Stability analysis of a continuous time self tuner

This paper reports a new result on the robustness of an indirect continuous self tuner consisting of two modules: parameter estimation and synthesis of a tuner. The estimation is based on a gradient algorithm with projection. It is shown that for arbitrarily bounded disturbances, global stability is ensured without any assumption on signals. Moreover, the robust robust self tuning controller can still retain the properties that earlier unmodified conventional adaptive controllers have when there is no disturbance. The apriori knowledge for the implementation of the simple adaptive controller is the (large) ranges of unknown parameters in the nominal system model.This work was supported by NTU under the Applied Research Project Grant RP 23/92.     

Tuning an adaptive controller using a robust control approach

This article proposes a new technique for the tuning of a discrete adaptive controller that is designed based on Lyapunov stability concepts. The tuning is based on the minimisation of a performance index that can be calculated from a generalised eigenvalue problem (GEVP) using LMI's (Linear Matrix Inequalities). The proposed technique results in an adaptive controller with time-varying tuning gains. The solution is based on an approximation of the optimal dual adaptive control problem. The tuning technique was used to perform on-line control of a first-order system and an isothermal and a non-isothermal CSTR. The results show that the proposed approach provides better performance than an adaptive algorithm with the same structure, but with constant adaptation gains. Also, the proposed algorithm is shown to be superior to an adaptive controller based on a Recursive Least Squares (RLS) estimator during sudden changes in model parameters.     

Stabilization of nonlinear nonminimum phase systems: adaptive parallel approach using recurrent fuzzy neural network

In this paper, an adaptive parallel control architecture to stabilize a class of nonlinear systems which are nonminimum phase is proposed. For obtaining an on-line performance and self-tuning controller, the proposed control scheme contains recurrent fuzzy neural network (RFNN) identifier, nonfuzzy controller, and RFNN compensator. The nonfuzzy controller is designed for nominal system using the techniques of backstepping and feedback linearization, is the main part for stabilization. The RFNN compensator is used to compensate adaptively for the nonfuzzy controller, i.e., it acts like a fine tuner; and the RFNN identifier provides the system's sensitivity for tuning the controller parameters. Based on the Lyapunov approach, rigorous proofs are also presented to show the closed-loop stability of the proposed control architecture. With the aid of the RFNN compensators, the parallel controller can indeed improve system performance, reject disturbance, and enlarge the domain of attraction. Furthermore, computer simulations of several examples are given to illustrate the applicability and effectiveness of this proposed controller.     

Experimental evaluations of proportional–integral–derivative type fuzzy controllers with parameter adaptive methods for an active magnetic bearing system

Abstract: This paper deals with the experimental control of a rotating active magnetic bearing (AMB) system using proportional–integral–derivative type fuzzy controllers (PIDFCs) with parameter adaptive methods. Three kinds of parameter adaptive method, including fuzzy tuner, function tuner and relative rate observer, have been proposed in the literature for tuning the coefficients of PIDFCs. However, only a simulation comparison between these methods for control of a second‐order linear system with varying parameters and time delay has been done. In general, theoretical models need to be confirmed and modified through experimental results. This paper provides experimental verification by applying PIDFCs with self‐tuning algorithms for control of a highly nonlinear AMB system. It is shown that the steady‐state error of the AMB system using the function tuner method is lower and the first resonant frequency of the AMB system using the relative rate observer method is higher than the other two methods, and the proportional–integral–derivative controller is quite unstable. The experimental results also show that all of the tuning methods can support a high rotation frequency of the AMB system. In practice, there are only a few differences between the three kinds of parameter adaptive methods.     

Adaptive backstepping sliding mode control with tuning functions for nonlinear uncertain systems

An adaptive backstepping tuning functions sliding mode controller is proposed for a class of strict-feedback nonlinear uncertain systems. In this control design, adaptive backstepping is used to deal with unknown or uncertain parameters and the matching condition restricting the Lyapunov based design. The main drawback of the Lyapunov based adaptive backstepping which is the overparametrisation is eliminated by the tuning functions. The adaptive backstepping tuning functions design is combined with the sliding mode control in order to overcome quickly varying parametric and unstructured uncertainties, and to obtain chattering free control. The proposed controller not only provides robustness property against uncertainty but also copes with the overparametrisation problem. Experimental results of the proposed controller are compared with those of the standard sliding mode controller. The proposed controller exhibits satisfactory transient performance, good estimates of the uncertain parameters, and less chattering.     

