scholarly journals Controller Design for Two-Input Single-Output Systems Exploiting Plant/Controller Alignment

2018 ◽  
Author(s):  
Nathan A. Weir ◽  
Andrew G. Alleyne
Keyword(s):  
Design Process ◽  
Closed Loop ◽  
Controller Design ◽  
Analysis Tool ◽  
Feedback Systems ◽  
Sensitivity Functions ◽  
Bode Plot ◽  
Single Output ◽  
Graphical Information ◽  
Alignment Angle

Due to the unique structure of TISO feedback systems, several closed loop properties can be characterized using the concepts of plant and controller “directions” and “alignment”. Poor plant/controller alignment indicates significant limitations in terms of closed loop performance. In general, it is desirable to design a controller that is well aligned with the plant in order to minimize the size of the closed loop sensitivity functions and closed loop interactions. Although the concept of alignment can be a useful analysis tool for a given plant/controller pair, it is not obvious how a controller should be designed to achieve good alignment. We present a new controller design approach, based on the well-known “PQ method”, which explicitly incorporates knowledge of alignment into the design process. This is accomplished by providing graphical information about the alignment angle on the Bode plot of the PQ frequency response. We show the utility of this approach through a design example.

scholarly journals A Graphical Design Approach for Two-Input Single-Output Systems Exploiting Plant/Controller Alignment: Design and Application

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Nathan A. Weir ◽  
Andrew G. Alleyne
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Linear Time ◽  
Design Approach ◽  
Analysis Tool ◽  
Feedback Systems ◽  
Linear Time Invariant ◽  
Single Output ◽  
Graphical Design ◽  
Time Invariant

Abstract Due to the unique structure of two-input single-output (TISO) feedback systems, several closed-loop properties can be characterized using the concepts of plant and controller “directions” and “alignment.” Poor plant/controller alignment indicates significant limitations in terms of closed-loop performance. In general, it is desirable to design a controller that is well aligned with the plant in order to minimize the size of the closed-loop sensitivity functions and closed-loop interactions. Although the concept of alignment can be a useful analysis tool for a given plant/controller pair, it is not obvious how a controller should be designed to achieve good alignment. We present a new controller design approach, based on the PQ method (Schroeck et al., 2001, “On Compensator Design for Linear Time invariant Dual-Input Single-Output Systems,” IEEE/ASME Trans. Mechatronics, 6(1), pp. 50–57), which explicitly incorporates knowledge of alignment into the design process. This is accomplished by providing graphical information about the alignment angle on the Bode plot of the PQ frequency response. We show the utility of this approach through a design example.

Reduction of Limit Cycle Amplitude in the Presence of Backlash

1999 ◽  
Vol 121 (2) ◽  
pp. 278-284 ◽  
Author(s):  
Ronen Boneh ◽  
Oded Yaniv
Keyword(s):  
Nonlinear Control ◽  
Limit Cycle ◽  
Closed Loop ◽  
Controller Design ◽  
Linear Time ◽  
Design Technique ◽  
Feedback Systems ◽  
Mass System ◽  
Cycle Amplitude ◽  
Limit Cycle Amplitude

The majority of feedback systems driven by an electric motor can be represented by a two-mass system connected via a flexible drive element. Owing to the presence of backlash, the closed-loop performance such as precision speed, position and force control that can be achieved using a linear time invariant controller is limited, and it is expected that a nonlinear control would be superior. In this paper a nonlinear control structure is proposed and a systematic design technique presented. The advantages of the proposed design technique are: (i) It is robust to plant and backlash uncertainty; (ii) it is quantitative to specifications on the maximum limit cycle amplitude; and (iii) the closed loop is superior to a linear controller design both in lower bandwidth and in lower limit cycle amplitude. A design example is included.

scholarly journals Stability Driven Optimal Controller Design for High Quality Images

