scholarly journals OPTIMAL ENERGY REGULATION PERFORMANCE OF DELAY-TIME SYSTEMS

2007 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
T. BAKHTIAR
Keyword(s):  
Delay Time ◽  
Linear Time ◽  
Closed Form Expression ◽  
Control Input ◽  
Energy Regulation ◽  
Minimum Phase ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Systems ◽  
Existing Result

This paper studies the regulation performance limi- tation of delay-time systems. The performance is measured by the energy of the control input with respect to an impulse dis- turbance function. We first provide the analytical closed-form expression of the optimal performance for minimum phase case by reviewing the existing result. We then extend the problem to non-minimum phase case by exploiting the results of linear time- invariant discrete-time and delta domain cases.

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.

Design and implementation of decoupled periodic control scheme for a laboratory-based quadruple-tank process

2021 ◽  
pp. 095965182110228
Author(s):  
Jatin K Pradhan ◽  
Arun Ghosh
Keyword(s):  
Real Time ◽  
High Frequency ◽  
Linear Time ◽  
Disturbance Attenuation ◽  
Minimum Phase ◽  
Periodic Control ◽  
Linear Time Invariant ◽  
Control Scheme ◽  
Gain Margin ◽  
Time Invariant

It is well known that linear time-invariant controllers fail to provide desired robustness margins (e.g. gain margin, phase margin) for plants with non-minimum phase zeros. Attempts have been made in literature to alleviate this problem using high-frequency periodic controllers. But because of high frequency in nature, real-time implementation of these controllers is very challenging. In fact, no practical applications of such controllers for multivariable plants have been reported in literature till date. This article considers a laboratory-based, two-input–two-output, quadruple-tank process with a non-minimum phase zero for real-time implementation of the above periodic controller. To design the controller, first, a minimal pre-compensator is used to decouple the plant in open loop. Then the resulting single-input–single-output units are compensated using periodic controllers. It is shown through simulations and real-time experiments that owing to arbitrary loop-zero placement capability of periodic controllers, the above decoupled periodic control scheme provides much improved robustness against multi-channel output gain variations as compared to its linear time-invariant counterpart. It is also shown that in spite of this improved robustness, the nominal performances such as tracking and disturbance attenuation remain almost the same. A comparison with [Formula: see text]-linear time-invariant controllers is also carried out to show superiority of the proposed scheme.

Optimal Nonlinear Estimation of Linear Stochastic Systems: The Multivariable Extension

1996 ◽  
Vol 118 (2) ◽  
pp. 350-353 ◽  
Author(s):  
M. A. Hopkins ◽  
H. F. VanLandingham
Keyword(s):  
Stochastic Systems ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Linear Time ◽  
Nonlinear Method ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant ◽  
Time Systems

This paper extends to multi-input multi-output (MIMO) systems a nonlinear method of simultaneous parameter and state estimation that appeared in the ASME JDSM&C (September, 1994), for single-input single-output (SISO) systems. The method is called pseudo-linear identification (PLID), and applies to stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer functions must be strictly proper. In the earlier paper, proofs of optimality and convergence were given. Extensions of those proofs to the MIMO case are also given here.

scholarly journals On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
M. De la Sen
Keyword(s):  
Continuous Time ◽  
Linear Time ◽  
Positive Real ◽  
Feedback Controllers ◽  
Linear Time Invariant ◽  
Continuous Time Systems ◽  
Strictly Positive Real ◽  
Forward Transfer ◽  
Time Invariant ◽  
Time Systems

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.

Periodic controller for guaranteed simultaneous stabilization of two plants with robust zero error tracking

2018 ◽  
Vol 233 (5) ◽  
pp. 480-490
Author(s):  
Arindam Chakraborty ◽  
Jayati Dey
Keyword(s):  
Design Methodology ◽  
Linear Time ◽  
Pole Placement ◽  
Control Input ◽  
Efficient Design ◽  
Simultaneous Stabilization ◽  
Bounded Control ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Periodic

The guaranteed simultaneous stabilization of two linear time-invariant plants is achieved by continuous-time periodic controller with high controller frequency. Simultaneous stabilization is accomplished by means of pole-placement along with robust zero error tracking to either of two plants. The present work also proposes an efficient design methodology for the same. The periodic controller designed and synthesized for realizable bounded control input with the proposed methodology is always possible to implement with guaranteed simultaneous stabilization for two plants. Simulation and experimental results establish the veracity of the claim.

Modal Control of Linear Time-Invariant Discrete-Time Systems

1969 ◽  
Vol 2 (8) ◽  
pp. T133-T136 ◽  
Author(s):  
B. Porter ◽  
T. R. Crossley
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Feedback Loops ◽  
Modal Control ◽  
Discrete Time System ◽  
Linear Time Invariant ◽  
Modal Theory ◽  
Discrete Time Systems ◽  
Time Invariant ◽  
Time Systems

Modal control theory is applied to the design of feedback loops for linear time-invariant discrete-time systems. Modal theory is also used to demonstrate the explicit relationship which exists between the controllability of a mode of a discrete-time system and the possibility of assigning an arbitrary value to the eigenvalue of that mode.

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