Non-minimum Phase Nonlinear Systems Research Articles

High-gain observer design for auxiliary systems of non-minimum phase nonlinear systems

To a non-minimum phase nonlinear system, it was supposed that, if there is an output feedback control that stabilizes the auxiliary system, then there is an output feedback that stabilizes the original system. The existing methods base designing output feedback for non-minimum phase nonlinear system on the hypothesis that there exists output feedback for auxiliary system. However, the auxiliary system could be unobservable. Alternatively, this study aims to create a way to design output feedback for auxiliary systems in unobservable situation. An output state is constructed in the last equation of auxiliary system, which artificially makes the internal dynamics of the auxiliary system observable. Then, a cascade high-gain observer is designed for the auxiliary system, consisting of an extended high-gain observer for external dynamics and a high-gain observer for internal dynamics of the auxiliary system. Therefore, the output feedback control for auxiliary system can be designed via the cascade high-gain observer and a state feedback. Finally, the proposed method is demonstrated by an academic example and an inverted pendulum on a cart in the simulation.

Decentralized robust adaptive backstepping control for a class of non-minimum phase nonlinear interconnected systems

In this paper, a class of interconnected systems is considered, where the nominal isolated subsystems are fully nonlinear and non-minimum phase. A decentralized Extended Kalman Filter-Extended High Gain Observer (EKF-EHGO) is designed to observe the system states. Then, a systematic backstepping design procedure is employed to develop a novel decentralized robust adaptive output feedback control, in which the adaptive law is designed to counter the effects of the interconnections and uncertainties. The proposed decentralized dynamic output feedback control scheme can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Both interconnections and uncertainties are allowed to be unmatched and bounded by an unknown high-order polynomial, which is a more general form when compared with existing work. Two MATLAB simulation examples are used to demonstrate the effectiveness of the proposed method including a system comprising translational oscillator with rotating actuator (TORA) sub-systems.

An Objective Holographic Feedback Linearization Based on a Sliding Mode Control for a Buck Converter with a Constant Power Load

As a typical load, the constant power load (CPL) has negative impedance characteristics. The stability of the buck converter system with a mixed load of CPL and resistive load is affected by the size of the CPL. When the resistive load is larger than the CPL, the buck converter with the output voltage as an output function is a non-minimum phase nonlinear system, because its linear approximation has a right-half-plane pole. The non-minimum phase characteristic limits the application of many control techniques, but the objective holographic feedback linearization control (OHFLC) method is a good control strategy that can bypass the non-minimum phase system and make the system stable. However, the traditional OHFLC method, in designing the controller, generally uses a linear optimal quadratic design method to obtain a linear feedback control law. It requires a state quantity component with a one-order relative degree to the system. But it is not easy to find such a suitable state quantity with a one-order relative degree to the system. In this paper, an improved OHFLC method is proposed for Buck converters with a mixed loads of CPL and resistive loads, using the sliding mode control (SMC) theory to design the controller, so that the output state quantity components with different relative degrees to the system can be used in the holographic feedback linearization method. Finally, the simulation and experimental results also demonstrate that this method has the same, or even better, dynamic response performance and robustness than the traditional OHFLC method.

Cascade Control of Non-Ideal Boost Power Converter

This article presents the analysis and design of a cascade controller for regulation of output voltage in a non-ideal boost power converter. Non-ideal boost power converter is a well-known nonlinear non-minimum phase system. Hence it is chosen to show the ability of the proposed control technique. The proposed technique involves sliding mode current loop and internal model-based voltage loop. Cascade controller based non-ideal boost power converter exhibits fast dynamic response, excellent tracking, and rejection of disturbances even though input voltage, load and parameters of the converter are uncertain. Validation on an experimental prototype followed by detailed analysis of results is presented.

Asymptotic Output Tracking of Non-minimum Phase Nonlinear Systems through Learning Based Inversion

Asymptotic Output Tracking of Non-minimum Phase Nonlinear Systems through Learning Based Inversion

Super twisting control of torsional vibration in non-minimum phase nonlinear drill string system

In this paper, a second order sliding mode control law for regulation of rotational speed in a non-minimum phase drill string system is proposed. In this regard, first, the nonlinear dynamic model of a drill string which is in contact with non-Newtonian mud is conducted. Next, a super twisting sliding mode control is designed that ensures the asymptotic regulation of output during sliding motion in a finite time and stable zero dynamics. It is shown that the proposed super twisting controller is capable of adjusting the output on a desired value by generating a proper sliding surface in a finite time. The convergence of the proposed controller for the dynamic model with a higher number of mode shapes is also investigated, and it is found that by increasing the number of obtained modes, the desired output needs less computation time with more accuracy.