Electronics ◽  
2018 ◽  
Vol 7 (12) ◽  
pp. 437 ◽  
Author(s):  
Sangmin Suh
Keyword(s):  
Optimal Design ◽  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Recognition Rate ◽  
Robot Vision ◽  
Sensitivity Functions ◽  
Closed Loop Systems ◽  
Conventional Methods ◽  
Performance Limitations

This note presents an optimal design method to enhance image quality in optical image stabilization (OIS) systems. First of all, performance limitations of conventional methods are shown and secondly, a new design framework based on convex optimization is proposed. The resulting controller essentially stabilizes the closed loop systems because the proposed method is derived from Lyapunov stability. From the test results, it is confirmed that this method reduces the effect of hand vibrations and makes images sharp. Additionally, it is shown that the proposed method is also effective in robot vision and recognition rate of deep neural network (DNN) based traffic signs and pedestrians detection in automotive applications. This note has three main contributions. First, performance limitations of the conventional method are shown. Second, from the relation between sensitivity and complementary sensitivity functions, an indirect design method for performance improvement is proposed, and finally, stability guaranteed optimal design is proposed. Unlike conventional methods, the proposed method does not require addition filters to suppress resonances of the plant and this note highlights phases of the closed loop systems on removing external vibrations.

Bounded-Input-Bounded-Output Stability of Nonlinear Feedback Systems in a Volterra Representation

2000 ◽  
Author(s):  
John W. Glass ◽  
Matthew A. Franchek
Keyword(s):  
Stability Condition ◽  
Closed Loop ◽  
Controller Design ◽  
External Disturbance ◽  
Design Procedure ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Volterra Kernels ◽  
The Stability ◽  
Nonlinear Feedback Systems

Abstract Presented in this paper is a stability condition for a class of nonlinear feedback systems where the plant dynamics can be represented by a finite series of Volterra kernels. The class of Volterra kernels are limited to p-linear stable operators and may contain pure delays. The stability condition requires that the linear kernel is nonzero and that the closed loop characteristic equation associated with the linearized system is stable. Next, a sufficient condition is developed to upper bound the infinity-norm of an external disturbance signal thereby guaranteeing that the internal and output signals of the closed loop nonlinear system are contained in L∞. These results are then demonstrated on a design example. A frequency domain controller design procedure is also developed using these results where the trade-off between performance and stability are considered for this class of nonlinear feedback systems.

A Control Design Approach for TITO Systems Using Measured Data

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Sofiane Khadraoui ◽  
Raouf Fareh ◽  
Hazem N. Nounou ◽  
Mohamed N. Nounou
Keyword(s):  
Frequency Domain ◽  
Closed Loop ◽  
Controller Design ◽  
Control Design ◽  
Intermediate Step ◽  
Single Input Single Output ◽  
Plant Modeling ◽  
Single Output ◽  
Performance Specifications ◽  
Tito Systems

This paper deals with the design of fixed-structure controllers for two-input two-output (TITO) systems using frequency-domain data. In standard control approaches, a plant model is first derived, then a suitable controller is designed to meet some user-specified performance specifications. Basically, there are two common ways for obtaining mathematical models: white-box modeling and black-box modeling. In both approaches, it is difficult to obtain a simple and accurate model that completely describes the system dynamics. As a result, errors associated with the plant modeling may result in degradation of the desired closed-loop performance. Moreover, the intermediate step of plant modeling introduced for the controller design is a time-consuming task. Hence, the concept of data-based control design is introduced as a possible alternative to model-based approaches. This promising methodology allows us to avoid the under-modeling problem and to significantly reduce the time and workload for the user. Most existing data-based control approaches are developed for single-input single-output (SISO) systems. Nevertheless, a large class of real systems involve several manipulated and output variables. To this end, we attempt here to develop an approach to design controllers for TITO systems using frequency-domain data. In such a method, a set of frequency-domain data is utilized to find an adequate decoupler and to tune a diagonal controller that meets some desired closed-loop performance measures. Two simulation examples are presented to illustrate and demonstrate the efficacy of the proposed method.

