Disturbance Rejection Through an External Model for Nonminimum Phase Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 39-44 ◽  
Author(s):  
Wei-Chi Yang ◽  
Masayoshi Tomizuka
Keyword(s):  
External Disturbance ◽  
Phase System ◽  
Control Input ◽  
External Disturbances ◽  
Nonminimum Phase ◽  
Nonminimum Phase Systems ◽  
External Model ◽  
Feedforward Controller ◽  
The Stability ◽  
Adaptive Feedforward

This paper considers the use of an external model for the cancellation of disturbances in a nonminimum phase system where disturbances can be regarded as the output of a stable (in the sense of Lyapunov) autonomous system. It is assumed that the parameters in the nonminimum phase system are unknown, but the orders of the numerator and denominator polynomials, and the delay steps are known. External model method is a kind of adaptive feedforward controller that the control input is the function of estimated external disturbance. In order to cancel the effect of disturbances, we use two consecutive recursive parameter identification algorithms to estimate external disturbances. The stability of the closed-loop system is proved.

Pseudo-Causal Tracking Control of a Nonminimum Phase System

2009 ◽  
Author(s):  
Pengfei Wang ◽  
M. Necip Sahinkaya ◽  
Sam Akehurst
Keyword(s):  
Transfer Function ◽  
Test Facility ◽  
Phase System ◽  
Hardware In The Loop ◽  
Nonminimum Phase ◽  
Software Models ◽  
Continuously Variable Transmissions ◽  
Future Value ◽  
Novel Method ◽  
Feedforward Controller

A novel method is described to implement noncausal feedforward compensators causally, i.e. without requiring any future value of the reference input trajectory. A hardware-in-the loop test facility developed for continuously variable transmissions is utilized in this paper. The test facility includes two induction motors to emulate engine and vehicle characteristics. Software models of an engine and vehicle, running in real-time, provide reference torque and speed signals for the motors, which are connected to a transmission that is the hardware in the loop. Speed control of the output motor that emulates the vehicle dynamics is used to demonstrate an application of the proposed technique. A feedforward compensator, based on transfer function inversion, is used to compensate for the nonminimum phase motor and drive system dynamics. The vehicle model cannot be run ahead of time to provide the future values required by the noncausal inversion technique because it requires the current torque at the output of the transmission. Therefore, the feedforward controller has to be applied causally. A frequency domain estimation technique and a multi-frequency test signal are utilized to estimate, within the frequency range of interest, a low relative order transfer function of the closed loop system incorporating a manually added delay in the feedback loop. A noncausal feedforward controller is designed for the delayed output of the system based on the identified transfer function. It has been shown experimentally that this compensator offers excellent tracking performance of the motor when subjected a multi-frequency speed demand signal.

Concurrent Design of Continuous Zero Phase Error Tracking Controller and Sinusoidal Trajectory for Improved Tracking Control

1998 ◽  
Vol 123 (1) ◽  
pp. 127-129 ◽  
Author(s):  
Hyung-Soon Park ◽  
Pyung Hun Chang ◽  
Doo Yong Lee
Keyword(s):  
Continuous Time ◽  
Phase Error ◽  
Phase System ◽  
Pass Filter ◽  
Nonminimum Phase ◽  
Tracking Controller ◽  
Feedforward Controller ◽  
Gain Errors ◽  
High Pass ◽  
Zero Phase

A trajectory control strategy for a nonminimum phase system is proposed. A continuous-time version of the Zero Phase Error Tracking Controller (ZPETC), which is a well-known discrete-time feedforward controller, is considered. In the continuous-time case, the overall transfer function consisting of the ZPETC and the closed-loop plant exhibits high-pass filter characteristics. This introduces serious gain errors between the desired and actual output if the desired output is made directly as the ZPETC’s input. This paper proposes the use of a specially designed sinusoidal trajectory to compensate for the gain errors. The sinusoidal trajectory imparts a synergic effect to tracking performance when combined with the continuous ZPETC. Continuous ZPETC with sinusoidal trajectory is evaluated successfully by applying to a nonminimum phase plant, single link flexible arm.

