Minimum Phase Systems Research Articles

Design of a Multi-loop PI Controller for Minimum Phase System Level Regulation in a Quadruple Tank: A Method for Constraint Optimization

Design of a Multi-loop PI Controller for Minimum Phase System Level Regulation in a Quadruple Tank: A Method for Constraint Optimization

Improving Robotic Milling Performance through Active Damping of Low-Frequency Structural Modes

Industrial robots are increasingly prevalent due to their large workspace and cost-effectiveness. However, their limited static and dynamic stiffness can lead to issues like mode coupling chatter and regenerative chatter in robotic milling processes, even at shallow cutting depths. These problems significantly impact performance, product quality, tool longevity, and can damage robot components. An active inertial actuator was deployed at the milling spindle to enhance dynamic stiffness and suppress low-frequency vibrations effectively. It was identified that the characteristics of the actuator change with its mounting orientation, a common scenario in robotic machining processes. This variation has not been reported in the literature. Our study includes the identification of model parameters for the actuator in both horizontal and vertical mountings. Additionally, the novelty of the present work lies in the specific design and implementation of compensation filters tailored for the active inertial actuator in both horizontal and vertical configurations. These filters address the unique challenges posed by low-frequency vibrations in robotic milling, offering significant improvements in dynamic stiffness and vibration suppression. Traditional model-based compensators were effective for vertical mounting, while pole-zero placement techniques with minimum phase systems were optimal for horizontal mounting. These compensators significantly enhanced dynamic stiffness, reducing maximum low-frequency robot structural modes by approximately 100% in horizontal mounting and approximately 214% in the vertical configuration of the actuator. This advancement promises to enhance industrial robot capabilities across diverse machining applications.

Robust output regulation of a class of uncertain nonlinear minimum phase systems perturbed by unknown external disturbances

This paper addresses the problem of robust output regulation for uncertain nonlinear minimum phase systems affected by an unknown external disturbance. We present a novel unknown input observer (UIO)-embedded high-gain stabilizer to completely reconstruct the disturbance in a finite time. A new saturation function is introduced to prevent finite time escape of the closed-loop trajectories. This allows us to achieve a semi-globally exponential regulation of the regulated output. The proposed method features the exact cancellation rather than approximate cancellation, for both structured and/or unstructured external disturbance. The presented controller is finite-dimensional and does not require the nominal model of the plant. Finally, a numerical experiment is conducted to demonstrate the effectiveness of the proposed method.

Experimental validation for the combination of funnel control with a feedforward control strategy

AbstractCurrent engineering design trends, such as lightweight machines and human–machine interaction, often lead to underactuated systems. Output trajectory tracking of such systems is a challenging control problem. Here, we use a two-design-degree of freedom control approach by combining funnel feedback control with feedforward control based on servo-constraints. We present experimental results to verify the approach and demonstrate that the addition of a feedforward controller mitigates drawbacks of the funnel controller. We also present new experimental results for the real-time implementation of a feedforward controller based on servo-constraints on a minimum phase system.

Robust cascade controller design for discrete minimum phase system using a novel data-driven virtual reference feedback tuning approach

Robust cascade controller design for discrete minimum phase system using a novel data-driven virtual reference feedback tuning approach

Robust cascade controller design for discrete minimum phase system using a novel data-driven virtual reference feedback tuning approach

Robust cascade controller design for discrete minimum phase system using a novel data-driven virtual reference feedback tuning approach

A Model-Following Control Approach to Peaking Attenuation in High-Gain Partial State Feedback for Nonlinear Systems

We consider the model-following control (MFC) scheme for a class of nonlinear minimumphase systems in Byrnes-Isidori form using the nonlinear model in the model control loop (MCL). For the control design we apply partial state feedback in the process control loop (PCL). In particular we consider a high-gain feedback of the external state in the PCL to stabilise the system globally. For the proposed MFC design the typical peaking phenomenon of the high-gain feedback can be overcome if a sufficiently accurate estimate of the initial process state is available. We further establish that the control effort of the proposed MFC design is guaranteed less than that of a comparable stabilising high-gain design using a single-loop feedback only. We demonstrate the design capability of peaking attenuation by a numerical example.

