Non-minimum Phase Systems Research Articles

Advanced Control Strategies for Rotary Double Inverted Pendulum

This paper presents the stabilization control of the rotational double inverted pendulum system. It is generally a non-linear, non-minimum phase, unstable, and underactuated system of high order. It has some significant real-life applications such as position control, aerospace vehicle control, and robotics. The objective is to determine the control law to the motor’s output torque such that the inverted pendulum motion will be stabilized about a vertical axis and position the rotary arm to a commanded angular position. In this study, multi-PID controllers, Linear-Quadratic Regulator (LQR), and Internal Model Control (IMC) controllers are designed and MATLAB-based simulations are performed to understand and compare the performance of the three control schemes.

Active disturbance rejection control for non-minimum phase systems under plant reconstruction

Active disturbance rejection control (ADRC) for non-minimum phase (NMP) systems is a challenging problem due to the conflict between stability and feedback tuning. The key point on this issue is to avoid heavy feedback tuning for robustness enhancement. We perform plant reconstruction to obtain an explicit expression of internal disturbance, such that it can be reduced by cascade compensation. Then, a new ADRC scheme is developed based on plant reconstruction and the internal stability criterion for ADRC system is derived. The stability conditions provide guidelines on the design of the cascade compensator and disturbance observer. It also indicates that the cascade compensation contributes to the robust stability of NMP systems. Simulation results of two typical NMP systems are provided to show the efficacy of the proposed ADRC scheme. Physical realizability is also demonstrated through experiments on a motion NMP system.

Performance Comparison of Control Strategies for a Variable-Thrust Solid-Propellant Rocket Motor

This paper deals with a performance comparison of the control algorithm for a variable-thrust solid-propellant rocket motor (VTSRM). To do this, we develop a simulation model of a VTSRM considering characteristic changes in the combustor and design control systems for pressure and thrust. We use three types of control algorithms for the pressure control: classical PID control, feedback linearization control, and fuzzy PID control, and two control algorithms for thrust control: classical PID control and fuzzy PID control. Finally, we compare the performance of each control system through a numerical simulation using step responses. Through this work, we check that feedback linearization is better in pressure control, and fuzzy PID control is more appropriate in thrust control. Especially using fuzzy PID control, we can get fast settling with a small undershoot even if the system is a nonminimum phase system.

Generalised model predictive controller design for A DC–DC non‐inverting buck–boost converter optimised with a novel identification technique

An on-line generalised model predictive control (GMPC) strategy is designed and optimised with a novel identification procedure in the presence of different disturbances. The principle of MPC is utilising a discrete-time model of a system to reach the control variables with a prediction over these values, which is followed by computing a cost function for the control aims. Non-inverting buck–boost converter is a non-minimum phase system based on its boost mode, which makes a challenging condition for designing a stable controller. The proposed control technique described in this paper removes the requirement for a system mathematical model adopting a black-box identification method which can decrease the computational burden. Numerous harmful disturbances can affect a DC–DC converter; thus, the GMPC scheme is used along with a novel improved exponential regressive least identification algorithm as an adaptive strategy for the controller to optimise the gains of the controller in an on-line way resulting in better disturbance rejection. A PID controller with particle swarm optimisation algorithm is designed for this converter to be compared with the GMPC controller. Finally, the efficiency of the GMPC is verified in various performances with experimental and simulation results.

Nonlinearity compensation based robust tracking control of nonlinear nonminimum phase hypersonic flight vehicles

This paper introduces a nonlinearity compensation based robust tracking controller for hypersonic flight vehicles. The controller focuses on robust control design with respect to the nonminimum phase feature and system uncertainties for the control-oriented model. Firstly, following the principle of decomposing the complex control problem into two simpler problems, the original robust tracking problem for nonlinear nonminimum phase hypersonic flight vehicles is decomposed into a simpler robust tracking problem for a linear nonminimum phase system with disturbances and a stabilization problem for a nonlinear system without disturbances. After the problem decomposition, a proportional–integral tracking controller and a feedback linearization controller are designed for the linear system and the nonlinear system, respectively. Then, the addition of the two designed controllers gives the final controller. By compensating for the system nonlinearity using the secondary system and its controller, the proposed control method can satisfy the robust tracking control requirements for nonlinear nonminimum phase hypersonic flight vehicles. The simulation results show, compared with a feedback linearization control method and a composite neural learning control method, the proposed method has superior tracking accuracy and robustness against system uncertainties and external disturbances.

