Intelligent Control for Artificial Damping in Hydraulic Crane Systems under Load Dynamics

Transcription

1 Intelligent Control or Artiicial Damping in Hydraulic Crane Systems under Load Dynamics Yang Yong,, Karl-Erik Rydberg 3. College o Inormation Science & Technology, Central South University, Changsha, China. Changsha University o Science & Technology, Changsha, China Yang_99@63.com 3. Department o Mechanical Engineering, Linköping University, SE Linköping, Sweden karry@ikp.liu.se Abstract In this paper, an intelligent uzzy-pi compound control which is composed o a uzzy control, a eedorward proportional control and an intelligent integral control, is proposed to adjust the damping in a hydraulic crane system under load dynamics. Position and pressure signals in the hydraulic system are ed back to control the damping o the crane tip. That the right artiicial damping without high losses in dynamical perormance will be realized by adding the compound control into the crane system. Simulation results show that this intelligent uzzy-pi eedback control can eectively coordinate the damping and dynamical characteristic in the hydraulic damping system. Also the adaptation o the system to dierent load conditions can be made stronger. Keywords Artiicial damping, hydraulic crane systems, load dynamics, intelligent uzzy-pi control Introduction Most o today s mobile machines with proper drive and working hydraulics have the problem o low requency oscillations during action []. As an example, the dynamics o a crane structure is complex. The hydro-mechanical system has a quite low damping. The resonance requencies o the hydraulic and mechanical systems are staying in a narrow range, which result in oscillation problems. Hereby, the machine rame and working parts are oscillating intensively and the driving velocity has to be reduced, especially during transporting heavy loads. O course, this will result in the lower productivity o the machine as well as worst operating conormability. To meet the needs o varying work environments, dierent hydraulic systems need dierent damping. In an open loop hydraulic system the damping is mainly determined by the characteristics o the control valves. Generally, high hydraulic damping in the system means high losses and slow response, but strong stability. On the contrary, low hydraulic damping in the hydraulic system means low power losses and ast response, but may result in system oscillations. Thus, the hydraulic mechanical system should be stabilized by designing an appropriate controller which adaptively adjusts the damping in real-time. In the past mobile hydraulic applications, passive oscillation damping systems are widely used based on high pressure hydro-pneumatic accumulators. The high cost or high pressure equipments and no adaptation are the main drawbacks in the passive oscillation damping systems. One demand or mobile machinery is to develop active oscillation or artiicial damping techniques. By introducing electronic eedback control the damping in the hydraulic system can be adjusted artiicially and smooth control with high damping can be implemented without high losses and slow response. At present, active or quasi-active oscillation damping systems are realized by means o various kinds control technologies [,]: irst and special damping approaches; damping by orce control; damping by pressure control; damping by velocity control; damping by combined

2 control; damping by acceleration control; damping by displacement control; and so on. Due to the simplicity o operation, ease to design, inexpensive maintenance, satisactory cost-eectiveness or more than 90% lower-order linear and quasi-linear industrial systems, the conventional proportionalintegral-derivative (PID) control has been extensively applied to industrial process control. However, the conventional PID controller could not work satisactorily or high-order time-variance linear or nonlinear systems. Since the concept o uzzy sets was irst put orward by Zadeh [3], a variety o uzzy technique applications have been ound worldwide. One o the most successul applications o uzzy sets is uzzy control [4]. In recent years, uzzy logic techniques combined with PID control leads to a compound uzzy-pid control [4]. The combination orms o PID and uzzy logic might be lexible and diversity. In this paper, an intelligent uzzy-pi controller is proposed to control the damping o the crane tip. Pressure and piston position signals o the hydraulic crane system are measured and ed back to the controller. Simulation results show that the damping o the crane is increased and the operation precision can be achieved satisactorily. by the pressure coeicient and the valve opening. Fig.: The test-up o a lorry crane Especially, the pressure low coeicient dominants the damping o the hydraulic systems. And the magnitude o this coeicient varies with the operation points. In order to improve the damping o the hydraulic crane, a position eedback control is introduced into the valve-controlled system, while a second eedback signal is chosen as the pressure o the piston chambers which can relect the load dynamics. Hydraulic Crane Model and Its Damping Problem The mechanical structure o mobile hydraulic applications is requently subjected to heavy oscillations because o the rough treatments by the operator or rapidly changing working conditions. These oscillations should be avoided since they limit the overall system perormance and might cause dangerous damage to the mechanical parts o mobiles. Mobile luid power systems, such as lorry crane shown in Fig., tend to oscillate because the luid in the hydraulic systems as well as the mechanical stucture has low stiness and generally acts like a spring. A orce is produced by a hydraulic piston and controlled by a hydraulic servo valve. The reasons or the oscillations in mobile hydraulic systems mainly lie on the damping states o both the hydraulic systems and mechanical parts. Viscous riction is the main course o damping against oscillations, while the low characteristics o the valve which are determined Fig.: Hydraulic eedback control system The crane jib can be looked as a two-degrees-o reedom system, because the jib itsel acts as a spring with a determined spring stiness while the load at the crane tip is regarded as a lump mass. Under this situation, a simpliied model shown in Fig. or the servo valve opening is expressed as ollows. X v K [( Y X ) K * P ] () * re le where X v is the servo valve opening (m), K is eedback control gain (-), K is pressure eedback gain (-), Y r is reerence input (m), X is piston position (m), P lev is the load pressure which is expressed as ollows. P le P A P A ()

