Non-minimum Phase Nonlinear Systems Research Articles

Robust Sliding Mode-Based Learning Control for MIMO Nonlinear Nonminimum Phase System in General Form.

The tracking control of a multi-input multioutput nonlinear nonminimum phase system in general form is discussed. This system is assumed to be suffering from parameter uncertainties and unmodeled dynamics, and the priori information of them is unknown. By considering both the exact model and uncertain model, the sliding mode-based learning controller is proposed. By designing an appropriate sliding surface and a learning controller, the stability of the closed-loop system is guaranteed for both the exact model and uncertain model. To overcome the disadvantage caused by parameter uncertainties and unmodeled dynamics, a fuzzy logical system is adopted here. A numerical simulation result carried on vertical takeoff and landing aircraft is taken as an example to validate the effectiveness of the presented controller.

Output Tracking of Some Classes of Non-minimum Phase Nonlinear Systems By Redefinition Output Approach

In this paper, we present the redefinition output approach for output tracking of some classes of non-minimum phase nonlinear systems without and with uncertainty. Input-Output linearization and gradient descent methods are applied to design the control. The good result of this approach is demonstrated by 3 examples.

Regulation of Non-Minimum-Phase Nonlinear Systems Using Slow Integrators and High-Gain Feedback

This paper investigates the regulation problem for nonminimum-phase nonlinear systems via slow integrators and high-gain feedback. The developed methodology involves four steps: in the first step, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in [18] . In the second step, we use high-gain feedback to stabilize the original system, which is able to recover the performance of the auxiliary system by choosing the gain high enough. In the third step, with a condition on the dc steady-state input–output map, a slow integrator is added that enforces the objective of regulation. In the last step, we extend the methodology into the output feedback case by utilizing the extended high-gain observer to estimate the derivatives of the output as well as one unknown term including system uncertainties. The use of the observer recovers the performance under full-information feedback. The design procedure is first presented for the linear model for the clarity of the proposed methodology. The effectiveness of such methodology is demonstrated on the nontrivial translational oscillator rotating actuator example. At last, the design for minimum-phase nonlinear systems is also provided. In this case, the performance recovery of the closed-loop auxiliary system by output feedback is verified.

Adaptive tracking control of MIMO nonlinear nonminimum phase system with unknown input nonlinearity

SummaryThis paper proposes a nonlinear adaptive control for output tracking of multi‐input multi‐output nonlinear nonminimum phase system with input nonlinearity. The parameters of the input nonlinearity are assumed to be unknown. This problem is challenging, not only because of the unstable internal dynamics of nonminimum phase system, but also the existence of the unknown input nonlinearity. The partially linearized model of the original system is obtained through input/output linearization, and a states tracking model is constructed based on the computed ideal internal dynamics. A nonlinear adaptive controller, which can guarantee the bounded of output tracking error in the existence of unknown input nonlinearity, is proposed. Finally, a numerical simulation on vertical takeoff and landing aircraft is given to show the effectiveness of the proposed control methods.

Adaptive sliding mode control of non‐linear non‐minimum phase system with input delay

This study proposes an adaptive sliding mode control (SMC) design method for multi-input multi-output non-linear non-minimum phase system with input delay. The problem is challenging, not only because of the unstable internal dynamics of the non-minimum phase system, but also the existence of input delay. The partially linearised model of the original non-linear system is obtained through input/output linearisation, and a state tracking model is constructed based on the computed ideal internal dynamics. A filtered tracking error is introduced to handle the input delay. A SMC strategy is proposed for the stability of filtered tracking error system, and an adaptive law is designed to estimate the upper bound of perturbations. Finally, comparison simulation results on vertical takeoff and landing aircraft are provided to verify the efficiency of the proposed method.

Transient tracking performance improvement for nonlinear nonminimum phase systems: an additive-state-decomposition-based control method

ABSTRACTTo study the problem of improving transient tracking performance for nonlinear systems, this paper proposes an additive-state-decomposition-based control method for a class of nonlinear nonminimum phase (NMP) systems. This method ‘additively’ decomposes the original problem into two more tractable problems, namely a tracking problem for a linear time-invariant NMP ‘primary’ system and a state stabilisation problem for a certain nonlinear ‘secondary’ system. Then, controller for each system is designed respectively by employing existing methods, i.e. the linear quadratic regulator (LQR) method for the primary system and the backstepping method for the secondary system. Next, these two controllers are combined together to achieve the original tracking goal. Furthermore, the adjustment of weighting matrix Q in the LQR regulates the transient response of the closed-loop nonlinear system. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed method.

