Adaptive one-step-ahead control for non-minimum phase systems with input magnitude and rate constraints

The adaptive control design for linear stable plants with input magnitude and rate constraints is addressed. The proposed algorithm adopts the self-tuning regulator (STR) adaptive control principle with one-step-ahead control as its underlying control design. An important governing equation relating the prediction error to the 'input discrepancy' between adaptive control and the corresponding non-adaptive control is identified, independent of how the parameter estimates are attained. Together with the convergence property of least-square type estimation algorithm, the governing equation leads to a successful analysis on the convergence and tracking performance of the adaptive constrained one-step-ahead controller. Specifically, globally input matching property is maintained in the sense that the adaptive constrained control asymptotically matches its corresponding non-adaptive one. Furthermore, the desired tracking performance of the adaptive controller can be achieved asymptotically if the corresponding non-adaptive control is eventually out of the constraints. The proposed adaptive control is applicable to both minimum and non-minimum phase stable systems.     

Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems

An adaptive output feedback control methodology is developed for a class of uncertain multi-input multi-output nonlinear systems using linearly parameterized neural networks. The methodology can be applied to non-minimum phase systems if the non-minimum phase zeros are modeled to a sufficient accuracy. The control architecture is comprised of a linear controller and a neural network. The neural network operates over a tapped delay line of memory units, comprised of the system's input/output signals. The adaptive laws for the neural-network weights employ a linear observer of the nominal system's error dynamics. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. Simulations of an inverted pendulum on a cart illustrate the theoretical results.     

Stable adaptive control of non-minimum phase systems

An adaptive pole placement design for not necessarily minimum phase systems is analyzed with respect to stability. Conditions are given for boundedness of closed-loop signals when the process is subject to bounded disturbances. The most restrictive one can be avoided in a local stability result.     

输出重定义下的非线性非最小相位系统迭代学习控制

讨论非线性非最小相位系统实现完全跟踪的迭代学习控制方法, 适于在有限作业区间上重复运行的受控系统. 在控制器设计时, 通过输出重定义以使非最小相位系统的零动态变成渐近稳定特性. 分别采用部分限幅和完全限幅两种学习算法设计控制器, 理论分析表明两种算法能够保证学习系统中所有变量的有界性和跟踪误差在整个作业区间上渐近收敛于零. 数值仿真验证了两种迭代学习控制系统的跟踪性能.     

Synthesis of optimal control systems for non-minimum phase plants

The features of the synthesis of a determinate system for non-minimum phase plant control by the polynomial equation method are considered. Results of the synthesis are compared according to the square (H²) and minimax (H^∞) criteria for the various types of reference models complying with the requirements specified for a synthesized system. The rational structure of the reference models is ascertained.     

Enhanced feedforward control of non-minimum phase systems for tracking predefined trajectory

This article proposes a novel feedforward controller for non-minimum phase systems by utilising the preview information of the desired trajectory. The performance of the proposed controller is analysed theoretically and verified through the simulation, including comparison with the optimal zero phase error tracking controller and the preview-based stable inversion. The simulation results show that the proposed controller can gain outstanding performance even if the preview time of the desired trajectory is limited.     

一类非线性非最小相位系统的直接自适应控制

针对一类不确定的离散时间非线性非最小相位动态系统,提出了一种基于神经网络和多模型的直接自适应控制方法．该控制方法由线性直接自适应控制器,神经网络非线性直接自适应控制器以及切换机构组成．线性控制器用来保证闭环系统输入输出信号有界,非线性控制器用来改善系统性能．切换策略通过对上述两种控制器的切换,保证闭环系统输入输出有界的同时,改善了系统性能．理论分析以及仿真结果表明了所提出的直接自适应控制方法的有效性．     

非最小相位系统的扩展Laguerre基函数迭代学习控制

针对非最小相位系统的跟踪问题,提出了一种新的基函数迭代学习控制算法.该算法利用新型的非因果Laguerre扩展基函数逼近系统逆传递函数,设计最优迭代学习律使系统输入收敛到系统的稳定逆,保证了控制性能.算法不依赖于系统的先验模型,仅需以基函数信号作为系统输入进行模型辨识,减少了模型不确定性的影响.通过对单连杆柔性机械臂这样的典型非最小相位系统跟踪问题的仿真,验证了该方法的良好效果.     

