Non-minimum Phase Systems Research Articles

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.

Phase response reconstruction for non‐minimum phase systems using frequency‐domain magnitude values

It is often more complicated to measure the phase response of a large system than the magnitude. In that case, one can attempt to use the Kramers-Kronig (KK) relations for magnitude and phase, which relates magnitude and phase analytically. The advantage is that then only the magnitude of the frequency response needs to be measured. We show that the KK relations for magnitude and phase may yield invalid results when the transfer function has zeros located in the right half of the complex s-plane, i.e. the system is non-minimum phase. In this paper we propose a method which enables to determine these zeros, by using specific excitation signals and measuring the resulting time responses of the system. The method is verified using blind tests among the authors. When the locations of the zeros in the right half of the complex s-plane are known, modified KK relations can be successfully applied to non-minimum phase systems. We demonstrate this by computing the phase response of the electric field, excited by a point dipole source inside a closed cavity with Perfect Electrically Conducting (PEC) walls. Also, the effects of simulated measurement noise are considered for this example.

ERIT for Non-Minimum Phase Systems

ERIT for Non-Minimum Phase Systems

A Hysteresis Dynamic Mathematical Model Approach to Parametric Estimation System

The main contribution of this paper is the proposal of a recent hysteresis dynamic model which is successfully employed within a posited signal modulator. The modulation of signals is a commonly required stage in many engineering applications, such as telecommunications, power electronics, and control, among others. In this paper, the effectiveness of a signal modulator based on the well-known Delta modulator when it contains a dynamic hysteresis system within its main structure is presented. To do that, it is resorted to an application of the granted Hysteresis-Delta Modulator. This application consists of including the modulator within an adaptive scheme, since it is well known that the persistent excitation condition is required, for instance, in parameter estimation tasks. Hence, the main functional property of the modulator with hysteresis is its ability of producing a modulated signal with uniform high-frequency content even when its input is not a permanent persistent excitation signal. To highlight the main contribution of this paper, a numerical experiment of a parameter estimation system is developed to compare the performance of the modulator with the proposed hysteresis model and two other previously reported hysteresis systems. That is, three different scenarios have been tested in the parameter estimation of a nonminimum phase system. Finally, the numerical experiments confirm that the proposed hysteresis model along with the modulator provides the best performance as expected.

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.

A novel robust Virtual Reference Feedback Tuning approach for minimum and non-minimum phase systems

In real-world applications, it is often desired that the design of a closed-loop system must attain not only high performance but also robustness. This paper presents a novel robustness-based formulation for control for discrete time minimum and non-minimum phase systems using the Virtual Reference Feedback Tuning (VRFT) framework. The proposed idea is to design robust lower and higher order Proportional Integral and Derivative (PID) controller using Maximum Sensitivity (Ms) based closed-loop reference model by minimization of the VRFT objective function (JVR) The efficacy of the approach is verified on various systems in simulation and also demonstrated on the Temperature Control Process and Level Control Process experimental setups. The proposed VRFT approach provides improved performance and robustness for set point tracking and disturbance rejection. Also, the proposed approach ensures stability and specific robustness of the closed-loop system. Further, the fragility of the controller is investigated for perturbations in the controller parameters.

Robust Queen Bee Assisted Genetic Algorithm (QBGA) Optimized Fractional Order PID (FOPID) Controller for Not Necessarily Minimum Phase Power Converters

Power electronic converters find application in diverse fields due to their high power conversion efficiency. Converters are often characterized by time response specifications, robustness and stability. Conventionally, converters employ the classic PID controller. The state space average linear time invariant model of a boost converter is known to be a non-minimum phase system. This paper demonstrates that the boost converter with a PID controller using the Queen Bee assisted Genetic Algorithm (QBGA) optimization is not robust to plant parameter variations. A fractional order PID controller based on QBGA optimization proposed here is shown to have improved robustness. The controller proposed here is applicable across converters, viz., buck, boost and buck-boost, equally.