Output tracking control of non‐minimum phase systems using on‐line output redefinition approach based on barrier function method

This paper considers the output tracking problem of non-minimum phase non-linear systems using the inverse dynamics control which is impossible in conventional methods due to unstable zero dynamics. The proposed method is based on the output redefinition approach defined as a parametric function. The tracking error is decomposed into two terms. The first one named redefined output tracking error is the difference between the redefined output and the reference signal, and the second one is the distance between the redefined output and the system output. For the first term, due to minimum phase property of the system with the redefined output, an inverse dynamics control is used to guarantee the convergence of the redefined output tracking error to zero. To minimize the second term, the parameters of the redefined output are set by solving an optimization problem whose constraints include minimum phase conditions. To solve the optimization problem which satisfies all constraints, the barrier function method as an interior point method is adopted. The optimization parameters are set using steepest descent algorithm. Due to on-line updating the redefined output parameters, the related zero dynamics is time varying. Therefore, sufficient conditions for exponential stability of the resulting time-varying zero dynamics are obtained.

Periodic Event-Triggered Control for a Class of Nonminimum-Phase Nonlinear Systems Using Dynamic Triggering Mechanism

In this paper, the output feedback based periodic event-triggered control problem is considered for a class of nonminimum-phase nonlinear systems via dynamic event-triggering mechanism. When only the sampled-data output is known, a new periodic event-triggered control method is proposed via output feedback and the control input updates based on a discrete-time dynamic event-triggering condition. Despite the unstable zero dynamics, the proposed control method can asymptotically stabilize the hybrid control systems by closing the loop only when it is necessary. In contrast to the continuous-time static one, the proposed dynamic triggering condition has several advantages including the easier digital implementation and the larger average inter-event time interval. The delicate analysis gives the explicit expression of the maximum allowable sampling period, and the global asymptotic stability can be achieved for the hybrid control systems. Finally, the effectiveness of the proposed periodic event-triggered control method is verified by a numerical simulation.

Output Tracking of Some Class Non-Minimum Phase Nonlinear Systems via linearization Input-Output

We present an output tracking problem for a non-minimum phase nonlinear system. In this paper, the input control design to solve the output tracking problem is to use the input output linearization method. The use of the input output linearization method cannot be initiated from output causing the system to be non-minimum phase. Therefore the output of the system will be redefined such that the system will become minimum phase with respect to a new output.

Stability of DC Boost converter Feeding Constant Power Load using Fuzzy Controller Based Lyapunov

ABSTRACT Tight voltage regulation of the DC microgrid bus may lead to instability issue which leads to microgrid system collapse. Constant power load (CPL) is a serious problem that exists in cascaded power electronic converters which must have a robust controller to mitigate instability issue. The controller based on mathematical model is vulnerable to model mismatch which could lead to instability especially with highly nonlinear plant. Boost converter feeding CPL is a highly nonlinear non-minimum phase system which is difficult to control based on mathematical model. In this paper a supervisory stable Fuzzy Logic Controller (SFC) based on Lyapunov theory is designed to mitigate the instability issue that is caused by the negative incremental impedance which behaves as CPL of dc boost converter. The proposed SFC is able to stabilise the output voltage of the boost converter under nominal and uncertain conditions. The proposed controller is validated through simulation using Matlab/Simulink. To the best of the authors’ knowledge this method hasn’t been introduced before.

Objective holographic feedbacks linearization control for boost converter with constant power load

As a typical load, the constant power load (CPL) is different from the resistive load and has destabilizing negative impedance characteristics, influencing the system stability. The boost converter with the output voltage as the feedback control variable is a non-minimum phase nonlinear system because its linear approximation has a right-half-plane (RHP) pole. The non– minimum phase system limits the application of control techniques such as input–output linearization (IOL). This paper presents an objective holographic feedbacks linearization control strategy (OHFLC) for DC power systems with constant power loads, bypassing non-minimum phase systems to stabilize the system. The analysis of the proposed method’s pole-zero points indicates that it is based on placing the pole-zero points of the system on their corresponding desired positions through feedback so as to achieve satisfactory dynamic and static performance of the control system. Finally, simulation and experimental verification demonstrate that the presented control approach provides superior dynamic response and robustness than the traditional proportional-integral (PI) control.