Self‐tuning regulator adaptive controller design for DC‐DC boost converter with a novel robust improved identification method

The design of a self-tuning regulator adaptive controller is presented for Boost converter using Pulse Width Modulation, which has been improved in dynamic with a novel Robust Improved Exponential Regressive Least Square identification scheme. Regarding the negative influences of harmful disturbances on the converters, the Minimum Degree Pole Placement technique is designed using an adaptive mechanism with an online identification technique, which is simple in structure and can provide more accurate parametric estimation and better efficiency in challenging situations, particularly against noise. Based on the right half-plane zero structure of the Boost converter, the open-loop system is called a non-minimum phase system which creates some challenging constraints for the controller design. The primary objective of designing a feedback loop controller is to ensure the stability of the system and appropriate regulation within a pre-determined range of operating conditions. This controller considers the system as a black-box structure; thus, the mathematical model of the system is not needed. This benefit can decrease the computational burden, and provides faster dynamics along with ease of implementation. Finally, the strength of this control strategy is tested by experimental and simulation results in different conditions.

Model error compensator design for continuous- and discrete-time non-minimum phase systems with polytopic-type uncertainties

Model error compensator design for continuous- and discrete-time non-minimum phase systems with polytopic-type uncertainties

Modified optimal series cascade control for non-minimum phase system

Abstract This article contributes to handling the Non-Minimum Phase (NMP) system with time delay in the existence of uncertainty and disturbances. The series cascade control scheme is used to overcome such problems. The secondary loop architecture in a series cascade scheme is formulated in the Internal Model Control (IMC) framework. The tuning of fractional-filter via a delayed version of Bodes’ ideal transfer function approach of primary loop controller in a series cascade arrangement shows the novelty of this work. The primary loop controller is designed in the IMC framework after accountability of inverse response and dead-time compensator. Furthermore, Particle Swarm Optimization (PSO) is adapted to accomplish the optimal value of controller settings. The Riemann sheet principle is used to determine stability. The sensitivity investigation is performed to know the robustness of the offered controller. For the effectiveness of the suggested scheme, two case studies are revealed in this paper.

Applicability analysis of extended state observer-based control for systems subject to parametric disturbances

This paper discusses the applicability of Extended State Observer (ESO)-based control when systems are subjected to different types of parametric disturbances. The applicability is analyzed by establishing the characteristic polynomial of the closed-loop system. It is found that High-Bandwidth ESO-based control is beneficial to the elimination of state-parameter disturbances, but it has a negative impact on the elimination of input-parameter disturbances. In spite of this, the ESO-based control with suitable bandwidth can still be applied to systems which are subject to input-parameter disturbances. A Full-Order ESO-based control scheme is proposed so that disturbance rejection-based control is realized for a class of non-minimum phase systems. Numerical simulations are carried out to verify the correctness of the conclusions and the effectiveness of the proposed controller.

Improved PID controller design for an unstable second order plus time delay non-minimum phase systems

Principally the fundamental limitations for achieving better control performance is caused due to the existence of positive zeros. This study proposes a method to stabilize the unstable non-minimum phase Second Order Plus Time Delay (SOPTD) process. It adopts the Taylor series expansion to produce the equal order of numerator and denominator for the closed loop transfer function. The coefficient of corresponding powers of s, s2 and s3 in numerators are equated to α, β, γ times of the denominator and solved for PID controller setting using multi-objective optimization problems. The stability of the controller is then analysed by minimizing the Integral Time weighted Absolute Error (ITAE) and maximum sensitivity function using MATLAB solvers. The observations from various simulation studies clearly suggests that the proposed method provides significant superior responses when compared with the methods reported.

