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Proceedings ArticleDOI

Robust Stabilization of Cart Inverted Pendulum System by 2-Rate Controller

TL;DR: This work proposes a 2-rate controller to stabilize the cart inverted pendulum system (CIPS) and shows that the GM of the overall system is improved considerably as compared to the results obtained using LDTI controllers.
Abstract: In a Multi(2)-rate controller the input and output of the plant are sampled at different rates. In this context, it is important to note that several attempts have been made in the literature to achieve zero-placement using 2-rate control. These attempts, however, involved only the fast-input type of control which, unfortunately, yields unacceptable oscillations in the output. The fast-output type, on the other hand, does not have this problem inherently, but it’s zero placement capability has been established recently by viewing it from a 2-Periodic perspective. This zero-placement capability of 2-rate control ensures robustness of the compensated system in terms of satisfactory gain margin (GM) values. This work proposes a 2-rate controller to stabilize the cart inverted pendulum system (CIPS) and shows that the GM of the overall system is improved considerably as compared to the results obtained using LDTI controllers.
Citations
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Proceedings ArticleDOI
07 Oct 2020
TL;DR: A PSO (Particle Swarm Optimization) based tuning rule for 2-rate controllers for the stabilization of cart-inverted pendulum system to have an efficient and effective search by a group of particles in the solution space to find out the optimal locations of the controller poles and loop-zeros that yield satisfactory loop robustness.
Abstract: This paper proposes a PSO (Particle Swarm Optimization) based tuning rule for 2-rate controllers for the stabilization of cart-inverted pendulum system. In [1] the 2-Rate controller, a special subset of 2-periodic controller, has been designed to achieve poles as well as loop-zero placement leading to an improved gain margin (GM) as compared to its LTI counterpart. In the work of [2], the 2-Rate compensation technique was employed to stabilize the cart inverted pendulum system. However, the controller design approach was based on trial and error method and the GM of the overall system depends on the choice of controller poles and loop-zeros. In order to formalize this problem of selecting the proper locations of the controller poles and loop-zeros, this paper proposes a PSO based approach. The objective is to have an efficient and effective search by a group of particles in the solution space to find out the optimal locations of the controller poles and loop-zeros that yield satisfactory loop robustness.

Cites methods or result from "Robust Stabilization of Cart Invert..."

  • ...GM, as compared to that achievable using 2-Rate controller as discussed in previous work [2]....

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  • ...In the work of [2], the 2-Rate compensation technique was employed to stabilize the cart inverted pendulum system....

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  • ...The robustness study of the 2-Rate controller is done by determining the maximum and minimum values of gain for which the system remains stable, which depicts the GM of the loops, and the values are tabulated in Table III along with the results obtained in [2]....

    [...]

  • ...The intelligent control approach, involving fuzzy logic control [5], neural network control [6], adaptive PID control [7], hybrid control [2], among others, on the other hand, does not need an accurate mathematical model....

    [...]

References
More filters
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TL;DR: The zeros of the discrete time system obtained when sampling a continuous time system are explored and theorems for the limiting zeros for large and small sampling periods are given.

866 citations

Journal ArticleDOI
TL;DR: In this article, the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants is considered. And the authors show that for a large class of robustness problems, periodic compensators are superior to time-inariant ones.
Abstract: This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of robustness problems, periodic compensators are superior to time-invariant ones. We will give explicit design techniques which can be easily implemented. In the context of periodic controllers, we also consider the strong and simultaneous stabilization problems. Finally, we show that for the problem of weighted sensitivity minimization for linear time-invariant plants, time-varying controllers offer no advantage over the time-invariant ones.

672 citations

Journal ArticleDOI
R. Meyer1, C.S. Burrus1
TL;DR: A unified approach to the analysis of periodically timevarying digital filters is introduced and it is shown that this method may be used to describe both time and frequency domain responses.
Abstract: A unified approach to the analysis of periodically timevarying digital filters is introduced. It is shown that this method may be used to describe both time and frequency domain responses. By considering multirate filters as a special class of periodically time-varying filters we have characterized the frequency response of a general multirate filter. A time domain synthesis procedure for periodically varying difference equations is also presented.

428 citations

Journal ArticleDOI
G. Kranc1
TL;DR: The original sampled-data system can be represented by an equivalent system containing switches operating with the same sampling rate, and the general solution of such equivalent systems is outlined.
Abstract: A general analytical technique described in this paper permits the extension of Z -transform methods to sampled-data systems containing synchronized switches which do not operate with the same sampling rate. Sampling periods of each switch are first expressed in the form T/p_{1} ... T/p_{n} (where p_{1} ... p_{n} are integers not equal to zero) and then it is shown that each switch with a period T/p can be replaced by a system of switches and advance and delay elements where each switch operates with a sampling period T . In this way, the original sampled-data system can be represented by an equivalent system containing switches operating with the same sampling rate. The general solution of such equivalent systems is outlined in this paper.

325 citations

Proceedings ArticleDOI
01 Dec 1980
TL;DR: In this paper, the zeros of the discrete time system obtained when sampling a continuous time system are explored and theorems for the limiting zeros for large and small sampling periods are given.
Abstract: The zeros of the discrete time system obtained when sampling a continuous time system are explored. Theorems for the limiting zeros for large and small sampling periods are given. A condition which guarantees that the sampled system only has stable zeros is also presented.

299 citations