Disturbance observer for non-minimum phase linear systems

Disturbance observer (DOB) approach has been widely employed in the industry thanks to its powerful ability to attenuate disturbances and compensate plant uncertainties. Motivated by the fact that the application of the DOB approach has been limited to minimum phase systems, we propose a new DOB configuration for non-minimum phase systems. Rigorous analysis for robust stability and performance recovery is presented in terms of a new filter Θ (s). By restricting the plant uncertainty to a multiplicative perturbation, we also present a systematic design methodology for the filter Θ(s) by virtue of the H_∞ synthesis technique. An illustrative example of autopilot design is presented to show the effectiveness of the proposed method for which it is not easy to design H_∞ controller to achieve some control goals. The simulation results show that the response of the perturbed system in the presence of disturbance can be recovered to the nominal system response in the absence of disturbance.     

Iterative learning control with advanced output data for nonlinear non-minimum phase systems

This paper investigates iterative learning control of nonlinear discrete time non-minimum phase systems in tracking problems. The main objective of this paper is to find an input-to-output mapping in order to stabilize the non-minimum phase systems and to obtain an input update law for handling uncertain systems. In conventional approaches on the tracking of non-minimum phase systems, zero dynamics is stabilized from the system equations and the input is calculated from the state information. For the learning of uncertain systems, conventional approaches depend on the output-to-state and state-to-input mappings. In the proposed method, the inverse system is stabilized using the input-to-output mapping for nonlinear non-minimum phase systems. A new input update law is proposed based on the relative degree and the number of non-minimum phase zeros. This makes the overall proposed learning system have a simple structure as in the classical ILC.     

Output feedback sliding mode control for non-minimum phase systems with non-linear disturbances

In this paper, robust stabilization for a class of systems with a non-linear disturbance is considered. The non-linear disturbance is mismatched and has a non-linear bound. The nominal system is allowed to be non-minimum phase. A dynamical compensator is designed to estimate the system state and a sliding surface, in the augmented space formed by the system output and the estimated state, is proposed. The stability of the corresponding sliding mode is analysed using the equivalent control approach. Based on the estimated state variables and system output, a variable structure control scheme is developed such that the system is driven to the sliding surface and maintained on it thereafter. Finally, a simulation for a nonminimum phase HIRM aircraft model is presented to illustrate the effectiveness of the results.     

Robust adaptive control of nonlinear non-minimum phase systems with uncertainties

This paper, presents a robust adaptive control method for a class of nonlinear non-minimum phase systems with uncertainties. The development of the control method comprises two steps. First, stabilization of the system is considered based on the availability of the output and internal dynamics of the system. The reference signal is designed to stabilize the internal dynamics with respect to the output tracking error. Moreover, a combined neuro-adaptive controller is proposed to guarantee asymptotic stability of the tracking error. Then, the overall stability is achieved using the small gain theorem. Next, the availability of internal dynamics is relaxed by using a linear error observer. The unmatched uncertainty is compensated using a suitable reference signal. The ultimate boundedness of the reconstruction error signals is analytically shown using an extension of the Lyapunov theory. The theoretical results are applied to a translational oscillator/rotational actuator model to illustrate the effectiveness of the proposed scheme.     

Output consensus control of multi-agent systems with nonlinear non-minimum phase dynamics

This paper considers the output consensus problem in non-minimum phase nonlinear multi-agent systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, a consensus protocol consisting of two terms is proposed. The first term is a linear function of the states of each agent employed in order to overcome the non-minimum phase dynamics, and the second term is a function of the output of neighbouring agents which provides coupling among agents and guarantees output consensus in the network. The asymptotic stability of output consensus errors and the boundedness of the states of agents are also studied. A numerical example is presented to show the effectiveness of the proposed approach.     