3 where P and P are the piston pressures (Pa) in Chamber and, respectively, A and A are piston areas (m ), respectively. In order to reduce the inluence o pressure signal on steady state error, the load pressure is iltered with a irst-order high pass ilter beore it is ed back. This ilter is given by G hp ( s ) s s + ω where ω hp is the ilter break requency (Hz). Meanwhile, a second-order low pass ilter shown in Eq. (4) is chosen to adapt to the valve s response speed. G (s) hp ω s + δ ω + ω where ω is the ilter break requency (Hz), δ is the eective damping (-). (3) (4) The input values o the controller are the system error (e(k)) and the incremental change o the system error ( e(k)) o the system error which are deined as, respectively. e ( k ) E ( k ) / (5) K e e( k) E( k) / K (6) where K e and KΔe are the scaling actors o the system error and change o system error. The output value is the uzzy control change ( U ) expressed as ollows u e ( k ) u ( k ) + u ( k ) (7) u ( k ) U ( k ) K (8) where U (k) and K u are the uzzy output o controller and the scaling actors o the controller output at the time kt, respectively. u 3 Design o Intelligent Fuzzy-PI Controller or Crane Damping In this paper, an intelligent uzzy-pi controller is designed, as shown in Fig. 3. The design o the intelligent uzzy-pi controller consists o the ollowing three steps. Fig. 3: Intelligent Fuzzy-PI control o crane system 3.. Fuzzy Reerence The uzzy set regions o input variables {E, E} and output variables U are all chosen as the ollows linguistic variables {PB, ZR, NB}, respectively, where PB represents Positive Big, ZR Zero, NB Negative Big, respectively. In the paper, the membership unctions are applied to deine the uzzy sets o the inputs and output variables, as illustrated in Fig.4. The Max-Product inerence method is adopted to determine the whole membership unction o the uzzy control output, which is expressed as ollowing Eq. (9). µ µ, µ ) max{ µ µ } (9) ( U l E i E j E i E j 3. Fuzzy Controller The design o the uzzy controller consists o three main steps: uzziication, uzzy reasoning, and deuzziication. The input signals are irst uzziied to allow a structured uzzy representation o the input signals. These uzzy signals are then ed into a uzzy inerence engine which can be a loop-up table or a series o IF-THEN statements. The engine produces a structured description o the control action which must be urther deuzziied to get a non-structured (traditional numerical) control output to drive the system. 3.. Fuzziication Fig. 4: Membership unctions o FC Table : Fuzzy control rules E U E NB ZR PB NB NB NB ZR ZR NB ZR PB PB ZR PB PB