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

ABSTRACTThis 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.

Approximate stable system centre approach to output tracking of non-minimum phase nonlinear systems

This paper proposes a novel method to approximate the ideal internal dynamics state trajectories which coincide with accurate output tracking for known non-minimum phase nonlinear systems. The proposed approach resembles the stable system centre method, but uses a lower order dynamic system than the stable system centre to generate an approximation of the ideal internal dynamics state trajectories. This approximate stable system centre is used to construct a sliding mode based output tracking controller which can achieve improved transient response at the cost of some tracking accuracy in comparison to the use of the stable system centre. The effectiveness of the proposed approach has been demonstrated considering the position control of a two-wheeled robot and has been found to be promising.

Output Feedback ILC for a Class of Nonminimum Phase Nonlinear Systems With Input Saturation: An Additive-State-Decomposition-Based Method

In this technical note, an additive-state-decomposition-based iterative learning control (ILC) method is proposed. Based on this method, the output feedback ILC problem is solved for a class of nonminimum phase (NMP) nonlinear systems with input saturation. This method is to “additively” decompose the output feedback ILC problem into two more tractable subproblems, namely an output feedback ILC problem for a linear time invariant (LTI) system and a state-feedback stabilization problem for a nonlinear system with input saturation. Then, a controller can be designed for each subproblem separately using existing methods, and the two designed controllers are combined together to achieve the original control goal. An illustrative example demonstrates the effectiveness of the proposed method.

A gradient descent control for output tracking of a class of non-minimum phase nonlinear systems

In this paper we present a new approach to design the input control to track the output of a non-minimum phase nonlinear system. Therefore, a cascade control scheme that combines input–output feedback linearization and gradient descent control method is proposed. Therein, input–outputfeedback linearization forms the inner loop that compensates the nonlinearities in the input–output behavior, and gradient descent control forms the outer loop that is used to stabilize the internal dynamics. Exponential stability of the cascade-control scheme is provided using singular perturbation theory. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed cascade control scheme.

Global Stabilization of a Class of Nonminimum-Phase Nonlinear Systems by Sampled-Data Output Feedback

In this technical note, global asymptotic stabilization by sampled-data output feedback is investigated for a class of nonminimum-phase nonlinear systems. Under a global Lipschitz condition imposing on both zero dynamics (i.e., the so-called driven system) and the driving system, together with a lower-triangular form, we prove that the nonminimum-phase system is globally stabilizable by a sampled-data dynamic output compensator that is composed of a nonlinear observer and a linear controller, both in discrete-time. The sampled-data feature makes the proposed output feedback controller easier for digital implementation.

Observation and output adaptive tracking for a class of nonlinear non-minimum phase systems

ABSTRACTIn this paper, the output tracking problem for a class of systems with unstable zero dynamics is addressed. The state is assumed not measurable. The output of the dynamical system to be controlled has to track a signal, which is the sum of a known number of sinusoids with unknown frequencies, amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviours of the internal dynamics. The proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state; therefore, a nonlinear observer is needed. Due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states, adaptive indirect methods are applied.

Output feedback control of a class of nonminimum-phase nonlinear systems

Summary The problem of global stabilization by output feedback is investigated in this paper for a class of nonminimum-phase nonlinear systems. The system under consideration has a cascade configuration that consists of a driven system known as the inverse dynamics and a driving system. It is proved that although the zero dynamics may be unstable, there is an output feedback controller, globally stabilizing the nonminimum-phase system if both driven and driving systems have a lower-triangular form and satisfy a Lipschitz-like condition, and the inverse dynamics satisfy a stronger version of input-to-state stabilizability condition. A design procedure is provided for the construction of an n-dimensional dynamic output feedback compensator. Examples and simulations are also given to validate the effectiveness of the proposed output feedback controller. Copyright © 2016 John Wiley & Sons, Ltd.

