Robust Optimal Model Matching Control Design for Flexible Manipulators

Chen, Bor‐Sen; Yang, Tsang-Yi

doi:10.1115/1.2897393

Cited by 18 publications

(7 citation statements)

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“…3 for three different values of µ. As it can be observed in this figure the weights f k (µ) in (28) change sign decussately similar to the weights g B,1 −k,n in (27). It means that the derivative term of the proposed LDPID controller also has the property of subtracting many two successive (positive-weighted) samples of the error signal and then forming the cumulative sum of results.…”

Section: Generalizationmentioning

confidence: 68%

“…It means that the derivative term of the proposed LDPID controller also has the property of subtracting many two successive (positive-weighted) samples of the error signal and then forming the cumulative sum of results. However, the difference equation (28) is, compared to (27), advantageous in the way that one can adjust the amplitude of weights simply by changing the value of µ (note that in case of using (27) we have no control on the amplitude of the weights g B,1…”

Section: Generalizationmentioning

confidence: 99%

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Discrete-Time Fractional-Order PID Controller: Definition, Tuning, Digital Realization and Experimental Results

Merrikh-Bayat¹,

Mirebrahimi²,

Khalili³

2014

Preprint

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In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractionalorder PID (FOPID). Commonly, after tuning the parameters of FOPID controller, its transfer function is discretized (for realization purposes) using the so-called generating function. This discretization is the origin of some errors and unexpected results in feedback systems. It may even happen that the controller obtained by discretizing a FOPID controller works worse than a directly-tuned discrete-time classical PID controller. Moreover, FOPID controllers cannot directly be applied to the processes modeled by, e.g., the ARMA or ARMAX model. The aim of this paper is to propose a discretetime version of the FOPID controller and discuss on its properties and applications. Similar to the FOPID controller, the proposed structure applies nonlocal operators (with adjustable memory length) to the error signal. Two methods for tuning the parameters of the proposed controller are developed and it is shown that the proposed controller has the capacity of solving complicated control problems with a high performance.

show abstract

Section: Generalizationmentioning

confidence: 68%

Section: Generalizationmentioning

confidence: 99%

Discrete-Time Fractional-Order PID Controller: Definition, Tuning, Digital Realization and Experimental Results

Merrikh-Bayat¹,

Mirebrahimi²,

Khalili³

2014

Preprint

View full text Add to dashboard Cite

show abstract

“…The following non-minimum phase transfer function appears in the one-link flexible arm robot [19]: j ±…”

Section: Examplementioning

confidence: 99%

Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications

Merrikh-Bayat

Mirebrahimi

Khalili

2014

Int. J. Control Autom. Syst.

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In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractional-order PID (FOPID). Commonly, after tuning the parameters of FO-PID controller, its transfer function is discretized (for realization purposes) using the so-called generating function. This discretization is the origin of some errors and unexpected results in feedback systems. It may even happen that the controller obtained by discretizing a FOPID controller works worse than a directly-tuned discrete-time classical PID controller. Moreover, FOPID controllers cannot directly be applied to the processes modeled by, e.g., the ARMA or ARMAX model. The aim of this paper is to propose a discrete-time version of the FOPID controller and discuss on its properties and applications. Similar to the FOPID controller, the proposed structure applies nonlocal operators (with adjustable memory length) to the error signal. Two methods for tuning the parameters of the proposed controller are developed and it is shown that the proposed controller has the capacity of solving complicated control problems.

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“…Next, the following example is investigated in this study. Applying the discrete-time PI λ D µ to the system of one-link flexible robot arm [33]. And Fig.3…”

Section: A Controller Verification and Parameter Settingmentioning

confidence: 99%

Optimal Setting and Control Strategy for Industrial Process Based on Discrete-Time Fractional-Order PI$^{\lambda}$ D$^{\mu}$

et al. 2019

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Generally, the main task of the optimal operation in the industrial process is to satisfy the process technical requirements, and the PID controller is a well-known controller in industrial control applications. Nevertheless, due to the complicated mechanisms and the dynamic characteristics of a complex industrial process, the conventional PID controller fails to provide effective control to such systems. In this paper, we develop a novel discrete-time fractional order PID (DFOPID) control strategy to achieve the technical requirements of the complex industrial process. The proposed work is conducted through a combination of three novel interdependent efforts. First, on the basis of the widely used Tustin operator and its Taylor series, a digital structure of the DFOPID is proposed. Second, in order to solve the stability problem of the complex industrial process, an optimal setting of the approximation function's order (N) and five parameters (λ, µ, K p , K i , K d) is necessary. Hence, an integral time absolute error (ITAE) criterion is applied to convert the optimal setting problem to a nonconvex optimization problem. Finally, a novel intelligent optimization search algorithm called state transition algorithm is employed to carry out the aforementioned design procedure. Furthermore, the performance of the DFOPID control strategy in some practical industrial control systems, including the copper removal process and the electrochemical process of zinc are also investigated. INDEX TERMS Discrete-time system, PI λ D µ control, state transition algorithm, discretization method, complex industrial process.

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Robust Optimal Model Matching Control Design for Flexible Manipulators

Cited by 18 publications

References 0 publications

Discrete-Time Fractional-Order PID Controller: Definition, Tuning, Digital Realization and Experimental Results

Discrete-Time Fractional-Order PID Controller: Definition, Tuning, Digital Realization and Experimental Results

Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications

Optimal Setting and Control Strategy for Industrial Process Based on Discrete-Time Fractional-Order PI$^{\lambda}$ D$^{\mu}$

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