Relaxation of output zeroing for bilinear non-minimum phase systems

Linear control design techniques for output setpoint tracking of regulation problems can be extended, through input output feedback linearization (IOFL), to non-linear, input-affine systems, but are not applicable to the case of equilibrium points that exhibit non-minimum phase characteristics. Rather than resort to minimum phase approximations, this paper instead proposes a relaxation of IOFL that does not require IOFL to be implemented at every sampling instant. The relaxation introduces degrees of freedom which, in the case of bilinear systems, can be used efficiently to achieve tracking/regulation, and to maintain this property (to within perturbations caused by the relaxation) until the desired state is reached. A way for expanding the region of attraction is considered and the results of the paper are demonstrated through simulation examples.     

Identification of non-minimum phase linear stochastic systems

The identification of time-invariant, non-minimum phase, stochastic systems driven by non-Gaussian white noise is considered, given only (the noisy observations of the system output. A two-step procedure is proposed. In the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements. In the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros. Knowledge of the probability distribution of the driving noise is not required. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are also presented in support of the theory.     

Approximate output tracking for nonlinear non-minimum phase systems with an application to flight control

An unstable zero-dynamics is a known obstruction to inducing exact asymptotic tracking for an open set of output trajectories with internal stability. This paper proposes a procedure for achieving approximate tracking for a nonlinear system whose linearization possesses real right-half plane zeros. The method is guaranteed to remove the right-half plane zeros while the other zeros remain in their previous location; moreover, it provides information on the class of signals for which good approximate tracking can be obtained. With other methods, the right-half plane zeros are eliminated but the final location of the remaining zeros is not known a priori. The design procedure is illustrated on a trajectory control problem of an aircraft in rapid manoeuvres. Simulations illustrate the computations involved and show that precise lateral and longitudinal manoeuvres can be performed, even in the presence of uncertainties.     

非线性非最小相位船舶舵减摇系统的滑模控制

建立了从舵到横摇角的非最小相位非线性船舶模型,利用滑模控制方法设计同步横摇阻尼和航向保持的稳定控制器。船舶减摇建模时假设模型误差的数量级和扰动已知,且设计的滑模控制器可实现对一阶波浪扰动的稳定调节。基于李亚普诺夫稳定性理论证明了整个闭环系统的稳定性,仿真实验的结果验证了所设计的控制器的优良跟踪性能和鲁棒性。     

基于稳定逆的非最小相位系统的迭代学习控制

针对迭代学习控制在非最小相位系统上应用效果差的缺点,根据最优化性能指标和非因果的稳定逆理论,提出了一种基于稳定逆的最优开闭环综合迭代学习控制,分析了学习律的收敛性并给出了此种非因果的学习律在实际应用中的运用方式.     

Adaptive restricted trajectory tracking for a non-minimum phase hypersonic vehicle model

The design of a nonlinear robust controller for a non-minimum phase model of an air-breathing hypersonic vehicle is presented in this work. When flight-path angle is selected as a regulated output and the elevator is the only control surface available for the pitch dynamics, longitudinal models of the rigid-body dynamics of air-breathing hypersonic vehicles exhibit unstable zero-dynamics that prevent the applicability of standard inversion methods for control design. The approach proposed in this paper uses a combination of small-gain arguments and adaptive control techniques for the design of a state-feedback controller that achieves asymptotic tracking of a family of velocity and flight-path angle reference trajectories belonging to a given class of vehicle maneuvers, in spite of model uncertainties. The method reposes upon a suitable redefinition of the internal dynamics of a control-oriented model of the vehicle dynamics, and uses a time-scale separation between the controlled variables to manage the peaking phenomenon occurring in the system. Simulation results on a full nonlinear vehicle model that includes structural flexibility illustrate the effectiveness of the methodology.     

非最小相位搅拌机的鲁棒控制

一种新的鲁棒控制设计过程被应用于连续搅拌机的控制.控制对象的非线性与模型参数误差作为不确定性,线性控制器的鲁棒性用来保证一定范围内操作点的控制.设计中考虑了以右半平面零点为特点的非最小相位特性的影响和输入输出比例调节.仿真结果表明所设计的控制器至少与 μ-控制器的性能一样好.