VU 325.019 State Space Control of MIMO Systems
In Control Automation there are generally two methodical approaches - the so-called "classic" and the "modern methods". The classic approach mostly includes PID controllers and corresponding methods for their design and is covered by the basic lectures. In doing so, problems are usually considered in which a controlled variable is to be controlled with the aid of a manipulated variable under the influence of disturbances.
In the many practical applications, however, it is necessary to keep several controlled variables at a set value at the same time or to guide them along trajectories. The controlled and manipulated variables are often strongly linked and the desired behavior of the controlled system can only be achieved through coordinated intervention on several actuators. In such cases, i.e. when the coupling between the manipulated and/or controlled variables cannot be neglected, multivariable control systems are used.
In this context, the "modern methods" of control engineering enable a more formal mathematical approach to the design of control loops. In this way, the treatment of complex multivariable systems is formalized and significantly simplified. The controlled system is described by a so-called state space system, the strength of which lies in the fact that multiple-input-multiple-output (MIMO) systems are represented in the same way as single-input-single-output (SISO) systems. The state space representation thus enables the design of complex multivariable control systems, such as those used in vehicle and flight control.
This lecture is initially devoted to the modeling of single and multivariable systems in the state space, as well as the possibilities for the analysis and the transformation of state space systems. The other contents of the VU include the design of state controllers for single and multi-variable systems, whereby in the latter case special attention is paid to the decoupling of the control loops. The design of state observers for the single and multi-variable case is explained analogously. The practical application of the methods presented is illustrated using examples from current research projects (e.g. state of charge monitor for traction batteries).
When designing linear controllers, it is always assumed that the operating point of the system under consideration can be described with sufficient accuracy by the linear model. The aim of this course is also to give insights into the controller design for non-linear multivariable systems. Using exact linearization, a non-linear state controller is designed in such a way that the non-linearity of the system is compensated and a linear control loop is created again overall.
Another chapter covers the controller design through optimization (Linear Quadratic Regulator, LQR). The design goal here is no longer the placement of poles of the closed control loop, but the minimization of a cost function that takes into account the future course of the system state. This methodology enables intuitive access to tune the controller or to achieve the desired control performance. The VU is supported by extensive examples that are available to students as complete MATLAB/Simulink packages (e.g. ESP control, damping of torsional vibrations, multi-tank system).
Through the comprehensive use of MATLAB/Simulink, the participants should be able to design complex multivariable control systems and test them in the simulation. The areas under consideration also form a solid basis for further research projects at the Department of Control Engineering and Process Automation (Institute for Mechanics and Mechatronics).