High-performance control of fast tool servos with robust disturbance observer and modified [formula omitted] control

Fast tool servo (FTS) is an effective technique for the generation of complicated surfaces in modern precision manufacture industry. In this paper, a novel three-degree-of-freedom (3-DOF) control scheme is proposed for the FTS to achieve good tracking and disturbance rejection performance. Specifically, the 3-DOF control scheme contains a hysteresis compensation term, a modified H∞ feedback control term, a robust disturbance observer (RDOB) term and a feedforward control term. Firstly, a hysteresis compensator is developed based on the modified Prandtl–Ishlinskii (MPI) model to eliminate the intrinsic hysteresis nonlinearity so as to identify the linear dynamic model of the FTS system. A modified mixed-sensitivity-based H∞ feedback control is then proposed to simultaneously provide an excellent damping and tracking performance with a deliberately designed input weighting function. A RDOB is designed for non-minimum phase (NMP) system based on all-pass factorization of the linear dynamics model and the standard H∞ control framework to compensate uncertain external disturbances as well as unmodeled dynamics while guaranteeing the robust stability of closed-loop system. To remove phase delay and enlarge control bandwidth, a closed-loop-inversion feedforward controller is synthesized by integrating a zero-phase error tracking control (ZPETC) with a finite impulse response (FIR) filter. A series of comparative experiments are conducted on a self-developed flux-biased normal-stressed electromagnetic actuated FTS. The experimental results consistently validate the effectiveness and superiority of the proposed scheme in terms of outstanding tracking performance and disturbance rejection.

Performance, robustness and noise amplification trade-offs in Disturbance Observer Control design

In this work, we propose a Disturbance Observer (DOB) with a low pass filter with a single tuning parameter. The DOB can be added to a standard PI controller that is assumed to be controlling the system. Our DOB design can be applied to delayed and non-minimum phase systems and is decoupled from the PI control design. We analyse the impact of the DOB filter time constant in disturbance rejection performance, closed loop robustness and measurement noise amplification. The case of First Order plus Time Delay has been studied leading to a set of figures that highlight the trade-offs between those factors and can guide the designer. For arbitrary systems we propose simple rules and instructions for tuning the single parameter of the DOB, taking into account the trade-off between performance, robustness and noise amplification. Finally, we test our proposal experimentally in a real two-tank system setup.

Integrated design of adaptive fault-tolerant control for non-minimum phase hypersonic flight vehicle system with input saturation and state constraints

In this paper, for the six-degree-of-freedom (six-DOF) model of hypersonic flight vehicle (HFV) subject to actuator faults, state constraints, parametric uncertainties, and external disturbances, an adaptive fault tolerant control (FTC) scheme is proposed based on barrier Lyapunov functions (BLFs). The study is begun with a series of control-oriented manipulations: at first, due to the high complexity of the six-DOF model, the corresponding simplified model is proposed under reasonable assumptions; then, through the stability analysis of the internal dynamics, we can conclude that the vehicle model is a non-minimum phase system, namely, having unacceptable zero-dynamics. In order to solve the non-minimum phase problem, the elevator-to-lift coupling term is regarded as uncertainty of the model. Subsequently, in consideration of the insufficient control torque caused by the fault of the rudder or elevators, an adaptive fault-tolerant controller is designed based on BLFs, backstepping method, and Nussbaum gains. In the control law, the uncertain parameters are replaced by their estimates updated by adaptive laws. And the angle of attack and the roll angle of the aircraft are constrained in the preset range. Additionally, the convergence of the proposed FTC algorithm and the boundedness of all the signals of the closed system is proved by Lyapunov stability theory. At last, the numerical simulation results of the six-DOF model are carried out to manifest the effective tracking performance of the proposed FTC scheme.

Analysis of a Cart-Inverted Pendulum System with Harmonic Disturbances Based on its Criterion Matrix

The control of an inverted pendulum is a classical benchmark control problem. Its dynamics resemble that of many real-world systems of interest like pendulous, missile launchers, segways, and many more. The control of this system is challenging as it is a highly unstable, highly non-linear, non-minimum phase system, and underactuated. Furthermore, the physical constraints on the track position also pose complexity in its control design. A great deal of nonlinearity is present inherently and as well as affected by the surrounding external disturbances. The paper presents an approach for analysis of a cart-inverted pendulum system with harmonic disturbances. The approach is based on the index of the criterion matrix of the system named a degeneration factor. The degeneration factor is constructed with the singular values of the criterion matrix of the system and allows us to find frequency range, where the system operates as a whole. A linear-quadratic regulator is used to control the cart-inverted pendulum system. The results are supported with an example.