Output Tracking of Uncertain Nonminimum Phase Systems by Experience Replay

The precision output tracking problem of multi-input-multi-output (MIMO) uncertain nonlinear nonminimum phase systems is investigated in this paper. The challenge lies in the difficulty in solving the ideal internal dynamics (IID), which is a bounded solution for the uncertain zero dynamics. First, the experience replay technique is applied to identify the uncertain parameters in the zero dynamics. It uses the recorded past data concurrently with current data which can greatly speed up the identification convergence. With the identified parameters, a novel approach called optimal bounded inversion is proposed to obtain the IID by solving a trajectory optimization problem using GPOPS-II. The boundedness of the IID is guaranteed by setting state constraints and the feasibility is achieved by minimizing the initial condition mismatch. Moreover, a piecewise IID updating scheme is adopted to reduce the computational burden. The benchmark nonminimum phase system, a vertical take-off and landing (VTOL) aircraft is used to validate the effectiveness of the proposed method.

Output tracking for a class of non-minimum phase nonlinear systems: A two-point boundary value problem formulation with a hybrid regulator

The asymptotic output tracking problem is studied for a class of non-minimum phase nonlinear systems without requiring the a priori knowledge, or even the existence, of a finite-dimensional exosystem that generates the prescribed periodic reference signal. The design strategy is illustrated in two steps. First, it is shown that the knowledge of a solution to a certain two-point boundary value problem involving the underlying zero-dynamics of the plant is instrumental and sufficient to construct a state feedback regulator that achieves boundedness of the trajectories and (exact) asymptotic tracking, hence completely circumventing the need for solving partial differential equations. Then, since the computation of the latter solution may be affected by numerical errors that are particularly detrimental in the presence of unstable zero-dynamics, the above architecture is robustified by means of an additional hybrid feedback loop whose trajectories converge to a solution of the two-point boundary value problem. Once the latter scheme has been established and discussed, the extension to the case of output feedback is presented, firstly in the specially structured case in which the input vector field depends only on the measured output and then extended to the generic case. The theory is then corroborated by means of a physically motivated numerical example involving an inverted pendulum on a cart. Interestingly, it is also shown that the solution provided by the hybrid scheme above coincides with the limiting solution of a suitably defined cheap optimal control problem.

Extended state observer based robust sliding mode control for fourth order nonlinear systems with experimental validation

It is commonly known that the design of control is difficult for the systems with non-minimum phase behavior, the coupling between the controlled variables and integral instability. The paper presents such a typical class of nonlinear system and propose a new technique generalized extended state observer-based sliding mode decoupling control. The proposed control algorithm is also able to compensate for the matched and mismatched uncertainties encountered in such nonlinear non-minimum phase systems. The decoupling control approach is used to decouple the entire system framework into subsystems. The sliding surface of the individual subsystem was composed using the estimated states of GESO. The proposed technique can nullify the effect of external disturbances, parametric uncertainties and unmodelled dynamics due to the inclusion of disturbance compensation gain in the control law. The proposed methodology enables the system to accomplish asymptotic stability and better dynamic response with lesser IAE and ITAE values than existing decoupling control strategies. An experimental application of the proposed technique to Quanser’s rotary pendulum module is investigated.

Robust Adaptive Fuzzy Tracking Control for Uncertain MIMO Nonlinear Nonminimum Phase System

Parameter uncertainty and unmodeled dynamics are inevitable for an actual nonlinear system, and are hard to deal with in control design, especially when the internal dynamics of this nonlinear system are unstable. The control design for a multiinput multioutput nonlinear nonminimum phase system with parameter uncertainty and unmodeled dynamics is discussed in this paper. The internal dynamics of nonminimum phase system are unstable, the control of this kind of system is challenging. Ideal internal dynamics (IID) based controller design method are utilized here, and a partially linearized model is constructed. A state tracking model is constructed on account of the partially linearized model and IID. Then the robust fuzzy controller design problem is discussed and a fuzzy logical system is utilized to identify the parameter uncertainty and unmodeled dynamics. A robust adaptive fuzzy controller is proposed for the stability of the nonlinear nonminimum phase system with parameter uncertainty and unmodeled dynamics. Finally, by simulations on vertical takeoff and landing aircraft, the availability of the presented adaptive fuzzy controller is validated.

