Design of a dead time controller for pneumatic systems
This paper proposes a nonmodel-based design approach for pneumatic actuating systems, based on a novel timedelay compensation scheme. In practical electro-pneumatic or hydraulic servo mechanism there are usually unavoidable operating delay time in the solenoid valves. The time delay may sometimes cause closed-loop instability if it i s not treated carefully in the control system designs. In the proposed control system, two types of controllers are combined; one is a fuzzy-PID controller used to ensure tracking performance, the other is an adaptable wavelet neuro compensator used to compensate for the time delay resulting from the control valve. Performance and characteristics of the proposed design are verified to show its effectiveness. I. lntrcduction Pneumatic and hydraulic control system play very important roles in the industrial automation systems. However, there are weaknesses and difliculties in implementing a practical system equipped with a pneumatic or hydraulic driving mechanism Traditionally, a linearized mathematical model of a pneumatic servo control system must be built up, and then, the control system can be analyzed and designed. In general, a pneumatic control system is a nonlinear system because of the compressibility of air, deadhand due to stickiness, the friction force between the piston and the cylinder, the air mass flow rate through the servo valve [l, 21. Therefore, the fuzzy control technology with no strict requirement on,plant models has recently been applied for pneumatic control designs [3, 41. A considerable amount of research has also been devoted to the development of position-control systems for pneumatic actuators 15, 61. Because of the magnetic hysteresis and the mechanical motion of the spool valve, the high speed solenoid valves usually 0-7803-7896-2/03/$17.00 02003 IEEE have time delays. Considering the time-delay effect in a closed-loop system, it was pointed out in (71 that when the apparent delay time exceeded the dominant time constant of the system, the peak offsets. following a change in load, could approach those of the uncontrolled situation, even with the best PID tuning. In this paper, the pneumatic cylinder is operated by PWM-driven onaff solenoid valves. We propose a novel control scheme, based on an intelligent control method, to compensate for the time-delay phenomenon commonly occurring in pneumatic control systems. The objective is to develop a non-model-based control design methodology which ensures positioning accuracy while there are time delays and modeling uncertainties in the controlled plant. A fuzzy-PU)-PWM controller is used to provide primarily tracking control operations, and a wavelet basis function neural network compensator is applied as a delay-time compensator. 11. Pneumatic System Modeling Consider the model of the pneumatic driving circuit shown in Fig. I , in which A, = 4 = A are piston areas of the pneumatic cylinder, & and P2 are cylinder chamber pressures. Denote P; Pt = 6. Solenoid valve 3 is installed as a linkage valve between the cylinder chambers. From the continuity of mass flow rates in the cylinder, we have [2] G , + G , + 2 G 3 = c , l ; t ( a , + u , ) y (1) G, = ksS, kP& G, t G 2 = k , e (2) mass flow rate through each valve, y i s controlled piston position, V, and V, are cylinder chamber volumes; U is specific heat; 1715 Proceedings of Ihe American Control Conterence Denver, Colorado June 46,2003 R is gas constant; and T, is temperature of supply air, P,, and p,, are the supply pressures; S, and S, are the effective cross-sectional areas of valves 1 and 2; and k n , kpo and k, are valve coefficients. The dynamic equation for the cylinder is given by my +by = A c -F,sgn(y) (3) where A 6 is operating force exened on the position piston. m is total mass of the moving part, b is viscous damping coefficient, F, is coulomb friction. S, is equivalent effective cross-sectional area of valve 3. The starting condition of the piston is given by IA6I 2 F, (4) After starting, the motion of the piston position can be described by kw: S, ( s) k,y,'( s + z ) F, sgn( y ) ( 5 ) '(') ' s(s2 t 25-0,s t 0;) b + 2 bz . = . on= -+Jmm, 2 0 " where the coefficients are 2 k A k . 1 z=k ~ + Z k ~ o . Figure 2 shows the k = s I mc,o,' -"CO theoretically modeled system, where y , i s the desired piston position, and the operation of the PWM control is applied to this pnlumatic cylinder control system. ?he characteristic curves in Fig. 3 correspond to the relation between the duty cycle D and the piston speed Y measured at gradually increasing or decreasing D from the state where the piston stops. For PWM control, the odoff switching actions are operated instantly. However, the actual motion of the solenoid valves are unavoidably delayed and even only half-open due to the magnetic hysteresis and the mechanical motion of the spool valve. For a sufficiently high value of the carrier wave frequency, f,. the valve dynamics can be modeled as [Z] S,(s) = kme?D(s) (6) where the equivalent static gain of valve 3 is given by k, =as, laD ; Z is the operating delay time of the valve; and D ( s ) = L [ d ] , in which d denotes the change in D from the reference value of D = 50% , and L1.J denotes the Laplace transform, 111. Fuzzy-PID Control Design A. Two-parameter PID control scheme It is usually desirable in practice to design a controller by using only the error and error change rate as its inputs to simplify the design work so that it will have the tine characteristics of a PID controller. A direct way to this aim is to have a controller structure that simply connects a PD type controller and a PI type controller together in parallel, i.e.