A novel output redefinition method for nonlinear H∞attitude stabilization of a flexible spacecraft

AbstractThis paper addresses a novel output redefinition method for the nonlinear attitude stabilization problem of a flexible spacecraft. As an idea, the flexible appendage tip‐point can be selected as attitude output which may improve attitude pointing accuracy. However, it makes the system non‐minimum phase. The output redefinition method is an effective method to make the system minimum phase. In this paper, a novel output redefinition is proposed to overcome the non‐minimum phase property such that it improves the attitude control system performance. Then, a nonlinear controller is designed based on back‐stepping approach and a modal observer. The simulation results show the effectiveness of the proposed method in the presence of model uncertainties and environmental disturbances.

Global state regulation of time-delay minimum-phase systems by delay-free dynamic compensation

This paper studies the global control problem, in the sense of “almost stabilization” or state regulation, for a class of time-delay minimum-phase nonlinear systems via delay-free dynamic compensation. Both dynamic state and output feedback control schemes are developed. By taking advantage of dynamic rather than static feedback, we design delay-independent dynamic state and output feedback compensators, respectively, to achieve asymptotic state regulation with global stability. In the case of dynamic state feedback, a structural condition is imposed on the inverse dynamics that are nonlinear yet imply linear zero dynamics. In the case of dynamic output feedback, more strict conditions on the nonlinearity are characterized to guarantee the existence of a dynamic output controller. In both cases, it is proved by the Lyapunov–Krasovskii functional method, combined with the Barbalat’s lemma, that all the states of the time-delay minimum-phase systems are regulated to zero and boundedness of the closed-loop system is ensured. Two examples are given to validate the proposed delay-free dynamic compensators.

Funnel control of linear systems with arbitrary relative degree under output measurement losses

Abstract We consider tracking control of linear minimum phase systems with known arbitrary relative degree which are subject to possible output measurement losses. We provide a control law which guarantees the evolution of the tracking error within a (shifted) prescribed performance funnel whenever the output signal is available. The result requires a maximal duration of measurement losses and a minimal time of measurement availability, which both strongly depend on the internal dynamics of the system, and are derived explicitly. The controller is illustrated by a simulation of a mass-on-car system.

High-Precision Control of Industrial Robot Manipulator Based on Extended Flexible Joint Model

High-precision industrial manipulators are essential components in advanced manufacturing. Model-based feedforward is the key to realizing the high-precision control of industrial robot manipulators. However, traditional feedforward control approaches are based on rigid models or flexible joint models which neglect the elasticities out of the rotational directions and degrade the setpoint precision significantly. To eliminate the effects of elasticities in all directions, a high-precision setpoint feedforward control method is proposed based on the output redefinition of the extended flexible joint model (EFJM). First, the flexible industrial robots are modeled by the EFJM to describe the elasticities in joint rotational directions and out of the rotational directions. Second, the nonminimum-phase EFJM is transformed into a minimum-phase system by using output redefinition. Third, the setpoint control task is transformed from Cartesian space into joint space by trajectory planning based on the EFJM. Third, a universal recursive algorithm is designed to compute the feedforward torque based on the EFJM. Moreover, the computational performance is improved. By compensating the pose errors caused by elasticities in all directions, the proposed method can effectively improve the setpoint control precision. The effectiveness of the proposed method is illustrated by simulation and experimental studies. The experimental results show that the proposed method reduces position errors by more than 65% and the orientation errors by more than 62%.