Sampled-data repetitive control for a class of non-minimum phase nonlinear systems subject to period variation

ABSTRACTThe robust sampled-data repetitive control (RC, or repetitive controller, also designated RC) problem for non-minimum phase nonlinear systems is both challenging and practical. This paper proposes a sampled-data output-feedback RC design for a class of non-minimum phase systems with measurable nonlinearities to improve the robustness against the period variation. The design relies on additive-state decomposition, by which the output-feedback RC problem is decomposed into an output-feedback RC problem for a linear time-invariant component and a state-feedback stabilisation problem for a nonlinear component. Thanks to the decomposition, existing controller design methods in both the frequency domain and the time domain are employed to make the robustness and discretisation for a continuous-time nonlinear system tractable. In order to demonstrate the effectiveness, an illustrative example is given.

Robust Fixed-Time Integral Sliding Mode Control of a Nonlinear Hydraulic Turbine Regulating System

Abstract The hydraulic turbine regulating system (HTRS) plays an important role in the safe and stable operation of hydropower stations. In this paper, a fixed-time integral sliding mode controller (FTISMC) is designed to make the nonlinear HTRS with disturbances stable in a fixed time. The HTRS is a highly complex, strongly coupled, nonlinear nonminimum phase system, which can ensure the frequency and rotor angle of generator stability by adjusting the guide vane opening. In order to decouple the nonlinear HTRS, the input/output feedback linearization is applied to establish the relationship between the control input and the output of the HTRS. Based on sliding mode control (SMC) theory and fixed-time stability theory, FTISMC is proposed to stabilize the HTRS in a fixed time. Compared with the finite time control method (FTCM), the convergence time of nonlinear HTRS under FTISMC is independent of initial conditions and can be exactly estimated. Meanwhile, the integral sliding surface can avoid singularity, thus eliminating the chattering phenomenon. Finally, the numerical simulation is implemented to demonstrate the superior performances of the proposed FTISMC than the existing PID, SMC, and FTMC.

Robust Adaptive Control for Uncertain Input Delay MIMO Nonlinear Non-Minimum Phase System: A Fuzzy Approach

In this paper, the robust controller design problem of uncertain multi-input multi-output nonlinear non-minimum phase system is discussed. The nonlinear system is suffering from both uncertainty and input delay, so the controller design is difficult. The traditional stable inversion controller is utilized and extended to uncertain case. An integral of past control input is constructed and fuzzy logical system is utilized for approaching the unknown state matrix and input matrix. Then a robust adaptive control strategy is presented. Finally, a numerical simulation on vertical takeoff and landing aircraft is given to show the effectiveness of the proposed method.

Application of a multi-input multi-output (MIMO) nonlinear non-minimum phase system control method to hydro turbine unit

In this paper, in view of the non minimum phase characteristics of hydraulic turbine unit, a method of designing the controller of multi-input multi-output (MIMO) nonlinear non-minimum phase system is proposed and applied to hydraulic turbine unit system described by double control input fifth order model. The turbine output electromagnetic power and generator power angle are stabilized by wicket gate opening and excitation combined control. Firstly, the method for designing the controller of multi-input multi-output (MIMO) nonlinear non-minimum phase system is introduced. The method is based on state feedback theory, pole assignment theory and Lyapunov stability theory. Secondly, the control law of hydro turbine unit is given according to the method. Results of simulation indicate that this nonlinear non-minimum phase controller has a good effect when applied to the hydro turbine unit.

Repetitive control for nonlinear systems: an actuator-focussed design method

There exist at least two viewpoints on the internal model principle (IMP), namely the cancelation viewpoint and the geometrical viewpoint. However, neither of them is applicable to repetitive control (RC, or repetitive controller, also designated RC) of nonlinear systems directly. Because of this, error dynamics are often derived to transform a periodic signal tracking problem into a rejection problem. This not only fails to represent the special feature of periodic signals but also restricts the applications of RC. In view of this, this paper proposes a new viewpoint on IMP, namely the actuator-focussed viewpoint. With this, the periodic signal tracking problem can be converted into a stability problem without deriving error dynamics for linear periodic systems and nonlinear systems. In order to demonstrate its effectiveness, the proposed design approach is applied to RC problems for a linear periodic system, a minimum-phase nonlinear system and a nonminimum-phase nonlinear system.