Discrete sliding mode control with optimal generalized sliding function for non-minimum phase system

Discrete sliding mode control with classical sliding function for the input–output representation is not applicable in non-minimum phase systems, due to the presence of unstable zero. In fact, the presence of the unstable zero risks deteriorating or saturating the control law. In order to surmount this problem, a new discrete generalized sliding mode controller for non-minimum phase systems is proposed with a new sliding function called discrete generalized sliding function. Here, the determination of optimal coefficients of the discrete generalized sliding function is proposed in terms of linear matrix inequalities. Using the proposed method, a discrete generalized sliding mode control for non-minimum phase systems with input–output model is presented and compared with the discrete generalized sliding mode controller using the pole placement method. An illustrative example verifies the effectiveness of the proposed technique.

Research on Cascaded Single Phase PFC Based on Predictive PI Control

In order to improve the charging speed and reduce the occupied volume of an electric vehicle charger, a single-phase boost power factor corrector (PFC) system with cascade CHB (cascaded H-bridge) topology was adopted. Due to the periodic fluctuation of single-phase AC input, there is a large double power frequency ripple component in the output voltage of an AC-DC converter. When capacitor voltage is used as output for feedback control, the control system has the characteristics of a non-minimum phase system. In light of these factors that affect the dynamic stability of the system, a control method is proposed to improve the dynamic characteristics of the system without affecting its steady-state performance. The predictive PI control strategy was adopted to predict the error input signal of the lag process to attenuate the jitter in the control system and improve the dynamic performance and anti-interference of the system. Finally, the feasibility of the scheme was verified by experiments.

Suboptimal output consensus of a group of discrete-time heterogeneous linear non-minimum phase systems

This paper formulates the suboptimal output consensus problem for a discrete-time heterogeneous linear multi-agent system with unstable zero dynamics, where each agent possesses its own objective function and the sum of all these private objective functions, called the overall objective function, is to be minimized. Mild assumptions on the communication topology and the agent dynamics are made under which a parameterized distributed consensus protocol based on low gain feedback is proposed for each agent. The multi-agent system is shown to achieve suboptimal output consensus under the proposed protocols in the sense that the states of all agents remain bounded while their outputs converge to a pre-specified arbitrarily small neighborhood of the optimal point as long as the design parameter is chosen small enough. Simulation results are presented that demonstrate the proposed design.

Nonlinear control of the boost converter subject to unknown constant power load and parasitics

ABSTRACT A robust adaptive controller is developed to regulate the output voltage of the boost converter feeding an unknown constant power load (CPL) and subject to unknown parasitic parameters. The boost converter is a non-minimum phase system that is very prone to the destabilising effects of the negative incremental resistance of the CPL and presents a major challenge in the design of stabilising controllers. An adaptive controller is developed to tightly regulate the output voltage of the converter despite large load variations, parasitic elements in the converter parameters and instability effects induced by the CPL. A systematic procedure is developed to select the adaptive controller gains to achieve a satisfactory output response. Using simulation, the effectiveness of the proposed controller is validated and compared to a recent robust nonlinear controller.

Analysis of Non-Minimum Phase System for AC/DC Battery Charger Power Factor Correction Converter

Electric mobility is nowadays one of the more important trends regarding pollution reduction and global warming due to fuel consumption. Big efforts are done in order to develop efficient and reliable power electronic systems for electric vehicles. In two stage on board-battery chargers, one way of improving efficiency is by means of ensuring the DC-DC isolated converter always operates in the nominal input/output voltage ratio, that could be achieved with a variable DC-link operation. In this paper, a four-switch buck-boost based AC/DC converter is deeply analyzed in order to improve its dynamic performance, the power factor and the total harmonic distortion. The converter suffers from a non-minimum phase characteristic in different input–output transfer functions, which reduces the closed-loop bandwidth of the system. Therefore, after a deep converter analysis has been done, different solutions have been evaluated and tested. Finally, a control to different output transfer functions of the converter become minimum phase, which allows us to increase the system bandwidth and, consequently, high power factor, low harmonics distortion, single control structure and fast dynamics for wide output voltage range are achieved.

Control of non-minimum phase system using inverse response compensator with different approximations

Control of non-minimum phase system using inverse response compensator with different approximations