Sliding mode control design using generalized relative degree approach: Aerospace application

Relative degree (RD) approach is a powerful tool for obtaining system's input-output dynamics used for output tracking controller designs of minimum phase systems. Designs using the RD alone can fail due both to insufficient control authority in minimum phase systems, and instability of internal/zero dynamics attributed to nonminimum phase systems. A novel definition and a concept of Practical Generalized RD (PGRD) are proposed in this paper and are used in concert with Sliding Mode Control (SMC) to compensate for system perturbations in minimum phase systems. The use of known Generalized Relative Degree (GRD) in nonminimum phase systems allows for the elimination of internal dynamics. However, instability that emerges in the corresponding control dynamic extension is defeating any output tracking controller design. A novel methodology of using GRD for designing continuous SMC in nonminimum phase systems is presented. An algorithm for generating a bounded solution of the unstable dynamic extension is proposed and used in concert with SMC, allowing robust control design for nonminimum phase systems. The efficacy of the proposed GRD-based approaches is demonstrated on a minimum and nonminimum phase rocket attitude control problem both analytically and via simulation.

PI Stabilizing Control of Nonaffine MIMO Systems by Additive-State-Decomposition Dynamic Inversion Design

This paper addresses the stabilizing control issue for a class of non-affine MIMO (Multiple Input Multiple Output) nonlinear systems subject to time-varying disturbance using an additive-state-decomposition dynamic inversion control scheme. First, the original system is transformed into a minimum phase system through a proposed output redefinition method. Then, the transformed minimum-phase system is further additively decomposed into a primary subsystem and a secondary subsystem. Next, the dynamic inversion control scheme solves the non-affine control problem. Stability analysis shows that the proposed control method guarantees all closed-loop system signals being semi-globally uniformly ultimately bounded. Finally, a simulation and an attitude control experiment of a quadcopter show the effectiveness of the proposed control method.

Closed-loop load vectors for structural damage localization

The null vectors of a rank-deficient transfer matrix perturbation contain information on the spatial distribution of the perturbation. This property constitutes the basis of the well-established Dynamic Damage-Locating Vector (DDLV) method, which facilitates localization of stiffness-related damage in dynamical systems. The DDLV method operates by applying the null vectors of the transfer matrix perturbation – now referred to as DDLVs – as loads to the considered system, whereby damage will be confined to the subdomain exhibiting rigid-body motion in steady state. In real systems, where disturbances will render the transfer matrix perturbation non-singular, the DDLVs must be extracted from a quasi-null space, and this will impair the contrast between undamaged and damaged subdomains. The present paper proposes a closed-loop formulation of the DDLV method to enhance the localization robustness by improving the conditioning of the linear map that infers the damage location. The closed-loop formulation, which is feasible for minimum-phase systems where open-loop input–output data can be collected prior and posterior to damage formation, is implemented virtually and does not, therefore, impose any practical overhead on the original DDLV method. Numerical examples demonstrate how the proposed closed-loop formulation can lead to significant damage localization improvement compared to the original method.

Settling Angle-Based Stability Criterion for Power-Electronics-Dominated Power Systems

Impedance-based analysis methods are widely applied to the small-signal stability analysis of grid-connected converters. As the initial step to carry out the impedance-based stability analysis, it is critical to select whether to represent the converter as a Norton or Thevenin equivalent circuit. However, there is lack of definition on the representation of converters, and inappropriately selected impedance model choice leads to improper stability analysis. Moreover, existing impedance-based stability analysis methods, e.g., return-ratio matrix (RRM)-based method, only apply to minimum phase systems where the RRM does not contain right-half-plane poles. In complex and power-electronics-dominated power systems, interactions between multiple converters lead to nonminimum phase power systems, where current methods can no longer be directly applied. To address these problems, a stability criterion is proposed by introducing the concept of settling angle. As the main contribution of this article, the settling angle of total admittance is proven as the intrinsic hallmark of power systems and directly reflects the system stability. The proposed settling-angle-based stability criterion is validated by control hardware-in-the-loop experimental results for a three-terminal system that integrates grid-forming and grid-following converters through a common bus.

