Tracking Control of Linear Systems

Gruyitch, Lyubomir

doi:10.1201/b14942

Cited by 9 publications

(5 citation statements)

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“…Theory 1 [32], [33]: the poles of closed-loop system can be located at any place according to the desired control performances if the plant system is fully controllable.…”

Section: State Feedback Controller For Bq-01mentioning

confidence: 99%

Experimentally Verified Depth Control of an Unmanned Semi-Submersible Vehicle

Zhou

Liu

et al. 2019

IEEE Access

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This paper considers the control of one unmanned semi-submersible vehicle (USV), named BQ-01, where the submersible depth cannot exceed a few meters in the presence of environmental disturbances. Consequently, the depth control performance measures and the rejection of disturbances, such as those due to sea waves, must be within pre-determined ranges to ensure maximum use of such vehicles. This paper develops a control scheme that combines the state feedback control and rule-based supervision for depth control, where the entries in the feedback control matrix are adjusted by rules formulated from the state errors in the USV diving plane. Surge speed also plays an important role in adjusting control parameters because of its coupled relationship with the state depth of the diving plane. The results from sea trials are given and confirm the potential of the design.INDEX TERMS Depth control performance, feedback control, rule-based supervision, unmanned semisubmersible vehicle.

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“…Theory 1 [32], [33]: the poles of closed-loop system can be located at any place according to the desired control performances if the plant system is fully controllable.…”

Section: State Feedback Controller For Bq-01mentioning

confidence: 99%

Experimentally Verified Depth Control of an Unmanned Semi-Submersible Vehicle

Zhou

Liu

et al. 2019

IEEE Access

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“…The theoretical basis for this research is, first of all, the concept of the full transfer function matrix defined for linear discrete systems, and then the TS type of fuzzy systems, with application in modeling, identification and control of dynamical systems. A full transfer function matrix, which was introduced and developed in [43][44][45], resolved controversy between the system transfer function and the stability testing using a classical transfer function. It is well understood that system stability, by definition, represents a dynamical attribute of the system in the free working regime for all zero input and variable arbitrary unknown initial conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The concept of nondegenerate system full transfer function matrix was discovered and developed in [44,45] for continuous-time linear systems and further extended for discrete-time linear systems in [43]. According to [43] (Def.…”

mentioning

confidence: 99%

Discrete-Time System Conditional Optimization Based on Takagi–Sugeno Fuzzy Model Using the Full Transfer Function

et al. 2022

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The study proposes a novel method for synthesis of a discrete-time parallel distributed compensation (PDC) controller for the nonlinear discrete-time Takagi–Sugeno (TS) fuzzy plant model. For each of the fuzzy plant model linear subsystems, a local linear first order proportional-sum (PS) controller is designed. The algebraic technique is used in two-dimensional parameter space, utilizing the characteristic polynomial of the row nondegenerate full transfer function matrix. Each system’s relative stability is accomplished in relation to the selected damping coefficient. The supplementary criterion is the minimal value of the performance index in the form of the sum of squared errors (SSE). However, unlike the traditional technique, output error is impacted by all simultaneous actions on the system: nonzero inputs and nonzero initial conditions. The full transfer function matrix of the system allows for the treatment of simultaneous actions of the input vector and unknown unpredictable initial conditions. In order to show the improvement caused by the application of a new optimization method that considers nonzero initial conditions, a comparison of PDC controllers designed under zero and nonzero initial conditions is given, where the system in both cases starts from the same nonzero initial conditions, which is often the case in practice. The simulation and experimental results on a DC servo motor are shown to demonstrate the suggested method efficiency.

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“…In the most common statement, the tracking problem (so-called, output tracking) supposes the construction the system input or the control law for the dynamical system, such that the system output following the desired function. For the linear system we should to mention the classical monograph [4], see also [5].…”

Section: Introductionmentioning

confidence: 99%

“…way the system takes the following closed-loop form= ,The next theorem presents the main result of the paper. Let P , Y , 2 K be the solution of the minimization problem stabilizes system(4), and P is an invariant ellipsoid matrix for the closed-loop system with zero initial condition.Applying Theorem 1 for the system(8) and minimizing invariant ellipsoid with matrix P , we arrive at the following minimization problem Using Schur lemma[20], the first constraint can be reformulated as Let us introduce the auxiliary variable…”

mentioning

confidence: 99%

An Approach to Tracking Problem for Linear Control System Via Invariant Ellipsoids Method

Khlebnikov¹

2019

8th International Conference on Soft Computing, Artificial Intelligence and Applications

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In this paper, a simple yet universal approach to the tracking problem for linear control systems via the linear static combined feedback is proposed. The approach is based on the invariant ellipsoid concept and LMI technique, where the optimal control design reduced to finding the minimal invariant ellipsoid for the closed-loop system. With such an ideology, the control design problem directly reduces to a semidefinite programming and one-dimensional minimization. Another attractive property of the proposed approach is that it is equally applicable to discrete-time control systems. The efficacy of the technique is illustrated via a benchmark problem.

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Tracking Control of Linear Systems

Cited by 9 publications

References 0 publications

Experimentally Verified Depth Control of an Unmanned Semi-Submersible Vehicle

Experimentally Verified Depth Control of an Unmanned Semi-Submersible Vehicle

Discrete-Time System Conditional Optimization Based on Takagi–Sugeno Fuzzy Model Using the Full Transfer Function

An Approach to Tracking Problem for Linear Control System Via Invariant Ellipsoids Method

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