Precision Tracking Control of Discrete Time Nonminimum-Phase Systems

1993 ◽  
Vol 115 (2A) ◽  
pp. 238-245 ◽  
Author(s):  
Chia-Hsiang Menq ◽  
Jin-jae Chen
Keyword(s):  
Discrete Time ◽  
Tracking Control ◽  
Tracking Performance ◽  
Nonminimum Phase ◽  
Nonminimum Phase Systems ◽  
Control Scheme ◽  
Feedforward Controller ◽  
Precision Tracking ◽  
Phase Systems ◽  
Precision Tracking Control

In this paper, a precision tracking control scheme for linear discrete time nonminimum-phase systems is proposed. This control scheme consists of a preview filter, a tracking-performance filter, a command feedforward controller, and a feedback controller. A command feedforward controller, whose design is based on the minimal order inverse model of the plant being controlled, will result in a completely decoupled system. The preview filter is introduced to compensate the phase and gain errors induced by the nonminimum phase zeros or lightly damped zeros of the system. Using the command feedforward controller along with the proposed preview filter, the tracking performance of the proposed control scheme can be characterized by the frequency response of the tracking-performance filter. For the design of the preview filter, a generalized Nth order preview filter and its associated penalty function that quantifies the tracking error of a design are defined. It is shown that, given the desired bandwidth and the order of the preview filter, the optimal solution for the design of the preview filter can be obtained explicitly. The proposed control scheme together with the optimal preview filter is shown to be very effective in achieving precision tracking control of discrete time MIMO nonminimum phase systems. It is also shown that the tracking performance is improved as the order N of the preview filter is increased.

Preview-Based Output Tracking of Nonminimum-Phase Linear Systems via Trajectory Decomposition: Nanomanipulation Example

2010 ◽  
Author(s):  
Haiming Wang ◽  
Kyongsoo Kim ◽  
Qingze Zou ◽  
Hongbing Xu
Keyword(s):  
Control Technique ◽  
Control Input ◽  
Nonminimum Phase ◽  
Output Tracking ◽  
Actuation Time ◽  
Stable Inversion ◽  
Inversion Technique ◽  
Nonminimum Phase Systems ◽  
Phase Systems ◽  
Trajectory Decomposition

In this article, a trajectory-decomposition-based approach to output tracking with preview for nonminimum-phase systems is proposed. When there exists a finite (in time) preview of the future desired trajectory, precision output tracking of nonminimum-phase systems can be achieved by using the preview-based stable-inversion technique. The preview-based stable-inversion technique has been successfully implemented in various high-speed positioning applications. The performance of this approach, however, can become sensitive to system dynamics uncertainty. Moreover, the computation involved in the implementation of this approach can be demanding. In the proposed approach, such preview-based inversion related challenges are addressed by integrating the notion of signal decomposition and the iterative learning control technique together. Particularly, a library of desired output elements and their corresponding control input elements is constructed, and the ILC techniques such as the recently-developed model-less inversion-based iterative control (MIIC) are used to obtain the control input elements that achieve precision output tracking of the corresponding desired output elements. Then the previewed future desired trajectory is decomposed as a summation of desired output elements, and the control input is synthesized by using the input elements selected for the corresponding output elements with chosen pre-actuation time. Furthermore, the required pre-actuation time is quantified based on the stable-inversion theory. The proposed approach is illustrated through simulation study of a nanomanipulation application using a nonminimum-phase piezo actuator model.

scholarly journals Tracking Control of Linear Time-Invariant Nonminimum Phase Systems Using Filtered Basis Functions

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Keval S. Ramani ◽  
Molong Duan ◽  
Chinedum E. Okwudire ◽  
A. Galip Ulsoy
Keyword(s):  
Linear Time ◽  
Basis Functions ◽  
Control Input ◽  
Nonminimum Phase ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
The Stability ◽  
Time Invariant ◽  
Time Systems

An approach for minimizing tracking errors in linear time-invariant (LTI) single-input single-output (SISO) discrete-time systems with nonminimum phase (NMP) zeros using filtered basis functions (FBF) is studied. In the FBF method, the control input to the system is expressed as a linear combination of basis functions. The basis functions are forward filtered using the dynamics of the NMP system, and their coefficients are selected to minimize the error in tracking a given desired trajectory. Unlike comparable methods in the literature, the FBF method is shown to be effective in tracking any desired trajectory, irrespective of the location of NMP zeros in the z-plane. The stability of the method and boundedness of the control input and system output are discussed. The control designer is free to choose any suitable set of basis functions that satisfy the criteria discussed in this paper. However, two rudimentary basis functions, one in time domain and the other in frequency domain, are specifically highlighted. The effectiveness of the FBF method is illustrated and analyzed in comparison with the truncated series (TS) approximation method.

