Optimal discrete systems using time-weighted performance index with prespecified closed-loop eigenvalues

1988 ◽  
Vol 33 (11) ◽  
pp. 1078-1080 ◽  
Author(s):  
B.-H. Kwon ◽  
M.-J. Youn
Keyword(s):  
Performance Index ◽  
Closed Loop ◽  
Discrete Systems

scholarly journals Design of a PID-Lead Compensator for a Twin Rotor Aerodynamic System (TRAS)

2021 ◽  
Vol 27 (1) ◽  
pp. 79-88
Author(s):  
Rafal Fawzi Faisal ◽  
Omar Waleed Abdulwahhab
Keyword(s):  
Frequency Response ◽  
Rise Time ◽  
Performance Index ◽  
Closed Loop ◽  
Mimo System ◽  
Design Procedure ◽  
Absolute Error ◽  
Root Locus ◽  
Lead Compensator ◽  
Twin Rotor

This paper deals with a Twin Rotor Aerodynamic System (TRAS). It is a Multi-Input Multi-Output (MIMO) system with high crosscoupling between its two channels. It proposes a hybrid design procedure that combines frequency response and root locus approaches. The proposed controller is designated as PID-Lead Compensator (PIDLC); the PID controller was designed in previous work using frequency response design specifications, while the lead compensator is proposed in this paper and is designed using the root locus method. A general explicit formula for angle computations in any of the four quadrants is also given. The lead compensator is designed by shifting the dominant closed-loop poles slightly to the left in the s-plane. This has the effect of enhancing the relative stability of the closed-loop system by eliminating the oscillation in its transient part but at the expense of greater rise time. However, for some applications, long rise time may be an allowable price to get rid of undesired oscillation. To demonstrate the proposed hybrid controller's performance numerically, a new performance index, designated by Integral Reciprocal Time Absolute Error (IRTAE), is defined as a figure to measure the oscillation of the response in its transient part. The proposed controller enhances this performance index by 0.6771%. Although the relative enhancement of the performance index is small, it contributes to eliminating the oscillation of the response in its transient part. Simulation results are performed on the MATLAB/Simulink environment.

scholarly journals A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141881995
Author(s):  
Francisco G Salas ◽  
Jorge Orrante-Sakanassi ◽  
Raymundo Juarez-del-Toro ◽  
Ricardo P Parada
Keyword(s):  
Stability Analysis ◽  
Performance Index ◽  
Closed Loop ◽  
Tracking Error ◽  
Parallel Robots ◽  
Control Loop ◽  
Closed Loop System ◽  
Proportional Integral ◽  
The Stability ◽  
Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

scholarly journals On finite-time consensus objectives in time-varying interconnected discrete linear dynamic systems under internal and external delays

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878484 ◽  
Author(s):  
Manuel De la Sen ◽  
Santiago Alonso-Quesada
Keyword(s):  
Dynamic Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Discrete Systems ◽  
Open Loop ◽  
Time Varying ◽  
Common Error ◽  
Linear Dynamic Systems ◽  
External Point ◽  
Point Delays

This article formulates the properties of achievable consensus of linear interconnected discrete systems with multiple internal and external point delays. The formulation is stated in an algebraic generic context as the ability of achievement of (a non-necessarily zero) finite-time common error between the various subsystems. The consensus signals are generically defined so that they can be, in general, distinct of the output or state components. However, the consensus signals of all the interconnected subsystems have the same dimension for coherency reasons. A particular attention is paid to the case of weak interconnection couplings in both the open-loop case and the closed-loop one under, in general, linear output feedback. Some further extensions are given related to consensus over intervals and related to consensus of positive interconnected systems.

scholarly journals Mixed H2/H∞ Control for Itô-type Stochastic Time-Delay Systems with Applications to Clothing Hanging Device

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yan Qi ◽  
Min Zhang ◽  
Zhiguo Yan
Keyword(s):  
Time Delay ◽  
Performance Index ◽  
Closed Loop ◽  
Delay Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Closed Loop Systems ◽  
Mean Square Stability ◽  
Stochastic Time

This paper deals with the problem of mixed H2/H∞ control for Itô-type stochastic time-delay systems. First, the H2/H∞ control problem for stochastic time-delay systems is presented, which considers the mean square stability, H2 control performance index, and the ability of disturbance attenuation of the closed-loop systems. Second, by choosing an appropriate Lyapunov–Krasoviskii functional and using matrix inequality technique, some sufficient conditions for the existence of state feedback H2/H∞ controller for stochastic time-delay systems are obtained in the form of linear matrix inequalities. Third, two convex optimization problems with linear matrix inequality constraints are formulated to design the optimal mixed H2/H∞ controller which minimizes the guaranteed cost of the closed-loop systems with known and unknown initial functions, and the corresponding algorithm is given to optimize H2/H∞ performance index. Finally, a numerical example is employed to show the effectiveness and feasibility of the proposed method.

