Analysis of an Error Integral Driven MIMO SM Regulator for LTI Systems

2016 ◽  
Author(s):  
Kerim Yunt
Keyword(s):  
Parameter Uncertainty ◽  
Sliding Mode ◽  
Linear Time ◽  
Pole Placement ◽  
Sliding Mode Controller ◽  
Minimum Phase ◽  
Linear Time Invariant ◽  
Luenberger Observer ◽  
Optimization Routine ◽  
Time Invariant

In this work an error-integral-driven sliding mode controller (EID-SMC) for multi-input multi-output (MIMO) minimum phase linear time-invariant (LTI) systems with feedthrough controls and output disturbance is analyzed. Though the sliding variable remains in the vicinity of the sliding surface without reaching it, it is shown that the steady-state error vanishes exponentially asymptotically within the boundary layer even if parameter uncertainty and unmatched input/output disturbances exist. The pole-placement is accomplished indirectly by an iterative optimization routine by considering limits on controls and state contrary to the existing practice in SMC where either direct pole placement or quadratic norm optimality of a performance is used. For the proposed controller framework the Luenberger observer is presented.

Chattering-Free Error Integral Driven MIMO Sliding Mode Regulator for Linear Time-Invariant Systems

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Kerim Yunt
Keyword(s):  
Boundary Layer ◽  
Sliding Mode ◽  
Linear Time ◽  
Optimization Procedure ◽  
Pole Placement ◽  
Linear Time Invariant ◽  
Full State ◽  
Chattering Free ◽  
Linear Time Invariant Systems ◽  
Time Invariant

In this work, an error-integral-driven sliding mode controller (EID-SMC) is discussed for multi-input multi-output (MIMO) linear time-invariant (LTI) systems. The boundary layer approach is utilized in order to eliminate the chattering problem. Though the sliding variable remains in the vicinity of the sliding surface without reaching it, it is shown that the steady-state error vanishes exponentially asymptotically within a boundary layer, for systems of relative order one, even if parameter uncertainty and unmatched input disturbances exist. The pole placement is accomplished indirectly with an iterative optimization procedure by considering limits on controls and state. Finally, the output-feedback controller is augmented with a Luenberger full-state and disturbance observer.

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.

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.

Proportional–integral–derivative controller family for pole placement

2016 ◽  
Vol 231 (20) ◽  
pp. 3791-3797 ◽  
Author(s):  
Chimpalthradi R Ashokkumar ◽  
George WP York ◽  
Scott F Gruber
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Proportional Integral Derivative ◽  
Proportional Integral Derivative Controller ◽  
Proportional Integral ◽  
Linear Time Invariant ◽  
Generalized Eigenvalue ◽  
Square Systems ◽  
Time Invariant

In this paper, linear time-invariant square systems are considered. A procedure to design infinitely many proportional–integral–derivative controllers, all of them assigning closed-loop poles (or closed-loop eigenvalues), at desired locations fixed in the open left half plane of the complex plane is presented. The formulation accommodates partial pole placement features. The state-space realization of the linear system incorporated with a proportional–integral–derivative controller boils down to the generalized eigenvalue problem. The generalized eigenvalue-eigenvector constraint is transformed into a system of underdetermined linear homogenous set of equations whose unknowns include proportional–integral–derivative parameters. Hence, the proportional–integral–derivative solution sets are infinitely many for the chosen closed-loop eigenvalues in the eigenvalue-eigenvector constraint. The solution set is also useful to reduce the tracking errors and improve the performance. Three examples are illustrated.

H ∞ and Sliding Mode Observers for Linear Time-Invariant Fractional-Order Dynamic Systems With Initial Memory Effect

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Sang-Chul Lee ◽  
Yan Li ◽  
YangQuan Chen ◽  
Hyo-Sung Ahn
Keyword(s):  
Memory Effect ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Sliding Mode ◽  
Linear Time ◽  
Unknown Input ◽  
Unknown Input Observer ◽  
Linear Time Invariant ◽  
Sliding Mode Observers ◽  
Time Invariant

The H∞ and sliding mode observers are important in integer-order dynamic systems. However, these observers are not well explored in the field of fractional-order dynamic systems. In this paper, the H∞ filter and the fractional-order sliding mode unknown input observer are developed to estimate state of the linear time-invariant fractional-order dynamic systems with consideration of proper initial memory effect. As the first result, the fractional-order H∞ filter is introduced, and it is shown that the gain from the noise to the estimation error is bounded in the sense of the H∞ norm. Based on the extended bounded real lemma, the H∞ filter design is formulated in a linear matrix inequality form, and it will be seen that numerical methods to solve convex optimization problems are feasible in fractional-order systems (FOSs). As the second result of this paper, not only state but also unknown input disturbance are estimated by fractional-order sliding-mode unknown input observer, simultaneously. In this paper, it is shown that the design and stability analysis of the two estimation techniques are not related with the initial history. Through two numerical examples, the performance of the fractional-order H∞ filter and the fractional-order sliding-mode observer is illustrated with consideration of the initialization functions.

Decentralized controller design by continuous pole placement for neutral time-delay systems

2016 ◽  
Vol 39 (3) ◽  
pp. 297-311 ◽  
Author(s):  
HE Erol ◽  
A İftar
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Linear Time ◽  
Pole Placement ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Linear Time Invariant ◽  
Assignment Algorithm ◽  
Placement Algorithm ◽  
Time Invariant

The stabilizing decentralized controller design problem for (possibly descriptor-type) linear time-invariant neutral time-delay systems is considered. A design approach, based on the continuous pole placement algorithm and the decentralized pole assignment algorithm, is proposed. A design example is also presented, to demonstrate the proposed approach.

scholarly journals On Parametrizations of State Feedbacks and Static Output Feedbacks and Their Applications

2021 ◽  
Author(s):  
Yossi Peretz
Keyword(s):  
Linear Time ◽  
Linear Constraint ◽  
Pole Placement ◽  
Space Representation ◽  
Static State ◽  
Linear Time Invariant ◽  
State Space Representation ◽  
Time Invariant ◽  
Time Linear ◽  
Static Output

In this chapter, we provide an explicit free parametrization of all the stabilizing static state feedbacks for continuous-time Linear-Time-Invariant (LTI) systems, which are given in their state-space representation. The parametrization of the set of all the stabilizing static output feedbacks is next derived by imposing a linear constraint on the stabilizing static state feedbacks of a related system. The parametrizations are utilized for optimal control problems and for pole-placement and exact pole-assignment problems.

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.

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