초정밀 장비의 진동 저감을 위한 능동형 동조질량감쇠기

In an environment where ultra-high-precision equipment is used, vibration inevitably occurs due to various factors. These vibrations generate fatal effects, such as defect generation and reduced production yield, on ultra-high-precision production equipment. Among the multiple methods for solving vibration problems, a Tuned Mass Damper (TMD) is a useful technique that reduces vibration without changing the existing structure by attaching a passive dynamic system consisting of additional mass, spring, and damper. However, it is difficult to realize fine-tuning of the system parameters for optimal performance because the passive elements have structural limitations. An active TMD, which has a form wherein sensors, actuators, and a control device are added to the passive TMD structure, was introduced. It has higher performance than passive TMD because dynamic characteristics can be induced to stable and highly damped by a well-designed control algorithm realized by software in the control device. In this study, an active TMD was developed utilizing passive TMD with a voice coil actuator and attached to the center of both end fixed beam that assumed a single-degree-of-freedom structure. A dual-loop control algorithm using a non-minimum phase system was designed for a high-damped response while retaining stability. The modal test was performed for experimental evaluation and excellent performance of active TMD was verified.

Online Time Delay and Disturbance Compensation for Linear Non-Minimum Phase Systems

Online Time Delay and Disturbance Compensation for Linear Non-Minimum Phase Systems

Output tracking for a non-minimum phase robotic manipulator

We exploit a recently developed funnel control methodology for linear non-minimum phase systems to design an output error feedback controller for a nonlinear robotic manipulator, which is not minimum phase. We illustrate the novel control design by a numerical case study where we simulate end-effector output tracking of the robotic manipulator.

The Impact of Nonminimum-Phase Zeros on Human-in-the-Loop Control Systems.

We present results from an experiment in which 33 human subjects interact with a dynamic system 40 times over a one-week period. The subjects are divided into three groups. For each interaction, a subject performs a command-following task, where the reference command is the same for all trials and all subjects. However, each group interacts with a different dynamic system, which is represented by a transfer function. The transfer functions have the same poles but different zeros. One has a minimum-phase zero , another has a nonminimum-phase zero , and the last has a slower (i.e., closer to the imaginary axis) nonminimum-phase zero zsn ∈ (0,zn) . The experimental results show that nonminimum-phase zeros tend to make dynamic systems more difficult for humans to learn to control. We use a subsystem identification algorithm to identify the control strategy that each subject uses on each trial. The identification results show that the identified feedforward controllers approximate the inverse dynamics of the system with which the subjects interact better on the last trial than on the first trial. However, the subjects interacting with the minimum-phase system are able to approximate the inverse dynamics in feedforward more accurately than the subjects interacting with the nonminimum-phase system. This observation suggests that nonminimum-phase zeros are an impediment to approximating inverse dynamics in feedforward. Finally, we provide evidence that humans rely on feedforward-step-like-control strategies with systems (e.g., nonminimum-phase systems) for which it is difficult to approximate the inverse dynamics in feedforward.

Iterative Learning Control for a Repetitive 2D Process

To control the systems which operate in a repetitive mode is known to be a difficult task. For example, systems like robotic manipulators are used for doing the repetitive assigned task. This can be overcome by the iterative learning control (ILC) method. In this article, the DC motor model is discussed for controlling the speed of the motor by the design of an ILC algorithm, and its performance is compared with the conventional PID algorithm. The ILC algorithm is implemented for the minimum and non-minimum phase systems. The resulting response, absolute and integral absolute errors are plotted. The Z-N tuning method is used to implement PID control. The performance of the DC motor has been evaluated by comparing the Integral Square Error (ISE), Integral Absolute Error (IAE), and Integral Time Absolute Error (ITAE) with the conventional PID controller.