Convergence of PD-Type Iterative Learning Control of Nonlinear Discrete Systems and its Robustness

2012 ◽  
Vol 557-559 ◽  
pp. 2049-2053
Author(s):  
Chang Liang Liu ◽  
Wan Gen Jia
Keyword(s):  
Iterative Learning Control ◽  
Closed Loop ◽  
Discrete Systems ◽  
Open Loop ◽  
Iterative Learning ◽  
System Operation ◽  
Advantages And Disadvantages ◽  
Output Error ◽  
The Status ◽  
Nonlinear Discrete Systems

Abstract: For the control problem of nonlinear discrete systems, this paper describes the status of current research and analyzes the advantages and disadvantages of open-loop and closed-loop iterative learning controller. A class of nonlinear discrete systems will be extended to the general nonlinear discrete systems. To the general nonlinear discrete systems, a open-closed-loop PD-type iterative learning controller which based on current and last output error instead of last output error only is proposed. It makes use of information on system operation more fully and accurately. Besides, based on norm of λ and mathematical induction, its sufficient condition for convergence is given. In order to test its robustness, a simulation is done in the case of a persistent interference. Simulation results show that it is efficient.

Comments on ‘An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays’

2017 ◽  
Vol 40 (13) ◽  
pp. 3846-3850 ◽  
Author(s):  
Neha Agarwal ◽  
Haranath Kar
Keyword(s):  
Closed Loop ◽  
Cost Control ◽  
Initial Conditions ◽  
Discrete Systems ◽  
Guaranteed Cost Control ◽  
Lmi Approach ◽  
Technical Errors ◽  
Guaranteed Cost ◽  
State And Input Delays ◽  
Input Delays

This paper points out some technical errors in a recent paper that appeared in Transactions of the Institute of Measurement and Control entitled ‘An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays’ by Akshata Tandon and Amit Dhawan ( http://dx.doi.org/10.1177/0142331216667476 ). We reveal that the upper bound of the closed-loop cost function provided by their Lemma 4 is erroneous. Some critical issues associated with the system initial conditions assumed in their paper are highlighted. The closed-loop cost bound claimed by their Theorem 1 is found to be incorrect. The optimization problem formulated in their Theorem 2 for the selection of an optimal guaranteed cost controller is erroneous. Finally, the corrections over their results are made available.

scholarly journals Finite-Time H2/H∞ Control for Linear Itô Stochastic Systems with x,u,v-Dependent Noise

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Zhiguo Yan ◽  
Shiyu Zhong ◽  
Xingping Liu
Keyword(s):  
Optimization Algorithm ◽  
Finite Time ◽  
Performance Index ◽  
State Feedback ◽  
Closed Loop ◽  
Stochastic Systems ◽  
Transient Performance ◽  
Closed Loop Systems ◽  
Linear Stochastic Systems ◽  
Finite Time Boundedness

This paper deals with the problem of the H2/H∞ control based on finite-time boundedness for linear stochastic systems. The motivation for investigating this problem comes from one observation that the H2/H∞ control does not involve systems’ transient performance. To express this problem clearly, a concept called finite-time H2/H∞ control is introduced. Moreover, state feedback and observer-based finite-time H2/H∞ controllers are designed, which guarantee finite-time boundedness, H2 performance index, and H∞ performance index of the closed-loop systems. Furthermore, an optimization algorithm on the finite-time H2/H∞ control is presented to obtain the minimum values of the H2 index and H∞ index. Finally, we use an example to show the validity of the obtained results.

scholarly journals Design of a PID-Lead Compensator for a Twin Rotor Aerodynamic System (TRAS)

2021 ◽  
Vol 27 (1) ◽  
pp. 79-88
Author(s):  
Rafal Fawzi Faisal ◽  
Omar Waleed Abdulwahhab
Keyword(s):  
Frequency Response ◽  
Rise Time ◽  
Performance Index ◽  
Closed Loop ◽  
Mimo System ◽  
Design Procedure ◽  
Absolute Error ◽  
Root Locus ◽  
Lead Compensator ◽  
Twin Rotor

This paper deals with a Twin Rotor Aerodynamic System (TRAS). It is a Multi-Input Multi-Output (MIMO) system with high crosscoupling between its two channels. It proposes a hybrid design procedure that combines frequency response and root locus approaches. The proposed controller is designated as PID-Lead Compensator (PIDLC); the PID controller was designed in previous work using frequency response design specifications, while the lead compensator is proposed in this paper and is designed using the root locus method. A general explicit formula for angle computations in any of the four quadrants is also given. The lead compensator is designed by shifting the dominant closed-loop poles slightly to the left in the s-plane. This has the effect of enhancing the relative stability of the closed-loop system by eliminating the oscillation in its transient part but at the expense of greater rise time. However, for some applications, long rise time may be an allowable price to get rid of undesired oscillation. To demonstrate the proposed hybrid controller's performance numerically, a new performance index, designated by Integral Reciprocal Time Absolute Error (IRTAE), is defined as a figure to measure the oscillation of the response in its transient part. The proposed controller enhances this performance index by 0.6771%. Although the relative enhancement of the performance index is small, it contributes to eliminating the oscillation of the response in its transient part. Simulation results are performed on the MATLAB/Simulink environment.

Sign in / Sign up

Export Citation Format

Share Document