Crc Press Mechatronics Handbook 2002 By Laxxuss Episode 3 Part 13 pptx

resulting force, which actuates on the valve spool. (33.3) The displacement x v , obtained based upon the mentioned equations, is implemented in SIMULINK using the scheme from Fig. 33.7. This module of nonlinear MM includes two stages of electrohydraulic axis: the electrohydraulic and the hydromechanical one. The corresponding equations for the four flows that go through the servovalve are (33.4) where Q PA [m 3 /s], the flow to the hydraulic motor, from pump to the chamber A of the motor; Q AT [m 3 /s], the flow from the chamber A to reservoir; Q PB [m 3 /s], the flow from pump to the chamber B of the motor; Q BT [m 3 /s], the flow from the chamber B to reservoir; α D [-], the discharge coefficient; D v [m], the spool’s diameter; x 0 [m], the dimension of the lap of the spool; x v [m], the spool’s displacement; p A [N/m 2 ], the fluid pressure in chamber A ; p B [N/m 2 ], the fluid pressure in chamber B [kg/m 3 ] fluids density. The flows, which are transmitted to LHM and evacuated from LHM, are Q A and Q B , which are computed as following: (33.5) The lap of the spool is considered to be zero ( x 0 = 0), and, therefore, the static characteristic is linear around the origin and also in the rest. With Q 0 = α D ⋅ π ⋅ D v ⋅ , the flow equations become (33.6) Nonlinear Mathematical Model of Linear Hydraulic Motor The differential equations, based on which the MM of the linear hydraulic motor (LHM) was achieved, are i. the equation of the dynamic equilibrium of the forces reduced to the motor’s rod, and ii. the equation of movement and flow continuity. FIGURE 33.7 Nonlinear MM of the first stages of the servovalve. + x v max U ref 2 D v w 0 v 2 e + Σ K UI K IF + x v max I x v w 0 2 / c F F / m Σ − . x v x v . w 0 v 2 + − − − − x ˙˙ v t() 2 . D v . w 0v . x ˙ v t() w 0v 2 . x v t() ∑F m =++ x ˙˙ v t() k ∗ 2 . D v . w 0v . x ˙ v t() w 0v 2 . x v t()– where k ∗ ∑F m =–= Q PA a D . p . D v . 2 r . x 0 x v t()+(). p P p A t()– , x v x 0 , x max –[]∈= Q AT a D . p . D v . 2 r . x 0 x v – t()(). p A t() p T – , x v x max , x 0 –[]∈= Q PB a D . p . D v . 2 r . x 0 x v – t()(). p P p B t()– , x v x max , x 0 –[]∈= Q BT a D . p . D v . 2 r . x 0 x v t()+(). p B t() p T – , x v x 0 , x max –[]∈= Q A Q PA Q AT , Q B Q BT Q PB –=–= 2/r Q PA Q 0 . x v . p P p A – ,= Q AT Q 0 . x v –() . p A p T –= Q PB Q 0 . x v –() . p P p B – ,= Q BT Q 0 . x v . p B p T –= 0066_frame_Ch33.fm Page 6 Wednesday, January 9, 2002 8:00 PM ©2002 CRC Press LLC resulting force, which actuates on the valve spool. (33.3) The displacement x v , obtained based upon the mentioned equations, is implemented in SIMULINK using the scheme from Fig. 33.7. This module of nonlinear MM includes two stages of electrohydraulic axis: the electrohydraulic and the hydromechanical one. The corresponding equations for the four flows that go through the servovalve are (33.4) where Q PA [m 3 /s], the flow to the hydraulic motor, from pump to the chamber A of the motor; Q AT [m 3 /s], the flow from the chamber A to reservoir; Q PB [m 3 /s], the flow from pump to the chamber B of the motor; Q BT [m 3 /s], the flow from the chamber B to reservoir; α D [-], the discharge coefficient; D v [m], the spool’s diameter; x 0 [m], the dimension of the lap of the spool; x v [m], the spool’s displacement; p A [N/m 2 ], the fluid pressure in chamber A ; p B [N/m 2 ], the fluid pressure in chamber B [kg/m 3 ] fluids density. The flows, which are transmitted to LHM and evacuated from LHM, are Q A and Q B , which are computed as following: (33.5) The lap of the spool is considered to be zero ( x 0 = 0), and, therefore, the static characteristic is linear around the origin and also in the rest. With Q 0 = α D ⋅ π ⋅ D v ⋅ , the flow equations become (33.6) Nonlinear Mathematical Model of Linear Hydraulic Motor The differential equations, based on which the MM of the linear hydraulic motor (LHM) was achieved, are i. the equation of the dynamic equilibrium of the forces reduced to the motor’s rod, and ii. the equation of movement and flow continuity. FIGURE 33.7 Nonlinear MM of the first stages of the servovalve. + x v max U ref 2 D v w 0 v 2 e + Σ K UI K IF + x v max I x v w 0 2 / c F F / m Σ − . x v x v . w 0 v 2 + − − − − x ˙˙ v t() 2 . D v . w 0v . x ˙ v t() w 0v 2 . x v t() ∑F m =++ x ˙˙ v t() k ∗ 2 . D v . w 0v . x ˙ v t() w 0v 2 . x v t()– where k ∗ ∑F m =–= Q PA a D . p . D v . 