Relation Between Model Feedback Control Systems and Parameterization of All Stabilizing Controllers

2012 9th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technolog

Murakami

et al. 2012

Self Cite

In the present paper, we examine the parameterization of all robust stabilizing Internal Model Controllers (IMCs) for multiple-input/multiple-output plants with uncertainties. The parameterization problem is the problem in which all stabilizing controllers for a plant are sought. Since this parameterization can successfully search for all proper stabilizing controllers, it is used as a tool for many control problems. For stable plants, the parameterization of all stabilizing controllers can be represented by the IMC structure. The IMC structure has advantages such as closed-loop stability is assured simply by choosing a stable IMC parameter. Additionally, closed-loop performance characteristics are related directly to controller parameters, which make online tuning of the IMC very convenient. However, there exists a question whether or not, stabilizing controllers for unstable plants can be represented by the IMC structure. The solution to this problem, Morari and Zafiriou, Chen et al. and Mai et al. clarified that any stabilizing controller for unstable plants can be represented by the IMC structure by the parameterization of all stabilizing IMCs for unstable plants. However, their IMCs cannot guarantee the stability of control system for plants with uncertainties. In this paper, we clarify the parameterization of all proper robust stabilizing IMCs for multiple-input/multipleoutput plants such that the IMC and the internal model are proper.

Section: ) Rankmentioning

confidence: 99%

The parameterization of all robust stabilizing Internal Model Controllers for multiple-input/multiple-output plants

2012 9th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technolog

Murakami

et al. 2012

Self Cite

“…Yamada overcame these problems and proposed the parameterization of all proper internally stabilizing controllers for single-input/single-output minimum-phase plants [8]. The parameterization of all stabilizing controllers in [8] is applied to many control problems such as the parameterization of all stabilizing modified repetitive controllers for minimum-phase plants [10], adaptive control systems [11,12], model feedback control systems [13], parallel compensation technique [14], PI control [15] and PID control [16]. If the parameterization of all stabilizing controllers for multipleinput/multiple-output minimum-phase plants is obtained, results in [10,11,12,13,14,15,16] are expanded for multiple-input/multiple-output minimum-phase plants.…”

Section: Introductionmentioning

confidence: 99%

“…The parameterization of all stabilizing controllers in [8] is applied to many control problems such as the parameterization of all stabilizing modified repetitive controllers for minimum-phase plants [10], adaptive control systems [11,12], model feedback control systems [13], parallel compensation technique [14], PI control [15] and PID control [16]. If the parameterization of all stabilizing controllers for multipleinput/multiple-output minimum-phase plants is obtained, results in [10,11,12,13,14,15,16] are expanded for multiple-input/multiple-output minimum-phase plants. From these viewpoints, Yamada et al examined the parameterization of all stabilizing controllers for multiple-input/multiple-output minimum-phase plants [9].…”

Section: Introductionmentioning

confidence: 99%

A Design Method for Internal Model Controllers for Multiple-Input/Multiple-Output Unstable Plant

Murakami

et al. 2011

KEM

In the present paper, we examine the parameterization of all stabilizing Internal Model Controllers(IMC) for multiple-input/multiple-output unstable plant. The parameterization problem is theproblem in which all stabilizing controllers for a plant are sought [1, 2, 3, 4, 5, 6, 7, 8, 9]. Since this parameterizationcan successfully search for all proper stabilizing controllers, it is used as a tool for manycontrol problems. However, there exists a problem whether or not stabilizing controllers for unstableplant can be represented by IMC structure. The IMC structure has advantages such as closed-loop stabilityis assured simply by choosing a stable IMC parameter. Additionally, closed-loop performancecharacteristics are related directly to controller parameters, which makes on-line tuning of the IMCvery convenient[6]. The solution to this problem, Morari and Zafiriou[6] examined the parameterizationof all stabilizing IMC for unstable plant. Their parameterization remains difficulties. Their internalmodel is not necessarily proper. In addition, their parameterization includes improper IMC. In order toovercome these problems, Chen et al. proposed a design method for IMC for minimum-phase unstableplant[17]. However, the method proposed by Chen et al. cannot apply for multiple-input/multipleoutputunstable plant. Because many of actual plants are multiple-input/multiple-output plants, consideringfor multiple-input/multiple-output unstable plant is important. In this paper, we propose theparameterization of all proper stabilizing IMC for multiple-input/multiple-output unstable plant suchthat the IMC and the internal model are proper. In addition, we present an application of the result forcontroller design for multiple-input/multiple-output time-delay plant.

“…If the MFCS can represent all of the stabilizing controllers for a plant, then the model feedback control structure is more useful and important than if all stabilizing controllers are not thus represented. Yamada and Moki considered the problem such that the relation between the MFCS and the parameterization of all stabilizing controllers for minimum phase plants and clarified that the MFCS has the same structure of all stabilizing controllers for minimum phase plants [7]. However, no research has been reported whether or not MFCS can represent all of the stabilizing controllers for a non-minimum phase plant.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this paper is to expand the result in [7] and to give a solution to the question as to whether or not all stabilizing controllers for a class of non-minimum phase plant are expressible in the MFCS structure. A simple design method to specify the control characteristics is also presented.…”

Section: Introductionmentioning

confidence: 99%

Study on the Model Feedback Control System for a Class of Non-Minimum Phase Systems

Moki

et al. 2011

KEM

In the present paper, we examine model feedback control systems (MFCSs). Because MFCSis simple, the MFCS has been applied in many applications such as the trajectory control of robotmanipulators, serially connected water tanks, etc. The control structure of the MFCS is limited, butYamada and Moki reported about whether or not MFCS can represent all of the stabilizing controllersof a minimum phase plant. However, no research has been reported whether or not MFCS can representall of the stabilizing controllers of a non-minimum phase plant. The purpose of the present paper isto give a solution to the question as to whether or not all of the stabilizing controllers for a plantare expressible in the MFCS structure. The relation between MFCS and the parameterization of allstabilizing controllers for a class of non-minimum phase plants is shown. A simple design method tospecify control characteristics is also presented.