Synthesis of Digital PID Controllers for Discrete-Time Systems With Guaranteed Non-Overshooting Transient Response

2011 ◽  
Author(s):  
Navid Mohsenizadeh ◽  
Swaroop Darbha ◽  
Shankar P. Bhattacharyya
Keyword(s):  
Transfer Function ◽  
Impulse Response ◽  
Transient Response ◽  
Discrete Time ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Pid Controllers ◽  
Linear Time Invariant ◽  
Digital Pid ◽  
Error Transfer

In this paper, we present a new method of synthesizing digital PID controllers for discrete-time, Linear Time Invariant (LTI) Systems satisfying a class of transient response specifications. The problem of synthesizing a controller to achieve desirable transient specifications, such as requiring the transient response to be within an allowable range of overshoot, can be carried out as a problem of guaranteeing the impulse response of an appropriate closed loop error transfer function to be non-negative. An earlier result by the authors provides necessary and sufficient conditions for the impulse response of a discrete-time transfer function to be non-negative in terms of the requirement of a sequence of polynomials to be sign-invariant on the interval [1, ∞). An application of this result to the error transfer function yields a sequence of polynomials which are required to be sign-invariant on [1, ∞) but whose coefficients are polynomial functions of the controller gains k1, k2 and k3.

New Analysis/Design of Generalized Discrete PI Controller via Discrete Time Delay Control for Nonlinear Systems

2020 ◽  
Author(s):  
Suresh B. Reddy
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Pi Controller ◽  
Pid Controllers ◽  
Analysis And Design ◽  
Proportional Integral ◽  
Discrete Time Delay

Abstract Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controllers are among the most common schemes for control since their formulation nearly a century ago. They have been very successful in many applications, even as we have migrated from analog implementations to digital control systems. While there is rich literature for design and analysis of PI/PID controllers for linear time-invariant systems with modeled dynamics, the tools for analysis and design for nonlinear systems with unknown dynamics are limited, despite their known effectiveness. This paper extends previous observations about a form of discrete Time Delay Control’s equivalence to a generalized PI controller for more general canonical systems, with additional complimentary feedback linearization of known dynamics, as desired. In addition, sufficient conditions for Bounded Input-Bounded Output (BIBO) as well as exponential stability are developed in this paper for the form of discrete TDC that is closest to generalized discrete PI equivalent controller, for multi-input multi-output nonlinear systems, including nonaffine cases. Accordingly, design procedures are suggested for such discrete TDC, and generalized discrete PI controller for nonlinear systems.

Synthesis of a Stable Discrete-Time Repetitive Controller for MIMO Systems

1995 ◽  
Vol 117 (1) ◽  
pp. 92-98 ◽  
Author(s):  
Nader Sadegh
Keyword(s):  
Discrete Time ◽  
Mimo Systems ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Linear Time Invariant ◽  
Closed Loop Systems ◽  
Necessary And Sufficient ◽  
Time Invariant ◽  
Flexible Mechanical System

This paper presents some new results on synthesis and stability analysis of a class of repetitive controllers for discrete-time multi-input multi-output (MIMO) linear time-invariant (LTI) systems. In particular, the necessary and sufficient conditions for exponential stability of the resulting closed-loop systems are derived. A simulation case study featuring a flexible mechanical system is also presented.

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

2008 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Time Delay ◽  
Transfer Functions ◽  
Linear Time ◽  
Order System ◽  
Pid Controllers ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Plant Transfer ◽  
Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

Zeno-free adaptive event-triggered control design

2018 ◽  
Vol 41 (8) ◽  
pp. 2328-2337 ◽  
Author(s):  
Hassan Adloo ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Performance Criterion ◽  
Linear Time Invariant ◽  
Event Triggering ◽  
Linear Time Invariant Systems ◽  
System States ◽  
Time Invariant ◽  
Event Triggered

This paper presents a new general framework for adaptive event-triggered control strategy to extend average inter-event interval, while maintaining the performance of the system. The proposed event-triggering mechanism is acquired from input to state stability conditions, which is defined in terms of system states as well as an adaptation parameter. Under the Lipschitz assumption, a positive lower bound on sampling durations is also established that is essential to restrain the Zeno behavior. Applying the proposed method to linear time-invariant systems, leads to sufficient conditions to guarantee asymptotic stability in the form of matrix inequalities. Moreover, it is shown that there exist more degrees of freedom to improve the performance criterion from theoretical aspects. Finally, in order to show capability of the proposed method and its better performance compared with some recent works, numerical simulations are presented.

Coupled Stability of Multiport Systems—Theory and Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 419-428 ◽  
Author(s):  
J. E. Colgate
Keyword(s):  
Stability Property ◽  
Force Feedback ◽  
Linear Time ◽  
Experimental Studies ◽  
Sufficient Conditions ◽  
Direct Drive ◽  
Property A ◽  
Linear Time Invariant ◽  
The Stability ◽  
Necessary And Sufficient

This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

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