继电反馈多模型控制及应用

作为简单、鲁棒的设计方法,基于继电反馈的PID控制器巳广泛应用于工业过程控制。它可以由继电反馈引起的振荡近似估计过程临界信息进行控制器的设计。多模型控制是解决系统时变、非线性、参数不确定性等复杂问题得一种有效方法。该文将继电反馈控制与多模型控制相结合,对时变、非线性的电厂主汽温系统过进行控制。首先在各个工况点应用继电反馈方法设计子控制器。然后在系统整个运行区间进行多模型自适应控制以克服非线性、时变对系统的影响。仿真表明本方法所建立的控制系统具有良好的控制品质及较强的自适应能力。     

Self-tuning control with additional feedback signals

Conventional self-tuning controllers utilise only the controlled output for feedback. In this paper a new minimum prediction error self-tuning controller which utilises additional system outputs for feedback is developed. The advantages of such an approach are assessed. The application of the new self tuner to power system stabilisation is considered. Simulation studies demonstrate an improvement in the dynamic performance of a synchronous generator equipped with the new self tuner instead of the conventional self-tuning stabiliser.     

一类直接模型参考Backstepping自适应控制

提出一种新的直接模型参考Backstepping自适应控制系统结构:谈系统在直接模型参考卓适应控制(MRAC)结构的基础上,增加了Beckstepping控制信号发生器,通过Backstepping方法的灵活设计获得良好的过渡过程品质,得到直接MRAC在稳定性和鲁棒性设计等方面的优点.采用高阶调节器设计了未具规范化的直接模型参考Backstepping自适应律,克服了传统自适应律引入规范化信号后使系统过渡过程品质下降的缺点.     

Adaptive hierarchical tuning of fuzzy controllers

Fuzzy controller design includes both linear and non-linear dynamic analysis. The knowledge base parameters associated within the fuzzy rule base influence the non-linear control dynamics while the linear parameters associated within the fuzzy output signal influence the overall control dynamics. For distinct identification of tuning levels, an equivalent linear controller output and a normalized non-linear controller output are defined. A linear proportional-integral-derivative (PID) controller analogy is used for determining the linear tuning parameters. Non-linear tuning is derived from the locally defined control properties in the non-linear fuzzy output. The non-linearity in the fuzzy output is then represented in a graphical form for achieving the necessary non-linear tuning. Three different tuning strategies are evaluated. The first strategy uses a genetic algorithm to simultaneously tune both linear and non-linear parameters. In the second strategy the non-linear parameters are initially selected on the basis of some desired non-linear control characteristics and the linear tuning is then performed using a trial and error approach. In the third method the linear tuning is initially performed off-line using an existing linear PID law and an adaptive non-linear tuning is then performed online in a hierarchical fashion. The control performance of each design is compared against its corresponding linear PID system. The controllers based on the first two design methods show superior performance when they are implemented on the estimated process system. However, in the presence of process uncertainties and external disturbances these controllers fail to perform any better than linear controllers. In the hierarchical control architecture, the non-linear fuzzy control method adapts to process uncertainties and disturbances to produce superior performance.     

指令跟踪自适应广义预测控制及其应用

现有的广义预测控制系统其闭环性能受可调参数影响较大,它的目标函数无法直接规定闭环性能.该文提出一种具有独立跟踪和调节目标的新型自适应广义预测控制算法,并将其应用于快速时变的导弹控制系统设计中.这种算法利用参考模型规定对指令信号的跟踪性能,减少了可调参数对闭环性能的影响.仿真结果证实了该算法的有效性.     

Adaptive backstepping with a high-order tuner

The paper proposes a new type of adaptive backstepping design. At each step of the design procedure a virtual control directly counteracts the transients of adjustable parameters, while the time derivatives of these parameters up to the desired order are generated by a special adaptation law (high-order tuner) defined at the final step. Thus, the proposed approach combines adaptive backstepping with high-order tuners. The resultant control law does not involve tuning functions and, at the same time, is free of overparametrization.     

A new approach to adaptive control: no nonlinearities

In adaptive control the goal is to design a controller to control an uncertain system whose parameters may be changing with time. Typically the controller consists of an identifier (or tuner) which is used to adjust the parameters of a linear time-invariant (LTI) compensator, and under suitable assumptions on the plant model uncertainty it is proven that good asymptotic behaviour is achieved, such as model matching (for minimum phase systems) or stability. However, a typical adaptive controller does not track time-varying parameters very well, and it is often highly nonlinear, which can result in undesirable behaviour, such as large transients or a large control signal. Furthermore, most adaptive controllers provide only asymptotic tracking, with no ability to design for a pre-specified settling time.Here we propose an alternative approach, which yields a linear periodic controller. Rather than estimating the plant or compensator parameters, instead we estimate what the control signal would be if the plant parameters were known. In this paper we argue the utility of this approach and then examine the first order case in detail, including a simulation. We also explore the benefits and limitations of the approach.     

