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Coprime Factor Reduction of Parameter Varying Controller
Roberd Saragih,Widowati 대한전기학회 2008 International Journal of Control, Automation, and Vol.6 No.6
This paper presents an approach to order reduction of linear parameter varying controller for poly topic model. Feasible solutions which satisfy relevant linear matrix inequalities for constructing full-order parameter varying controller evaluated at each poly topic vertices are first found. Next, sufficient conditions are derived for the existence of a right coprime factorization of parameter varying controller. Furthermore, a singular perturbation approximation for time invariant systems is generalized to reduce full-order parameter varying controller via parameter varying right coprime factorization. This generalization is based on solutions of the parameter varying Lyapunov inequalities. The closed loop performance caused by using the reduced order controller is developed. To examine the performance of the reduced-order parameter varying controller, the proposed method is applied to reduce vibration of flexible structures having the transverse-torsional coupled vibration modes.
Balanced Truncation for Unstable Infinite Dimensional Systems Via Reciprocal Transformation
Fatmawati,Roberd Saragih,Riyanto T. Bambang,Yudi Soeharyadi 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.2
We discuss a model reduction for unstable infinite dimensional systems using balanced truncation of reciprocal systems. The systems considered are assumed to be exponentially stabilizable and detectable, with bounded and finite rank input and output operators. We decompose the systems into their stable and unstable parts and perform reciprocal transformation only on the stable part. Bal-anced truncation is carried out on the reciprocal systems. This yield is then translated using reciprocal transformation as the reduced-order model of the stable part. Finally, we added the unstable part to the reduction of the stable part as the overall reduced-order model for the systems. To verify the effectiveness of the proposed approach, numerical simulations are applied to the heat equation. The performance of the proposed reduction method is compared to the balanced truncation method.
Bilinear Robust Control Design for Virotherapy Model
Anita Kesuma Arum,Roberd Saragih,Dewi Handayani 제어로봇시스템학회 2019 제어로봇시스템학회 국제학술대회 논문집 Vol.2019 No.10
In this paper we concerned with the application bilinear robust control for virotherapy model. In designing the controller, it requires a solution to the state dependent algebraic Riccati equation (SDARE). However, it is difficult to solve the SDARE. Successive method is one of the methods that can be used to solve this issue. The idea of this method is converting the bilinear systems into time-varying linear system. This method has the following step: firstly, we need to obtain the robust control for the linear system by ignoring the multiplicative term of bilinear system. Second, convert the bilinear systems into the time-varying linear systems using the previous result, and then solve the SDARE by the new performance index and the associated Hamilton-Jacobi-Isaacs equation. Last, iterate the steps until the convergence of state satisfied. The virotherapy model has been widely developed and can be considered as a model in bilinear system. There are four groups in this model: quiescent cells (Q), cancer cells (S), virus (V), and infected cells (I). Virus are injected into the human body as the control input to control the amount of the cancer cells. In this case, virus can only infect the cancer cells, and the infected cells will die when the lysis process occurs. Virus, as a control, is given with the aim of minimizing the energy used in the system. In this model we consider the body"s immune response as an additive disturbance to the model. From the simulation results, it is shown that virotherapy can reduce the number of cancer cells in the body on day 50th, so the number of cancer cells in the body is only 16.6%. Based on the simulation, the next virototherapy can be done after the day 50th.
Control Design on a Non-minimum Phase Bilinear System by Backstepping Method
Ahmadin,Janson Naiborhu,Roberd Saragih,Khozin Mu’tamar 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.10
In this paper, we construct a control design of a non-minimum phase bilinear system. Here we apply a coordinate transformation to determine the normal form and the relative degree of the system with a particular class. We use the backstepping method to determine the control variable so that the bilinear system becomes stable. From this design, the output system can track the desired output.