Output-feedback dynamic surface control for a class of nonlinear non-minimum phase systems

In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems. To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let the stability of the internal dynamics depend on that of redefined output, thus we only need to consider the new external dynamics rather than internal dynamics in the process of designing control law. To overcome the explosion of complexity problem in traditional backstepping design, the dynamic surface control (DSC) method is firstly used to deal with the problem of tracking control for the nonlinear non-minimum phase systems. The proposed output-feedback DSC controller not only forces the system output to asymptotically track the desired trajectory, but also drives the unstable internal dynamics to follow its corresponding bounded and causal ideal internal dynamics, which is solved via stable system center method. Simulation results illustrate the validity of the proposed output-feedback DSC controller.

Fuzzy stable inversion-based output tracking for nonlinear non-minimum phase system and application to FAHVs

In this paper, a novel fuzzy stable inversion-based output tracking control for multi-input multi-output (MIMO) nonlinear non-minimum phase system is investigated. By applying input/output linearization, the nonlinear system is transformed into a standard form. By applying T–S fuzzy based non-causal inversion approach, more reliable ideal internal dynamics (IID) of the nonlinear system are obtained. The output tracking problem is transformed into a state tracking one, then the T–S fuzzy model technology, which can get a more practical description than simple linearization, is utilized to approach the complex nonlinearity of the internal dynamics. A fuzzy controller design method is proposed for the constructed T–S fuzzy model. The proposed method can improve the control performance of the stable inversion based method, and can be easily solved by standard numerical algorithms. Moreover, the proposed control scheme is applied to solve the output tracking problem of flexible air-breathing hypersonic vehicles (FAHVs).

Modification of a steepest descent control for output tracking of some class non-minimum phase nonlinear systems

The problem of output tracking for a class of nonlinear systems whose zero dynamics are not necessarily stable is addressed in this paper. To solve the problem, we transform the systems into a normal form which is minimum phase with respect to a virtual output, which is a linear combination of state variables. By applying the modified steepest descent control, the system output track to the desired output.

Repetitive control for TORA benchmark: An additive-state-decomposition-based approach

The repetitive control (RC) or repetitive controller problem for nonminimum phase nonlinear systems is both challenging and practical. In this paper, we consider an RC problem for the translational oscillator with a rotational actuator (TORA), which is a nonminimum phase nonlinear system. The major difficulty is to handle both a nonminimum phase RC problem and a nonlinear problem simultaneously. For such purpose, a new RC design, namely the additive-state-decomposition-based approach, is proposed, by which the nonminimum phase RC problem and the nonlinear problem are separated. This makes RC for the TORA benchmark tractable. To demonstrate the effectiveness of the proposed approach, a numerical simulation is given.

A LMI Approach to Tracking Control of Nonlinear Polynomial Systems

This paper presents a tracking control approach for a class of nonlinear non-minimum phase systems. This control approach is the combination between an input-output feedback linearization technique and a gain scheduling method to obtain a tracking control structure. The latter is mainly based on the Linear Matrix Inequalities method which allows us to estimate and to enlarge the domain of attraction around operating points. The nonlinear system is represented locally by variation polynomial models. The polynomial models are then used to design a family of feedback controllers. We propose a nonlinear gain scheduling procedure for the problem of guaranteed transition from an actual operating point to a desired one along the reference trajectory. The theoretical results are applied to a non-minimum phase continuously stirred tank reactor in order to illustrate the effectiveness of the proposed approach

Fundamental methodologies for control of nonlinear nonminimum-phase systems: An overview

In this article, an overview of principle research works regarding control of nonlinear nonminimum-phase systems is presented. Key concepts of some research of fundamental importance that has been done in this area are discussed. The research is categorized into the five fundamental methodologies, and further work based on particular methodology is also discussed. Limitations of each concept are also highlighted at the end.

Robust adaptive control of flexible link manipulators using multilayer perceptron

This paper presents a robust adaptive control method based on neural networks for flexible link manipulators which is a nonlinear non-minimum phase system. The development of the control method comprises of two steps First, an appropriate reference signal is designed such that the internal dynamic subsystem become input-to-state practical stable. Then an output feedback control, which does not rely on the state estimation, is designed such that the output of system asymptotically tracks this reference signal. This controller is comprised of a dynamic linear controller, an adaptive neural network and a discontinuous robustifying term. Stability of the overall system is proved using the small gain theorem.