Towards a unified theory of parameter adaptive control: tunability

The author illustrates some of the advantages of thinking of a parameter adaptive control system as a system consisting of a process, a parameterized controller, and a tuner interconnected in a particular way. The proposed structure has the virtue of being general enough to describe many different kinds of adaptive systems, including those of the model-reference, self-tuning, and high-gain feedback types. While error models are not used in this setting, special emphasis is placed on the importance of a tuning error. Within this framework, the concept of weak tunability is defined, characterized, and shown to be necessary for adaptive stabilization. The main result is to prove that a slightly stronger property called tunability is sufficient for adaptive stabilization, provided a tuning algorithm which possesses certain typical capabilities is used     

Adaptive cruise control of a HEV using sliding mode control

This paper presents adaptive cruise control of a hybrid electric vehicle. First, the mathematical model of the vehicle is formulated. Next, a classical controller is applied to the vehicle model. Swarm optimisation is implemented for self parameter tuning of the controller. The model is simulated and the result of the response to a variable speed is analysed. The results reveal that the controller is not a powerful means to manage the rapid transformation of the desire set point. Accordingly, a sliding mode controller is developed next. The performance of this controller is compared with the classical controller.     

A new linear adaptive controller: design, analysis and performance

The certainty equivalence and polynomial approach, widely used for designing adaptive controllers, leads to “simple” adaptive control designs that guarantee stability, asymptotic error convergence, and robustness, but not necessarily good transient performance. Backstepping and tuning functions techniques, on the other hand, are used to design adaptive controllers that guarantee stability and good transient performance at the expense of a highly nonlinear controller. In this paper, we use elements from both design approaches to develop a new certainty equivalence based adaptive controller by combining backstepping based control law with a normalized adaptive law. The new adaptive controller guarantees stability and performance, as well as parametric robustness for the nonadaptive controller, that are comparable with the tuning functions scheme, without the use of higher order nonlinearities     

一种自适应PID控制及其在发电机性能测试装置中的应用

针对经典PID控制参数整定困难且受时变、非线性等因素影响不能达到预期控制效果的实际情况,设计了一种具有自学习能力的自适应PID控制器,利用Widrow-Hoff学习算法实现系统在线自动调整最佳控制参数,从而提高系统的自适应能力、改善系统的动态性能,并成功地将其应用到发电机性能自动化测试装置中。     

Adaptive neural network control for strict-feedback nonlinear systems using backstepping design

This paper focuses on adaptive control of strict-feedback nonlinear systems using multilayer neural networks (MNNs). By introducing a modified Lyapunov function, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant. Then, an extension is made to high-order nonlinear systems using neural network approximation and adaptive backstepping techniques. The developed control scheme guarantees the uniform ultimate boundedness of the closed-loop adaptive systems. In addition, the relationship between the transient performance and the design parameters is explicitly given to guide the tuning of the controller. One important feature of the proposed NN controller is the highly structural property which makes it particularly suitable for parallel processing in actual implementation. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

General tuning procedure for the nonlinear balance-based adaptive controller

This paper presents the intuitive and ready-to-use, general procedure for tuning the balance-based adaptive controller (B-BAC) based on its equivalence to the controller with PI term and with additional improvements shown for the linearised approximation of the dynamics of the nonlinear controlled process. The simple formulas are suggested to calculate the B-BAC tunings based on the PI tunings determined by any PI tuning procedure chosen accordingly to the desired closed-loop performance. This methodology is verified by comparing the closed-loop performance of the equivalently tuned B-BAC and PI/PI+feedforward controllers under the same scenario, both by the simulation and practical experiments.     

An adaptive controller for batch feed bioprocess application to lysine production

This paper presents an adaptive algorithm designed for batch feed bioprocess control, The proposed algorithm is based on a non-linear ‘grey box’ model, which is adapted on-line to the process behaviour by the estimation of a key parameter. Stability and convergence analysis of this algorithm is presented, and from this, a practical tuning method is given. The proposed algorithm is compared to a standard adaptive generalized predictive controller approach, and is shown to exhibit similar performance while being easier to use. A real application of this adaptive algorithm to a batch feed lysine process is presented. Good results are obtained, which show that this control scheme is a worthwhile alternative for batch feed bioprocess control.     

A new model-free adaptive sliding controller for active suspension system

Active suspension systems are designed to provide better ride comfort and handling capability in the automotive industry. Since the active suspension system has nonlinear and time-varying characteristics, it is difficult to establish an accurate dynamic model for designing a model-based controller. Here, a functional approximation (FA) based adaptive sliding controller with fuzzy compensation is proposed for an active suspension system. The FA technique is employed to represent the unknown functions, which releases the model-based requirement of the sliding mode control. In addition, a fuzzy control scheme with online learning ability is employed to compensate for the modeling error of the FA with finite number of terms for reducing the implementation difficulty. To guarantee the control system stability, the update laws of the coefficients in the approximation function and the fuzzy tuning parameters are derived from the Lyapunov theorem. The proposed controller is employed on a quarter-car active suspension system. The simulation results and experimental results show that the proposed controller can suppress the oscillation amplitude of the sprung mass effectively. To evaluate the performance improvement of inducing a fuzzy compensator in this FA adaptive controller, the dynamic responses of the proposed hybrid controller are compared with those of FA-based adaptive sliding controller only.