Performance Improvement of an NMP Mini Segway Using Sample and Hold Inputs

Early analytical work showed that it is possible to discretize a continuous-time non-minimum phase (NMP) system using special sample and hold inputs (SHIs) and obtain a discrete-time minimum phase (MP) system with a higher sampling rate than that of conventional zero-order sample and hold. As a result, high-gain discrete-time control law can be used to further improve closed-loop system performance since the resulting discrete-time system is MP. In this paper, this technique is adopted for performance improvement on a mini-Segway (MS), a developed robot equipped with an extremely low-cost microcontroller (Arduino). A dual-loop control tuning method was developed to optimize the overall closed-loop system performance. The system performance improvement is demonstrated by the reduction of the mini-Segway oscillation magnitude under idle conditions. The experimental results show that the low-cost microcontroller can be used for the dual-loop SHI control scheme, and the MS cart displacement oscillation magnitude is significantly reduced by more than 65% over the baseline controller. The main contribution of this paper is implementing the proposed sample and hold input (SHI) scheme into an extremely low-cost micro-controller (Arduino) and demonstrating that low-cost microcontrollers can effectively utilize the proposed SHI.

Trajectory-tracking control from a multibody system dynamics perspective

The development of modern mechatronic systems is often driven by the desire for more efficiency and accuracy. These requirements not only result in more complex system designs, but also in the simultaneous development of improved control strategies. Therefore, control of multibody systems is an active field of research. This contribution gives an overview of recent control-related research from the perspective of the multibody dynamics community. A literature review of the research activity in the journal Multibody System Dynamics is given. Afterwards, the framework of servo-constraints is reviewed, since it is a powerful tool for the computation of a feedforward controller and it is directly developed in the multibody system dynamics community. Thereby, solution strategies for all possible system types, such as differentially flat systems, minimum phase and non-minimum phase systems are discussed. Selected experimental and simulation results are shown to support the theoretical results.

Transmission synchronization of multiple memristor chaotic circuits via single input controller and its application in secure communication

This article mainly studied the transmission synchronization of multiple memristor chaotic circuits by using a single input controller strategy. For transmission synchronization model, the definition of synchronization is established, and based on the stability of minimum phase system, the sufficient conditions of system stability are obtained to ensure that the system error curves of multiple memristor chaotic circuits can maintain asymptotical synchronization. Furthermore, the results of synchronization circuit experiment illustrate that the designed controller works well for the synchronization of multiple memristor chaotic circuits. Finally, the results of secure communication experiment based on transmission synchronization show that the scheme is feasible.

Generalized Relative Degree Approach to Sliding Mode Control Design for Nonminimum Phase Systems

The relative degree (RD) approach is a powerful tool for obtaining system's input-output dynamics used for output tracking controller designs of minimum phase systems. Designs based on the RD approach alone may fail due to instability of internal dynamics attributed to nonminimum phase systems. The use of generalized relative degree allows for the elimination of internal dynamics via replacing it by the unstable dynamic extension. An algorithm for generating a bounded solution of this unstable dynamic extension is proposed, allowing for a sliding mode controller (SMC) design for nonminimum phase systems. The efficacy of the proposed approach is demonstrated on a nonminimum phase rocket attitude control problem analytically and via simulations.

Robust Output Regulation for Uncertain Linear Minimum Phase Systems under Unknown Control Direction⋆

This paper investigates the problem of disturbance rejection for SISO uncertain linear minimum phase systems perturbed by an unmeasurable external disturbance under the framework of robust output regulation. The model parameters of systems in question are largely uncertain, including the control direction. In addition, the external disturbance is unstructured but bounded. Towards this end, a novel Unknown Input Observer (UIO)-based regulator is developed to reject the external disturbance, and a switching mechanism with a monitor function is designed to handle the control direction uncertainty. Notable features are that the unstructured external disturbance can be directly estimated and completely rejected by a sliding mode-based observer, and this new scheme can be applied for systems with non-unity relative degree under unknown control direction. The boundedness of closed-loop system and its asymptotic convergence properties are rigorously proved, which is verified by a numerical example.