Control and Optimization of Mechatronic Systems | 12 | v2

ABSTRACT

Control of mechatronic systems is aimed to ensure best performance and achievable capabilities (functionality, controllability, stability, robustness, and immunity) by designing sound control laws and implementing them by analog or digital controllers. One needs to design closed-loop electromechanical systems optimizing their dynamic behavior, thereby enabling the steady-state performance as well. As was emphasized in Chapter 1, optimization may have a broader meaning and implies various aspects leading to distinct tasks. The optimization in the behavioral domain by means of controlling is considered with the ultimate objective to ensure best performance and achievable capabilities assuming optimal design in the structural and functional domains. In this chapter, the dynamic (behavioral) optimization problems, under their narrow meaning, will be solved by synthesizing optimal control laws which should be sound from device physics and implementable from hardware standpoints. We focus on the solution of various control problems to improve dynamics, efﬁciency, acceleration, and accuracy. Control and optimization in the behavioral domain are closely related problems, and frequently, they are used interchangeably. In fact, in order to design optimal control algorithms (called control laws and sometime controllers), one solves the optimization problem by minimizing the performance functionals and uses various stability criteria. This chapter documents various methods in the design of closed-loop system applying

sound methods. Some methods of control theory result in control laws which assume that all state variables are directly or indirectly measurable or observable. Many variables cannot be measured or observed. Therefore, minimal-complexity optimal control laws are synthesized to (1) guarantee near-optimal performance (capabilities), (2) minimize system complexity, and (3) ensure hardware-software soundness. Mechatronic systems integrate a variety of components. Due to the fast dynamics of ICs

and sensors, the overall behavior of electromechanical systems is usually predeﬁned by the dynamics of electromechanical motion devices with the attached kinematics. The basics of electromagnetics, energy conversion, torque production, and other important descriptive featureswere studied. Thederivedmathematicalmodels, in the formofnonlinear differential equations, allow one to accomplish analysis and control tasks. Closed-loop systems are designed to ensure the best performance as measured against a

spectrum of speciﬁcations and requirements. Analog and digital controllers can be derived and implemented for a large class of dynamic systems. The hardware solutions predeﬁne system performance and capabilities, while control laws affect the system performance and capabilities. For example, for a high-performance 30 kW electric drive (automotive application), through the structural design one deﬁnes that a permanent-magnet synchronous

Analysis, and Design with

motor with a pulse-width modulation (PWM) ampliﬁer should ensure the best performance and capabilities. This electric drive is open-loop stable and operational. However, the tracking control should be ensured by synthesizing a tracking controller, thereby guaranteeing cruise control features. Unsound design may lead to control laws which may destabilize the stable system (leading to unstable closed-loop system) or to control laws which may degrade the overall performance. Efﬁciency, stability, robustness, accuracy, and disturbance attenuation are obvious criteria among other requirements. Minimization of tracking error and settling time may result in an attempt to apply some methods yielding high feedback gains or discontinuous (relay-type) control laws. The chattering phenomena, oscillatory dynamics, losses, low efﬁciency, and other undesirable phenomena are observed in relay-type and highgain control laws. Therefore, control lawswhich could be sound frommathematical prospective may not be applicable or may be inadequate to various electromechanical systems. The designer must apply sound methods including minimal-complexity control which result in minimal-complexity hardware solutions. The speciﬁcations imposed on closed-loop systems are given in the performance (behav-

ioral) and capability domains, which are related. The features and criteria under the consideration can be

. Electromagnetics-centered control soundness and efﬁciency: Control laws should be designed utilizing device physics integrating energy conversion, torque production, etc.