scholarly journals Backstepping Control of an Unmanned Helicopter Subjected to External Disturbance and Model Uncertainty

2021 ◽  
Vol 11 (12) ◽  
pp. 5331
Author(s):  
Wenlong Zhao ◽  
Zhijun Meng ◽  
Kaipeng Wang ◽  
Haoyu Zhang
Keyword(s):  
External Disturbance ◽  
Flight Test ◽  
Lyapunov Theory ◽  
Outdoor Environment ◽  
Wind Gust ◽  
External Disturbances ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Highly Nonlinear ◽  
The Stability

A helicopter is a highly nonlinear system. Its mathematical model is difficult to establish accurately, especially the complicated flapping dynamics. In addition, the forces and moments exerted on the fuselage are very vulnerable to external disturbances like wind gust when flying in the outdoor environment. This paper proposes a composite control scheme which consists of a nonlinear backstepping controller and an extended state observer (ESO) to handle the above problems. The stability of the closed-loop system can be guaranteed based on Lyapunov theory. The external disturbances and model nonlinearities are treated as a lumped disturbance. Meanwhile, the ESO is employed to compensate the influence by estimating the lumped disturbance in real-time. Numerical simulation results are presented to demonstrate that the algorithm can achieve accurate and agile attitude tracking under the external wind gust disturbances even with model uncertainties. When coming to the flight test, a block dropping device was designed to generate a quantifiable and replicable disturbance, and the experimental results indicate that the algorithm introduced above can reject the external disturbance rapidly and track the given attitude command precisely.

Analytical Statistical Study of Linear Parallel Feedforward Compensators for Nonminimum-Phase Systems

2019 ◽  
Author(s):  
Keyvan Noury ◽  
Bingen Yang
Keyword(s):  
Feedback Loop ◽  
Closed Loop ◽  
Controller Design ◽  
Phase System ◽  
Main Concern ◽  
Nonminimum Phase ◽  
Loop Design ◽  
Nonminimum Phase Systems ◽  
Phase Systems ◽  
Feedforward Compensators

Abstract In this work, a new parallel feedforward compensator for the feedback loop of a linear nonminimum-phase system is introduced. Then, analytical statistical arguments between the existing developed methods and the innovated method are brought. The compelling arguments suggest the parallel feedforward compensation with derivative (PFCD) method is a strong method even though at its first survey it seems to be optimistic and not pragmatic. While most of the existing methods offer an optimal integral of squared errors (ISE) for the closed-loop response of the nominal plant, the PFCD offers a finite ISE; in reality, typically, the nominal plant is not of main concern in the controller design and the performance in the presence of mismatch model, noise, and disturbance has priority. In this work, there are several arguments brought to bold the importance of the innovated PFCD design. Also, there is a closed-loop design example to show the PFCD effectiveness in action.

scholarly journals Simulation and Experimental Studies on Perfect Tracking Optimal Control of an Electrohydraulic Actuator System

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
R. Ghazali ◽  
Y. M. Sam ◽  
M. F. Rahmat ◽  
Zulfatman ◽  
A. W. I. M. Hashim
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Tracking Control ◽  
Phase Error ◽  
Experimental Studies ◽  
Phase System ◽  
Nonminimum Phase ◽  
Gain Error ◽  
Feedforward Controller ◽  
Electrohydraulic Actuator

This paper presents a perfect tracking optimal control for discrete-time nonminimum phase of electrohydraulic actuator (EHA) system by adopting a combination of feedback and feedforward controller. A linear-quadratic regulator (LQR) is firstly designed as a feedback controller, and a feedforward controller is then proposed to eliminate the phase error emerged by the LQR controller during the tracking control. The feedforward controller is developed by implementing the zero phase error tracking control (ZPETC) technique in which the main difficulty arises from the nonminimum phase system with no stable inverse. Subsequently, the proposed controller is performed in simulation and experimental studies where the EHA system is represented in discrete-time model that has been obtained using system identification technique. It also shows that the controller offers better performance as compared to conventional PID controller in reducing phase and gain error that typically occurred in positioning or tracking systems.

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