4 Each linguistic term has been descried by a related membership unction as shown in Fig. 4. A uzzy rules base can be established rom expert experience and knowledge, which makes it easier to realize artiicial intelligent control. Based upon the uzzy IF-THEN rules description manner, a uzzy control rules base can be expressed as in Table Deuzziication The center o gravity method is selected or deuzziication operation. Thus, the control output is obtained in Eq. (0). U m l µ l U l (0) m l where μ l is the grade o the lth output membership unction, Δ U l is the output label or the value contributed by the lth membership unction, ΔU is the output variable, m is the rules number. 3. Intelligent Integral Controller Fig. 5 shows the general step response o a common nonlinear system. Dierent process stage has dierent dynamical characteristic. An adaptive intelligent integral action u i (k) is introduced into the control signal to meet the need o dynamical process. An intelligent integral can not only improve the control precision but also increase response speed. µ l Z, a hold action can be chosen to let the system states move continuously toward desired place, i.e. u i (k)hold; (3) In the area o Z3, a reset action can be used to limit or reduce the possibility o overshoot as could as possible, i.e. u i (k)reset;(4) In the area o Z4, an integral action should be added to eliminate the steady state error o the system, i.e. u i (k)integral;(5) In the area o Z5, a reset action is used and integral saturation should be avoided, i.e. u i (k)reset. Fig. 6: Phase plane o system error and system error change 3.3 Feedorward P Controller The proportional-integral-derivative (PID) controller is widely used in various control ields because o its simple structure and robust perormance. Here, a eedorward proportional control is expressed as u ( k ) K Y () p p where K p is eedorward proportional gain. Thereore, the sum control input into the system rom the intelligent uzzy-pi controller is represented as r u ( k ) u ( k ) + u ( k ) u ( k ) () p + where u p (k), u (k), and u i (k) are the eedorward proportional control, uzzy control, and intelligent integral control, respectively. i Fig. 5: Step response o a common nonlinear system Fig.5 can also be expressed by using the ollowing phase plane shown in Fig.6. The system error and its change can be divided into ive areas rom Z to Z5. The intelligent integral action u i (k) include three states: integral, hold, and reset. These three integral actions are utilized due to the dierent response stages. As an example, () In the area o Z, an integral action can be used to orce the system states move toward desired place as soon as possible, i.e. u i (k)integral;() In the area o 4 Simulation Experimental Results and Discussions A HIAB 070 lorry crane in a lab is shown in Fig.. This crane is controlled by a Vickers proportional valve which is equipped with electrohydraulic controllers. The hydraulic power supply is a constant pressure system. And the hydraulic pistons o the crane are itted with built-in position transducers and both piston chambers with pressure sensors. A PC 586 is employed to control the damping system. In order to transer the data between

5 computer and test-up, an IQAN (intelligent CAN) produced by Parker Co. Ltd is equipped to control and monitor the crane s dynamics. A co-simulation method o Matlab and HOPSAN [] is adopted to study crane damping under load dynamics. To some extend, the position o the piston rod relects the control precision, while the dynamical perormance o the crane lorry is relected by the acceleration o the crane tip which contains the inormation on the oscillations magnitude or damping as well as response speed. In order to veriy the eectiveness o the proposed controller or the crane damping, simulation experiments are done. The reerence input signal to the servo valve is a step with cm amplitude. Simulation results are shown in Figs. 7~8. Fig. 7: Step response o crane system keeping a higher damping under load dynamics. This hes improve both the productivity and operation saety. 5 Conclusions Active controlled damping is a very important issue in the applications o mobile hydraulic systems. This paper proposes an intelligent uzzy-pi control or damping control in a hydraulic crane system. A basic uzzy controller, a eedorward proportional control and an intelligent integral control are combined to be a compound controller. A simple simulation model o the crane jib is created consisting only o two masses and a spring which are actuated through a hydraulic piston. The simulation results show that the crane tip oscillations decay aster when pressure and position eedbacks are applied. By using intelligent uzzy-pi control, the damping o the crane tip under load dynamics can be eectively controlled. Meanwhile, the proposed uzzy-pi control is a valuable way o combining the conventional PID control with artiicial intelligence to solve the conliction between ast response and high damping in the application o hydraulic damping crane. And no rigorous mathematical model o the system is necessary or the design o the controller. Acknowledgement---The irst author would like to thank or the supports o the Natural Science Foundation o Hunan (Grant: 04JJ6033), and the Research Foundation o Hunan Education Bureau (Grant: 03C066) Reerences: Fig.8: Step response o crane system In Fig. 7 the piston rod position (continued line), the acceleration o the crane tip (dashed line), the reerence input (Y r 0.6 m) to the system are shown only under a pure position eedback control. Fig. 8 shows the same three signals as in Fig.7 but under the intelligent uzzy-pi control. It can be easily seen that the damping o the crane in Fig.7 is not so strong as that in Fig. 8. Compared the results in Fig.8 to that in Fig.7, it can also be ound that the intelligent uzzy-pi control has a superior ability o making the hydraulic crane response ast as well as [] Rahmeld, R., Ivantysynova, M.. An overview about active oscillation damping o mobile machine structure. International Journal o Fluid Power, Vol.5(), pp. 5-4, 004. [] Krus, P.. Damping o luid power systems in machines with high inertia loads. Linköping Studies in Science and Technology, Thesis No. 98, Linköping University, Linköping, 994. [3] Zadeh, L. A.. Fuzzy sets. Inormation and Control, Vol. 8, pp , 965. [4] Li Wei. Design o a hybrid uzzy logic proportional plus conventional integral-derivative controller. IEEE Trans on Fuzzy Systems, Vol.6(4), pp ,998.