A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.     

Robust MPC for systems with output feedback and input saturation

In this work, it is proposed an MPC control algorithm with proved robust stability for systems with model uncertainty and output feedback. It is assumed that the operating strategy is such that system inputs may become saturated at transient or steady state. The developed strategy aims at the case in which the controller performs in the output-tracking scheme following an optimal set point that is provided by an upper optimization layer of the plant control structure. In this case, the optimal operating point usually lies at the boundary of the region where the input is defined. Assuming that the system remains stabilizable in the presence of input saturation, the design of the robust controller is performed off-line and an on-line implementation strategy is proposed. At each sampling step, a sub optimal control law is obtained by combining control configurations that correspond to particular subsets of available manipulated inputs. Stability of the closed-loop system is forced by considering in the off-line step of the controller design, a state contracting restriction for the closed-loop system. To produce an offset free controller and to attend the case of unknown steady state, the method is developed for a state-space model in the incremental form. The method is illustrated with simulation examples extracted from the process industry.     

A model-free design of reduced-order controllers and application to a DC servomotor

This paper presents a new model-free technique to design fixed-structure controllers for linear unknown systems. In the current control design approaches, measured data are used to first identify a model of the plant, then a controller is designed based on the identified model. Due to errors associated with the identification process, degradation in the controller performance is expected. Hence, we use the measured data to directly design the controller without the need for model identification. Our objective here is to design measurement-based controllers for stable and unstable systems, even when the closed-loop architecture is unknown. This proposed method can be very useful for many industrial applications. The proposed control methodology is a reference model design approach which aims at finding suitable parameter values of a fixed-order controller so that the closed-loop frequency response matches a desired frequency response. This reference model design problem is formulated as a nonlinear programming problem using the concept of bounded error, which can then be solved to find suitable values of the controller parameters. In addition to the well-known advantages of data-based control methods, the main features of our proposed approach are: (1) the error is guaranteed to be bounded, (2) it enables us to avoid issues related to the use of minimization methods, (3) it can be applied to stable and unstable plants and does not require any knowledge about the closed-loop architecture, and (4) the controller structure can be selected a priori, which means that low-order controllers can be designed. The proposed technique is experimentally validated through a real position control problem of a DC servomotor, where the results demonstrate the efficacy of the proposed method.     

基于Matlab/xPC的直流电机参数辨识及双闭环控制研究

针对直流电机精确数学模型的获取及其双闭环控制器参数的整定问题,在Matlab/xPC目标环境使用递推最小二乘法对某型直流电机进行参数的在线辨识,获得某工作转速下的动态结构图参数.针对该结构图,在Simulink环境下对速度调节器和电流调节器的PI参数进行整定并仿真,达到满意效果后,将控制器下载到xPC目标机中,采用毫秒...     

水厂混凝投药大滞后过程的数据驱动直接控制方法

以自来水厂混凝投药大时滞过程为研究对象,在迭代反馈整定(IFT)方法的基础上,结合Smith预估控制结构,提出了一种混凝投药过程数据驱动直接控制算法.着重针对过程大时滞的特点,在性能指标中加入了预估误差惩罚因子.提出了一种新的步长设置方法,使得步长的下降速率可调.设计了3个闭环实验来求取性能指标梯度向量的无偏估计,完全...     

基于辅助变量的压缩采样匹配追踪闭环系统辨识方法

针对被控对象和反馈通道均具有未知时滞的闭环系统,提出一种基于辅助变量的压缩采样匹配追踪辨识方法.该方法利用辅助变量方法对压缩采样匹配追踪算法进行改进,获得过参数化辨识模型稀疏参数向量的估计,根据稀疏向量的结构得到前向通道的参数估计和时滞估计,进而根据模型等价原理获得反馈通道的参数估计.仿真结果表明,所提出方法仅需少量的迭代即可获得这类闭环系统参数与时滞的有效估计.     

利用模糊系统的直升机的自适应控制

针对直升机动力学为非线性,且存在不确定因素和状态变化,设计利用模糊系统的自适应控制器.设计的控制器是系统的输出跟踪参考模型输出的直接调整模糊控制器参数的自适应控制器.又利用Lyapunov函数保证了闭环控制系统的稳定性并推导最优的自适应规律.实验结果表明,有外部扰动的情况下所设计的自适应控制器比模糊控制器对直升机控制具有良好的动态响应和稳定性,是一种非常有效的控制方法.     