Improved Hydroturbine Control and Future Prospects of Variable Speed Hydropower Plant

Hydroturbine control system (HTCS) is a nonlinear, nonminimum phase system comprising of speed/frequency sensors, hydraulic servo motors, wicket gates, gate position feedback mechanism, and proportional integral derivative (PID) controller (governor). Governor controls the guide vane opening (GVO) corresponding to the input (speed/frequency). Nowadays, HTCS becomes more intricate insight of variable speed doubly-fed induction generator for compensating wide variation in water head. Hence, robust control techniques are necessary for the optimal utilization of hydropower potential. In this article, a brief review of HTCS is given and a complimentary sliding-mode controller (CSMC) is designed for GVO serving a 250 MW hydrogenerating unit. The CSMC control law is derived and the stability is verified through the Lyapunov function. Simulation is carried out through the MatLab Simulink environment for a 250 MW HTCS. Then, the performance of CSMC for GVO and its influence on the generator characteristics are analyzed and compared with the traditional PID controller. The simulation results demonstrate the efficacy of the controller during the startup process, subsynchronous, and super synchronous mode of operations. It is inferred that the proposed CSMC has three times faster settling time than that of the traditional PID controller. Experimental validation is carried out with a scaled-down laboratory prototype. Furthermore, future scope and design challenges associated with the hydropower control system are illustrated.

Transient analysis of systems exhibiting inverse response and their control with CSTR as a case study

<span>In this paper the phenomenon of inverse response from systems was investigated and its transient response thoroughly analyzed. Inverse response is shown by non-minimum phase systems and some minimum phase systems. Transient analysis of these systems is lacking in literature A case study was done for a non-linear, non-minimum phase CSTR (Continuous Stirred Tank Reactor), which was identified and a novel optimized trajectory for temperature feed was synthesized, which is a non-linear dynamic constrained optimization problem solved using ACADO for a particular chemical reaction. Different control schemes were also implemented on other systems as well, which exibhit inverse responses, including model reference adaptive control. The finding shows that PID-ZN goes with the inverse response, is unable to suppress it and requires large control effort which can have serious hardware limitations. Robustness is another area where PID is lacking with these systems. MRAC shemes were able to overcome all these issues. For CSTR also, these findings hold true thus points at using advance stratigies in process control industries for maximzing product yield.</span>

On the synthesis of a stable and causal compensator for discrete-time high-order repetitive control systems

This paper presents a novel methodology to design a discrete-time compensator for a high-order repetitive control system. An optimization-based approach is applied to design the compensator, which is required to be stable and causal. This methodology is applicable to both minimum and non-minimum phase systems, for which stability and tracking error convergence are ensured. The compensator is yielded in the form of a proper transfer function and can be implemented separately without being merged with a high-order internal model. The high-order internal model is used to provide robustness against period variations of the reference signal. Simulation and experimental results are provided to show the effectiveness of the compensator design methodology.

Static output feedback passivation revisited and global asymptotic stabilizing properties of a controller

SummaryThe class of systems that can be globally asymptotically stabilized by the well‐known control law , is extended, in respect to literature. This control law is suitable for application to systems of unknown structure, and it is shown that it is more advantageous than the linear control law. The stability proof is based on solutions of a newly introduced problem, which is a specialization of the passivation by static output feedback control of a system with nonzero feedforward matrix. Necessary and sufficient conditions for existence of a solution of the problem are given, which include the minimum phase property of the given system. It is explained why the new concept cannot be applied to nonminimum phase systems. It is proved that a class of nonminimum phase systems can be stabilized by the same control law, where is a matrix function, rather than a constant matrix. Illustrative example are given.

Iterative learning approach to active noise control of highly autocorrelated signals with applications to machinery noise

This study describes an iterative learning approach to the active control of machinery noise with high autocorrelation properties. In contrast to typical active noise control solutions, which work by adapting the transfer function of the controller, in the iterative learning control one adapts the control signal itself. Special care was taken to develop a generic solution that can handle different sorts of secondary path models including very long and non-minimum phase finite impulse response filters. To achieve that, the authors used spectral factorisation and exploit the fact that, for non-minimum phase systems, a stable inverse can be constructed if the causality constraint is relaxed and later restored by taking advantage of the periodicity of the attenuated signal. The resulting controller can be efficiently implemented on a sample-to-sample calculation basis. The behaviour and the performance of the proposed scheme are studied using computer simulations and real-world experiments on noises from an electric transformer and functional magnetic resonance imaging device. The proposed solution was also compared to normalised feedforward filtered-X least mean squares algorithm and performed much better in terms of attenuation, convergence, and robustness.

