The Quadruple-Tank Process: A Multivariable Laboratory Process with an Adjustable Zero

The Quadruple-Tank Process: A Multivariable Laboratory Process with an Adjustable Zero

May 2000 | Karl Henrik Johansson, Member, IEEE
The quadruple-tank process is a multivariable laboratory process consisting of four interconnected water tanks and two pumps. The system's linearized dynamics have a multivariable zero that can be moved along the real axis by adjusting a valve. This zero can be placed in either the left or right half-plane, making the process ideal for illustrating multivariable control concepts, particularly performance limitations due to right half-plane zeros. The zero's location and direction have clear physical interpretations, making the process suitable for control education. The process is built using two double-tank processes, which are standard in many control laboratories. The system is simple but can demonstrate various multivariable phenomena. The linearized model of the quadruple-tank process has a multivariable zero that can be located in either the left or right half-plane by changing a valve. The location and direction of the zero are important for control design and have direct physical interpretations for the quadruple-tank process. The paper describes the quadruple-tank process, its physical model, and the interpretation of multivariable zeros. It also discusses the relative gain array (RGA) and its role in control structure design. The RGA is derived and shown to depend only on the valve settings. The paper also presents experimental data and validates the physical model against real process data. The quadruple-tank process is used to illustrate multivariable system identification techniques. Decentralized PI control is demonstrated, showing that it is much more difficult to control the process in the nonminimum-phase setting than in the minimum-phase setting. The paper also discusses the performance limitations of multivariable control systems due to right half-plane zeros and the importance of the zero's location and direction in control design. The quadruple-tank process is used in several courses in control education at Lund Institute of Technology and KTH, Stockholm. The process is suitable for illustrating multivariable control concepts and their limitations. The paper concludes that the quadruple-tank process is an effective tool for teaching multivariable control and its limitations.The quadruple-tank process is a multivariable laboratory process consisting of four interconnected water tanks and two pumps. The system's linearized dynamics have a multivariable zero that can be moved along the real axis by adjusting a valve. This zero can be placed in either the left or right half-plane, making the process ideal for illustrating multivariable control concepts, particularly performance limitations due to right half-plane zeros. The zero's location and direction have clear physical interpretations, making the process suitable for control education. The process is built using two double-tank processes, which are standard in many control laboratories. The system is simple but can demonstrate various multivariable phenomena. The linearized model of the quadruple-tank process has a multivariable zero that can be located in either the left or right half-plane by changing a valve. The location and direction of the zero are important for control design and have direct physical interpretations for the quadruple-tank process. The paper describes the quadruple-tank process, its physical model, and the interpretation of multivariable zeros. It also discusses the relative gain array (RGA) and its role in control structure design. The RGA is derived and shown to depend only on the valve settings. The paper also presents experimental data and validates the physical model against real process data. The quadruple-tank process is used to illustrate multivariable system identification techniques. Decentralized PI control is demonstrated, showing that it is much more difficult to control the process in the nonminimum-phase setting than in the minimum-phase setting. The paper also discusses the performance limitations of multivariable control systems due to right half-plane zeros and the importance of the zero's location and direction in control design. The quadruple-tank process is used in several courses in control education at Lund Institute of Technology and KTH, Stockholm. The process is suitable for illustrating multivariable control concepts and their limitations. The paper concludes that the quadruple-tank process is an effective tool for teaching multivariable control and its limitations.
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Understanding The quadruple-tank process%3A a multivariable laboratory process with an adjustable zero