2 r . x 0 x v t()+(). p P p A t()– , x v x 0 , x max –[]∈= Q AT a D . p . D v . 2 r . x 0 x v – t()(). p A t() p T – , x v x max , x 0 –[]∈= Q PB a D . p . D v . 2 r . x 0 x v – t()(). p P p B t()– , x v x max , x 0 –[]∈= Q BT a D . p . D v . 2 r . x 0 x v t()+(). p B t() p T – , x v x 0 , x max –[]∈= Q A Q PA Q AT , Q B Q BT Q PB –=–= 2/r Q PA Q 0 . x v . p P p A – ,= Q AT Q 0 . x v –() . p A p T –= Q PB Q 0 . x v –() . p P p B – ,= Q BT Q 0 . x v . p B p T –= 0066_frame_Ch33.fm Page 6 Wednesday, January 9, 2002 8:00 PM ©2002 CRC Press LLC 34 Design Optimization of Mechatronic Systems 34.1 Introduction 34.2 Optimization Methods Principles of Optimization • Parametric Optimization • General Aspects of the Optimization Process • Types of Optimization Methods • Selection of a Suitable Optimization Method 34.3 Optimum Design of Induction Motor (IM) IM Design Introduction • Classical IM Design Evaluation • Description of a Solved Problem • Achieved Results 34.4 The Use of a Neuron Network for the Identification of the Parameters of a Mechanical Dynamic System Practical Application 34.1 Introduction Electromechanical systems form an integral part of mechanical and mechatronic systems. Their optimi- zation is a necessary condition for a product to be competitive. In engineering practice, a large number of optimization and identification problems exist that could not be solved without the use of computers [5]. The present level of technological development is characterized by increasing the performance of machines with the production costs kept at a satisfactory level. The demands on the reliability and safety of operation of the designed machines are also considerable. From practical experience we know that the dynamic properties of electromechanical systems have a considerable influence on their reliability and safety. On the other hand, the tendency to push the price of a machine down often leads to unfavorable dynamic properties that result in increased vibrations and noise during operation. Also, electrical properties dramatically deteriorate as the amount of active materials in a machine is reduced. The increased load leads to, among other things, excessive heat formation, which, in turn, has a negative effect on insulation, shortening the service life of a machine. 34.2 Optimization Methods Principles of Optimization The properties of electromechanical systems can be described mathematically using physical quantities. The degree of these properties is then described using mathematically formulated objective (preference) functions. Structural parameters ranging between limit values given as satisfying secondary conditions are the independent variables of these functions. The particular form of the functions depends on the type of machine and its mathematical description. The solutions of a mathematically formulated optimization Tomas Brezina Technical University of Brno Ctirad Kratochvil Technical University of Brno Cestmir Ondrusek Technical University of Brno ©2002 CRC Press LLC . Q BT Q 0 . x v . p B p T –= 0066_frame_Ch 33. fm Page 6 Wednesday, January 9, 2002 8:00 PM 2002 CRC Press LLC resulting force, which actuates on the valve spool. (33 .3) The displacement x v ,. Q BT Q 0 . x v . p B p T –= 0066_frame_Ch 33. fm Page 6 Wednesday, January 9, 2002 8:00 PM 2002 CRC Press LLC 34 Design Optimization of Mechatronic Systems 34 .1 Introduction 34 .2 Optimization Methods . actuates on the valve spool. (33 .3) The displacement x v , obtained based upon the mentioned equations, is implemented in SIMULINK using the scheme from Fig. 33 .7. This module of nonlinear