A comparison of linear discrete-time design methods for servosystem control

1997 ◽  
Vol 211 (4) ◽  
pp. 281-300 ◽  
Author(s):  
A R Plummer
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Solution Method ◽  
Controller Design ◽  
Pole Placement ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Time Model ◽  
Sensitivity Functions

Three linear discrete-time model-based controller design techniques are compared: pole placement, linear quadratic Gaussian (LQG) and H∞ control. It is shown that design choices can be made for all three controllers by considering the effect on the sensitivity functions of the closed-loop system. Also all three controllers can be implemented using an identical controller structure. A comparative study of the application of the techniques to an electromechanical servosystem is made. The controllers are designed from a discrete-time plant model estimated from experimental data, and a polynomial-based solution method is used in each case. It is concluded that acceptable performance can be achieved using any of the controllers if informed design choices are made.

scholarly journals Iterative Data-Driven Control for Closed Loop with Two Unknown Controllers

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hong Jianwang ◽  
Ricardo A. Ramirez-Mendoza ◽  
Ruben Morales-Menendez
Keyword(s):  
Stability Analysis ◽  
Unknown Parameter ◽  
Closed Loop ◽  
Transfer Functions ◽  
Controller Design ◽  
Classical Model ◽  
Data Driven ◽  
Model Matching ◽  
Matching Problem ◽  
Sensitivity Functions

Iterative idea is combined with data-driven control and is used to design the feedforward controller and feedback controller simultaneously. Consider one closed loop system with two controllers, the classical model-based control holds on the condition of known plant. To alleviate the modeling process for plant, data-driven control is applied to design the two controllers. After these two controllers are parametrized by two unknown parameter vectors, the iterative idea is introduced to identify these two parameter vectors. Furthermore, for more general case of controllers, the closed relations between controllers and expected transfer functions are derived. Then, the iterative idea is also introduced to achieve the controller design. To be of benefit for latter stability analysis, some equities are derived for output-input sensitivity functions with three kinds of disturbances. Generally, after formulating the problem of the controller design as one model-matching problem, the purpose of this paper is threefold. First, we derive that, in case of two parametrized controllers, the iterative idea is performed to identify these two unknown parameter vectors, even when parameters converge to their true values. Second, we show how to design the two controllers iteratively for more general forms and find the closed relations between these controllers and expected closed loop transfer functions. Third, we provide some heuristic considerations on output-input sensitivity functions, which are of benefit for our stability analysis on data-driven control. Finally, one example is given to show the feasibility of our proposed theories.

Mode-Based Controller Design for Hammerstein Models Using Closed-Loop Tranjent Response Data

2016 ◽  
Vol 136 (5) ◽  
pp. 625-632
Author(s):  
Yoshihiro Matsui ◽  
Hideki Ayano ◽  
Shiro Masuda ◽  
Kazushi Nakano
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Response Data ◽  
Hammerstein Models

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

Impedance Reduction Controller Design for Mechanical Systems

2013 ◽  
Author(s):  
Hanseung Woo ◽  
Kyoungchul Kong
Keyword(s):  
Case Studies ◽  
Closed Loop ◽  
Controller Design ◽  
Mechanical Impedance ◽  
Open Loop ◽  
Mechatronic Systems ◽  
Closed Loop Systems ◽  
Guaranteed Stability ◽  
Reaction Forces ◽  
Definition Of

Safety is one of important factors in control of mechatronic systems interacting with humans. In order to evaluate the safety of such systems, mechanical impedance is often utilized as it indicates the magnitude of reaction forces when the systems are subjected to motions. Namely, the mechatronic systems should have low mechanical impedance for improved safety. In this paper, a methodology to design controllers for reduction of mechanical impedance is proposed. For the proposed controller design, the mathematical definition of the mechanical impedance for open-loop and closed-loop systems is introduced. Then the controllers are designed for stable and unstable systems such that they effectively lower the magnitude of mechanical impedance with guaranteed stability. The proposed method is verified through case studies including simulations.

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