized adaptive laws

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control (MRAC) with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter axe also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.     

离散时间直接型模型参考自适应控制

本文针对一类离散时间系统, 研究了具有规范化自适应律的直接型模型参考自适应控制 (MRAC). 我们重新证明了离散时间系统的输入与输出间的 Lp 范数与 L2δ 范数关系特性和离散时间的交换引理 1 与引理 2. 并建立了离散时间自适应律的性质, 定义了规范化信号, 把闭环系统中的所有信号与其建立联系. 从而, 正如连续时间系统一样, 以一种系统化的方法严格分析了离散时间 MRAC 方案的稳定性与收敛性.     

Gain Margins of Adaptive Control Systems

This paper presents a systematic study of the gain margins (GM) of adaptive control systems: the specification of the parameter range of a control gain matrix in a designed adaptive control system for maintaining the desired closed-loop signal boundedness and asymptotic tracking performance. It is proved that the GM is infinity for continuous-time direct model reference adaptive control (MRAC) schemes applied to multi-input, multi-output (MIMO) linear time-invariant (LTI) systems, while it is finite with an upper bound for the discrete-time case. The derived GM results are applicable to systems with adaptive nonlinear or pole placement control designs. Analytical GM result is also obtained for some indirect multivariable MRAC systems; in particular, the GM is infinity but with a lower bound for such systems. Methods for enlarging the GM by proper choices of design parameters are presented. Moreover, the effect of sample time on the GM of sampled-data adaptive control systems is studied, which establishes the relationship between the continuous-time and discrete-time GM results. A simulation example is provided to illustrate some of the theoretical results.      

A discrete-time parameter estimation based adaptive actuator failure compensation control scheme

This article studies discrete-time adaptive failure compensation control of systems with uncertain actuator failures, using an indirect adaptive control method. A discrete-time model of a continuous-time linear system with actuator failures is derived and its key features are clarified. A new discrete-time adaptive actuator failure compensation control scheme is developed, which consists of a total parametrisation of the system with parameter and failure uncertainties, a stable adaptive parameter estimation algorithm, and an on-line design procedure for feedback control. This work provides a new design of direct adaptive compensation of uncertain actuator failures, using an indirect adaptive control method. Such an adaptive design ensures desired closed-loop system stability and tracking properties despite uncertain actuator failures. Simulation results are presented to show the desired adaptive actuator failure compensation performance.     

Smooth indirect adaptive sliding mode control

In this paper, an indirect approach to the dual‐mode adaptive robust controller (DMARC) is proposed, which combines the typical transient and robustness properties of variable structure systems with a smooth control signal in steady state, typical of conventional adaptive controllers, as model reference adaptive controller. The aim of this indirect version, here named indirect DMARC, is to provide a more intuitive controller design, based on physical plant parameters, as resistances, inertia moments, capacitances, and so on, maintaining DMARC properties. In this paper, a stability analysis for the proposed controller and simulations to an unstable second‐order plant will be presented. Copyright © 2013 John Wiley & Sons, Ltd.     

互质因子摄动系统最优е1鲁棒控制: 连续性与自适应控制

针对具有互质因子摄动和未知干扰的离散时间系统研究了一种自适应鲁棒控制策略. 本文的主要工作包括三个方面. 首先建立了互质因子摄动系统最优е1鲁棒控制设计的连续性. 然后,提出了一种带变死区的参数鲁棒估计投影算法. 最后, 结合所提出的参数估计算法和最优е1鲁棒控制,利用确定性等价原理提出了互质因子摄动系统的一种新的自适应鲁棒控制方法. 基于本文建立的е1优化设计的连续性, 证明了自适应鲁棒控制的全局稳定性,给出了自适应控制系统稳定性的后验可计算条件.     

间接型的混杂模型参考自适应控制

针对相对阶为1的理想系统,本文考虑了具有混杂自适应律的间接型模型参考自适应控制问题.通过建立系统和控制器的离散参数估计和它们的插值四者之间关系的性质,严格地分析了闭环系统的稳定性,证明了闭环系统中所有的信号都一致有界,并且跟踪误差渐进收敛于零.     

Auto-tuning and adaptive control of sheet metal forming

This paper describes the design and implementation of automatic controller tuning and model reference adaptive control (MRAC) to improve part quality in stamping and extends previous work on a manually-tuned fixed-gain process controller. Automatic tuning is described with a discussion of implementation issues in the presence of plant disturbances. Design of a direct MRAC, whose controller gains are continuously adjusted to accommodate changes in process dynamics and disturbances, is investigated, including simulation-based robustness analysis of the adaptation law and a consideration of constrained estimation in the recursive least squares algorithm to address practical implementation issues. The performance of the MRAC process controller designed through simulation is experimentally validated. Good tracking of the reference process variable (i.e., punch force), and significant part quality improvement in the presence of disturbances, is achieved.     

基于扰动补偿的无微分模型参考自适应控制系统设计

针对一类含有参数不确定性和未知非线性扰动的系统,本文提出一种基于扰动补偿的无微分模型参考自适应控制方法,实现系统输出对参考模型输出信号的高精度跟踪.首先,利用被控对象模型信息设计扰动估计器,对系统非线性扰动进行在线估计;其次,基于非线性扰动估计值设计参考模型和无微分参数更新律,构建无微分模型参考自适应控制器,建立基于扰动补偿和状态反馈的自适应控制律,以消除参数不确定性和非线性扰动对系统输出的影响,保证系统输出对参考模型输出的准确跟踪;然后,给出闭环系统误差信号收敛条件和控制器参数整定方法;最后,通过数值仿真验证所提方法的有效性和优越性.     

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Without any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.