Stable Inversion Based Fault-tolerant Trajectory Tracking Control of Civil Aircrafts Autolanding

This paper deals with aircraft autoland control in the presence of wind disturbances and actuator faults. To solve this problem, a fault-tolerant trajectory tracking controller is presented to autoland a commercial aircraft. Firstly, the dynamics models of the aircraft with faults and winds are built. Secondly, the stable inversion based fault-tolerant autolanding control architecture is proposed. The stable inversion control is used to improve output tracking precision. The H_∞ control is applied for robust stability against uncertainties caused by wind disturbances and the faults. Compare with common fault-tolerant autolanding control, the stable inversion based fault-tolerant autolanding control has more robust capability including stabilizing the non-minimum phase system. Finally, two scenario simulations are carried out for automatic landing control of a large civil aircraft under winds and elevator failures. The results indicate that the proposed stable inversion based fault-tolerant autolanding controller has better tracking performances than those of the stable inversion control and fault-tolerant autolanding control, even in control surface faults and large winds.

U-model enhanced control of non-minimum phase systems

Control of non-minimum phase (NMP) dynamic systems has been a widely and intensively studied challenging topic from its academic research to industrial applications. With the emergence of U-model based control system design, this study presents a new solution in designing such control systems. In technique, different from pole-zero cancellation (i.e. in force of multiplication/division), this study proposes a pulling principle (i.e. in force of summation/subtraction) to relocate zeros and poles through Infinite Impulse Response (IIR) filters, then introduces a U-model based universal control framework with invariant controller plus U-model inverter so that it separates the treatment of NMP issue from stable control system design. By integration of the above techniques, this study presents a systematic procedure to complement those classical approaches in designing NMP control systems. The associated properties and performance are proved analytically and demonstrated numerically (with Matlab simulation of bench test examples). To follow the study, the computational experiment results provide a user-friendly step by step procedure for the readers/users with interest in their ad hoc applications.

Frequency model of an essentially nonlinear steering drive with a digital microcontroller

When designing a stabilization system for highly maneuverable unmanned aerial vehicles (UAVs), one of the relevant tasks is to study the operation of the steering drive in the frequency band corresponding to the flexural vibrations of the UAV body. To ensure the stability of the UAV stabilization system, quite conflicting requirements may be imposed on the dynamic characteristics of the drive. In particular, the requirement for a sharp suppression of the amplitude-frequency characteristic at the frequency of UAV bending vibrations with minimal phase distortions in the control band of the longitudinal and lateral channels of the stabilization system can significantly complicate the task of researching the stability of the UAV motion control system. The article discusses an electric drive prototype with a digital microcontroller, designed for a highly maneuverable UAV. Adaptive algorithms of the digital controller make it possible to provide the necessary phase delays in the control frequency band and at the same time almost completely suppress the harmonic components of the control signals at the frequencies of the bending vibrations of the UAV body. The algorithms are essentially nonlinear in nature and are based on a change in the gain of the direct circuit of the drive depending on the frequency of the input signal, which greatly complicates the calculation of the transfer function of the steering drive for use in the frequency model of the stabilization system. Generally, the steering drive is described by a linear minimum-phase system, presented as a transfer function of one of the typical blocks of the first or second order, but for the specified steering drive with given dynamic characteristics, this approach is untenable. As a result of the study, a method for obtaining a frequency model of the steering drive is proposed, which is implemented as a non-minimum phase system, the main property of which is the independence of the amplitude-frequency and phase-frequency characteristics. In the process of research, the results obtained on the proposed model are compared with the results of experiments on a drive prototype and its complete non-linear time model. The main advantage of the proposed frequency model is a fairly simple description of the steering drive in the frequency domain, convenient for use as part of the frequency model of the stabilization system in the study of problems of ensuring the stability of UAV flight.