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.     

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.     

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.     

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.     

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.     

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.     

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.     

Output-feedback model-reference sliding mode control of uncertain multivariable systems

This note considers the robust output tracking problem using a model-reference sliding mode controller for linear multivariable systems of relative degree one. It is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties. The strategy is based on output-feedback unit vector control to generate sliding mode. The only required a priori information about the plant high frequency gain matrix K/sub p/ is the knowledge of a matrix S/sub p/ such that -K/sub p/S/sub p/ is Hurwitz which relaxes the positive definiteness requirement usually needed by other methods.     

基于反馈线性化的MIMO非最小相位系统指数镇定

针对仿射多输入多输出非线性非最小相位系统,提出了一种新的镇定方案.用反馈线性化解耦系统输入输出关系,通过高增益状态反馈镇定系统外部动态,用模型预测控制镇定内部动态,所设计控制器能保证闭环系统的指数稳定性.仿真结果表明了所提出方法的有效性和优越性.     

Bounded tracking for non-minimum phase nonlinear systems with fast zero dynamics

In this paper, we derive tracking control laws for non-minimum phase nonlinear systems with both fast and slow, possibly unstable, zero dynamics. The fast zero dynamics arise from a perturbation of a nominal system. These fast zeros can be problematic in that they may be in the right half plane and may cause large magnitude tracking control inputs. In this paper, we combine the ideas from some recent work of Hunt, Meyer and Su with that of Devasia, Chen and Paden on an asymptotic tracking procedure for non-minimum phase nonlinear systems. We give (somewhat subtle) conditions under which the tracking control input is bounded as the magnitude of the perturbation of the nominal system becomes zero. Explicit bounds on the control inputs are calculated for both SISO and MIMO systems using some interesting non-standard singular perturbation techniques. The method is applied to a suite of examples, including the simplified planar dynamics of VTOL and CTOL aircraft.     

Robust control for a specific class of non-minimum phase dynamical networks

The problem of robust control of dynamic networks with non-minimum phase subsystems, where only scalar inputs and outputs are available for measurement, is solved. Conditions on the parameters of the network model and the control system are obtained that ensure that the control algorithm designed for minimum phase network systems remains valid for non-minimum phase network systems as well. Control of the dynamic network in the cases when it includes and does not include a master subsystems is considered. Examples of simulation are presented to illustrate the results.     

Direct pole placement adaptive tracking of non-minimum phase systems

In this paper, we propose a direct pole placement adaptive tracking scheme for non-minimum-phase, open-loop stable, linear plants with time delays. This controller utilizes the internal model principle to eliminate steady-state tracking error for signals with known distinct frequencies. The controller order depends only on the number of frequencies in the reference input, but not on the order of the plant. It is shown that with sufficiently small loop gain, the controller can guarantee stable closed loop, and asymptotic tracking.     

Convolution profiles for right inversion of multivariable non-minimum phase discrete-time systems

The problem of the non-causal inversion of linear multivariable discrete-time systems is analyzed in the geometric approach framework and is solved through the computation of convolution profiles which guarantee perfect tracking under the assumption of infinite-length preaction and postaction time intervals. It is shown how the shape of the convolution profiles is related to both the relative degree and the invariant zeros of the plant. A computational setting for the convolution profiles is derived by means of the standard geometric approach tools. Feasibility constraints are also taken into account. A possible implementation scheme, based on a finite impulse response system acting on a stabilized control loop, is provided.     

Experimental evaluation of iterative learning control algorithms for non-minimum phase plants

The purpose of this paper is two-fold, firstly it describes the development and modelling of an experimental test facility as a platform on which to assess the performance of Iterative Learning Control (ILC) schemes. This facility includes a non-minimum phase component. Secondly, P-Type, D-Type and phase-lead types of the algorithm have been implemented on the test-bed, results are presented for each method and their performance is compared. Although all the ILC strategies tested experience eventual divergence when applied to a non-minimum phase system, it is found that there is an optimum phase-lead ILC design that maximizes convergence and minimizes error. A general method of arriving at this phase-lead from knowledge of the plant model is described. A variety of filters have been applied and assessed in order to improve the overall performance of the algorithm.