A closed-loop data based test for robust performance improvement in iterative identification and control redesigns

In robust iterative identification and control redesign techniques, a stabilizing controller connected in a closed loop is normally replaced by an alternative attractive stabilizing controller to improve robustness and performance of the closed-loop system. In this paper, novel test methods are proposed to check whether a new stabilizing controller improves performance or not when the existing controller is replaced by this new controller in the closed loop. The proposed tests are based on closed-loop data and no plant model, and can be used for both the SISO and MIMO linear time-invariant systems. For the proposed tests, the plant dynamics is assumed to be unknown whereas the existing and new controller transfer function matrices are known to the designer. These assumptions are common in iterative identification and control redesign techniques. The performance improvement test methods proposed in this paper build on the experimental set-up proposed in Dehghani, Lecchini, Lanzon, and Anderson (2009) which was used to only check whether controllers ensure internal stability of a feedback interconnection or not. In this paper, new test methods are proposed to ascertain robust performance improvement that cannot be obtained from test results of Dehghani et al. (2009). A numerical example is illustrated to show effectiveness of the proposed test methods.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

A measurement-based approach for designing reduced-order controllers with guaranteed bounded error

The objective of this paper is to present a measurement-based control-design approach for single-input single-output linear systems with guaranteed bounded error. A wide range of control-design approaches available in the literature are based on parametric models. These models can be obtained analytically using physical laws or via system identification using a set of measured data. However, due to the complex properties of real systems, an identified model is only an approximation of the plant based on simplifying assumptions. Thus, the controller designed based on a simplified model can seriously degrade the closed-loop performance of the system. In this paper, an alternative approach is proposed to develop fixed-order controllers based on measured data without the need for model identification. The proposed control technique is based on computing a suitable set of fixed-order controller parameters for which the closed-loop frequency response fits a desired frequency response that meets the desired closed-loop performance specifications. The control-design problem is formulated as a nonlinear programming problem using the concept of bounded error. The main advantages of our proposed approach are: (1) it guarantees that the error between the computed and the desired frequency responses is less than a small value; (2) the difficulty of finding the globally optimal solution in the error minimisation problem is avoided; (3) the controller can be designed without the use of any analytical model to avoid errors associated with the identification process; and (4) low-order controllers can be designed by selecting a fixed low-order controller structure. To experimentally validate and illustrate the efficacy of the proposed approach, proportional-integral measurement-based controllers are designed for a DC (direct current) servomotor.     

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.     

Comparison of the closed-loop identification methods in terms of the bias distribution

Several schemes for plant model identification in closed-loop operation including classical direct method, two-step identification and closed-loop output error algorithms are considered. These methods are analyzed and compared in terms of the bias distribution of the estimates for the case that the noise model is estimated as well as the case that a fixed model of noise is considered (output error structure). The problems concerning the filtered direct method which is often used in the iterative identification and control scheme are mentioned. It is shown that these problems may be solved by the closed-loop output error identification method.     

Adaptive control with optimal tracking performance

This paper provides a way to optimise the steady-state tracking performance of the adaptive control system in the presence of unknown external disturbances. A-priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. 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. Treating 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 synthesise the optimal closed-loop controller that minimises the steady-state absolute value of the tracking error. 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 steady-state tracking 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.     

Nonlinear adaptive control using multiple identification models

A multiple model adaptive controller is proposed for nonlinear systems in parametric-strict-feedback form. By running in parallel multiple identification models and designing a suitable switching scheme, some models close to the real plant can be selected quickly, so that transient performance can be improved significantly. Global asymptotic stability of the closed-loop switching system is proved. A simulation example is given to demonstrate the effectiveness of the proposed multiple model adaptive controller.     

Proportional stabilization and closed-loop identification of an unstable fractional order process

This paper deals with proportional stabilization and closed-loop step response identification of the fractional order counterparts of the unstable first order plus dead time (FOPDT) processes. At first, the necessary and sufficient condition for stabilizability of such processes by proportional controllers is found. Then, by assuming that a process of this kind has been stabilized by a proportional controller and the step response data of the closed-loop system is available, an algorithm is proposed for estimating the order and the parameters of an unstable fractional order model by using the mentioned data.     

基于神经网络补偿的非线性时滞系统时滞正反馈控制

A new adaptive time-delay positive feedback controller (ATPFC) is presented for a class of nonlinear time-delay systems. The proposed control scheme consists of a neural networks-based identification and a time-delay positive feedback controller. Two high-order neural networks (HONN) incorporated with a special dynamic identification model are employed to identify the nonlinear system. Based on the identified model, local linearization compensation is used to deal with the unknown nonlinearity of the system. A time-delay-free inverse model of the linearized system and a desired reference model are utilized to constitute the feedback controller, which can lead the system output to track the trajectory of a reference model. Rigorous stability analysis for both the identification and the tracking error of the closed-loop control system is provided by means of Lyapunov stability criterion. Simulation results are included to demonstrate the effectiveness of the proposed scheme.     

Some considerations for estimator-based compensator design

In this paper some criteria are presented for dividing the closed-loop system poles of a feedback system between the estimator and the controller when using an estimator-based compensator. The criteria are based on frequency response considerations, but are related to some well-known facts in the time domain. It is well known, for example, that the closed-loop system poles are the poles of the estimator in union with the controller poles. It is also well known that the time response of the closed-loop plant states due to a command depends only on the closed-loop control poles, and the response of the estimate error depends only on the closed-loop estimator poles. In the frequency domain, the following can be said: the open-loop compensator transfer function from the sensor measurement to the control and the closed-loop transfer function from the sensor measurement to the system output are both independent of how the closed-loop poles are distributed between the controller and the estimator, but the closed-loop transfer function from the command to the control or system output is not. Placing the slower closed-loop poles in the controller causes the control gains to be smaller, which in turn causes the effect of the command signal to be attenuated, both at the control and at the closed-loop system output. Making use of these facts allows the closed-loop poles to be divided between the controller and the estimator on a more intelligent basis than ‘the estimator poles should be three times faster than the controller poles’. In an example, these concepts are applied to the design of a platform despin control system for a dual-spin satellite.     

A bound on closed-loop performance based on finite-frequency response samples

A new, computationally tractable, bound is derived for the level of closed-loop performance achieved by a given finite-dimensional feedback compensator with a plant for which a finite number of frequency response samples are computable. The bound involves quantities reflecting the performance of the controller with a finite-dimensional, nominal model of the plant, quantities that can be determined from the finite number of frequency response samples of the true plant, and quantities related to the complexity (in the sense of Vinnicombe) of all systems involved. This bound can be used to ‘validate’ closed-loop performance in the case that the true plant frequency response samples are of a plant which is not completely known or, to measure the performance of a finite-dimensional controller with a computationally intractable (e.g. infinite-dimensional) model of the true plant.     

Accurate identification for control: the necessity of an iterativescheme

If approximate identification and model-based control design are used to accomplish a high-performance control system, then the two procedures must be treated as a joint problem. Solving this joint problem by means of separate identification and control design procedures practically entails an iterative scheme. A frequency-response identification technique and a robust control design method are used to set up such an iterative scheme. Each identification step uses the previously designed controller to obtain new data from the plant. The associated identification problem has been solved by means of a coprime factorization of the unknown plant. The technique's utility is illustrated by an example     

Adaptive non-linear compensation control based on neural networks for non-linear systems with time delay

This article investigates a new adaptive non-linear compensation controller for a class of time-delay non-linear systems with partly known dynamics. First, a non-linear neural-network(NN)-based identification model that includes a prior knowledge about the plant dynamics is discussed by using the approximation capabilities of NNs. Then, the adaptive non-linear compensation controller is developed to produce the desired tracking performance. The proposed controller based on the NN can reduce the effect of modelling uncertainties and provide the time-delay compensation, while stability of the closed-loop system is guaranteed. The effectiveness of the proposed scheme is demonstrated through the application to the control of a continuous stirred tank reactor.