Jun Wang， Yanbin Liu,?， Yi Jin and Youtong Zhang

（1. Department of Vehicle Engineering, Academy of Army Armored Force, Beijing 100072, China；2. School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China）

Abstract: To speedily regulate and precisely control a hydraulic power system in a unmanned walking platform (UWP), based on the brief analysis of digital PID and its shortcomings, dual control parameters in a hydraulic power system are given for the precision requirement, and a control strategy for dual relative control parameters in the dual loop PID is put forward, a load and throttle rotation-speed response model for variable pump and gasoline engine is provided according to a physical process, a simplified neural network structure PID is introduced, and formed mixed neural network PID(MNN PID)to control rotation speed of engine and pressure of variable pump,calculation using the back propagation(BP) algorithm and a self-adapted learning step is made, including a mathematic principle and a calculation flow scheme, the BP algorithm of neural network PID is trained and the control effect of system is simulated in Matlab environment, real control effects of engine rotation speed and variable pump pressure are verified in the experimental bench.Results show that algorithm effect of MNN PID is stable and MNN PID can meet the adjusting requirement of control parameters.

Key words: PID control；neural network；hydraulic power system；unmanned platform

Combined with different types of technology such as articulation mechanism, hydraulic pressure transmission, electronic control and intelligent control[1], unmanned walking platform(UWP) formed by four-legged burden robot can be qualified for different tasks in the villainous condition, it has played an important role in rescue and disaster relief. In order to make rapid response for the change of road surface and loads,good motion capability is demanded for UWP,high power density and flexible control are needed for power system, since there are some advantages, such as large torque and easy control for variable bump, small volume and easy starting for gasoline engine[2], small gasoline engine and variable bump are selected to form the power system. After gasoline engine is used as power resource, unlike traditional gasoline engine control according to pedal for steady load,control algorithm is key to quickly regulate engine rotation speed for transient load change in order to fulfill self-adapt control in varied profiles, its control functions and algorithms need to be optimized continuously. There are many research results so far, research papers about rotation speed control for gasoline engine have been published in periodicals. Xin Nianqi presented a two stage slide mode algorithm to rotation speed controller, the speed control all over the profile is well made, the robustness of this algorithm is better than that of tradition PID algorithm[3]. Xu Gaoyuan put forward a fuzzy PID algorithm to rotation speed control, fuzzy logic, fuzzy table and fuzzy inference engine are provided, the control effect in a typical profile is improved[4]. Liu Dao put through PID coefficient self-tuning by improved the particle swarm optimization algorithm, it simplified calculation of PID coefficient self-tuning[5]. Chai Hui introduced forward feed fuzzy PID into gasoline rotation speed control for hydraulic driven foot robot, fuzzy logic interface, fuzzy table and fuzzy inference engine are given, a solution fuzzy method of center even is used to output calculation[6]. Li Yibin presented a service control method to gasoline rotation speed control for hydraulic system on a leg-foot robot[7], hydraulic fluid variable is used to modify throttle position and rotation speed error is computed by basic throttle position, fuzzy table is looked up to set pulse width modulation(PWM) value, the method can meet different control demands, a better transient and steady performance was obtained. These papers published in periodicals were focused on independent calculation of PID coefficient and its effect for single loop control, double loop control is becoming more and more for process control and power transmission control, Xia Hong provided a kind of two loops ratio control system based on PID neuron network[8]. Hu Lingyan presented a double loop PID control scheme for the self balancing walking control of two wheeled robot,which adopts a positive and negative feedback[9].Yu Yang designed an optimal double loop PID controller for the inverted pendulum system, the coefficients of the two PID controllers were optimized by genetic algorithm[10]. Tian Ying put forward a dual loop control for the N/M mode of engine dynamometer by digital PID, a manual critical proportion method is used in PID coefficient tuning[11], there is little research in reducing the workload of double loop PID coefficient tuning. In order to overcome the defects of digital PID, such as complex coefficient self-tuning and poor control effect for variable target, a simplified neural network structure PID is introduced, and formed mixed neural network PID to control rotation speed of engine and pressure of variable pump.

1 Control Demand and Method

UWP is made up of hydraulic power system,junction structure, electronic control system,sensing system and top controller. Foreign gasoline engine with two-strokes, single cylinder is chosen as power resource, electronic controlled throttle valve and electrical control system are added to this gasoline engine and performed precision control, a transmission box is used to connect gasoline and bump with the transmission ratio 4 : 1, and a variable pump provides fluid pressure, as shown in Fig.1.

The specification of gasoline and variable bump is shown in Tab. 1.

Fig.1 Structure of hydraulic power system

Tab. 1 Power system specification

Gasoline engine provides power to variable bump and make variable bump rotate, variable bump continues to adjust flow rate according to road condition and burden weight change in order to keep hydraulic pressure stable, throttle position and flow rate need to automatically mediate in real time, so control parameter requirement of UWP is listed as follows:

① Throttle position is regulated quickly to output power when platform gait changes.

② Flow rate is adjusted to keep system pressure to given target to make platform gait when and external condition (road surface and burden weighty) transiently changes.

③ Accuracy and response time of rotation speed is in ±100 r/min and within 50 ms respectively.

④ Accuracy and response time of bump pressure is in 2 MPa and within 100 ms respectively.

Hydraulic power system needs to regulate the throttle position to ensure output rotation speed to meet variable pump demand, since the pressure of hydraulic system is varied with road condition and burden load of UWP in order to make UWP keep a suitable gait, the flow rate of variable pump is often changed to meet pressure demand of hydraulic system. Control of hydraulic power system is made up of two loops, as shown in Fig.2, one is rotation speed control according to different gaits of UWP, the other is pressure control to review throttle position. The digital PID algorithm is introduced into two control loops, because flow rate results in load change of gasoline engine and affects the stability of rotation speed, in the condition of road condition change, flow rate control is correlated with rotation speed control, when different targets of rotation speed and different disturbs of flow rate appear. In Fig.2, Gnp(s) is a disturb function of pedal actuator in gasoline engine to pressure control of variable pump, Gmi(s) is a disturb function of variable pump pressure to torque control in the gasoline engine.

Fig.2 Dual digital PID coupled control

PID parameter tuning is important to control parameter effect in real time regulation, dual PID control loop is independent and parallel connected, two loops can regulate in the same time only if the PID parameter of two loops and a suitable adjusting period is selected, and finally relative ideal target may be achieved, the control parameter and adjustment parameter of the speed control loop is the speed and the throttle position, their change cycles are 200 ms, 150 ms respectively, which is determined according to the actual operation of the two-stroke two cylinder gasoline engine and adjust time of electronic throttle separately. The control parameter and adjustment parameter in the hydraulic control circuit is pressure and control duty cycle of solenoid valve, their pressure change periods are 500 ms, 200 ms respectively, which are decided on the basis of the measured pressure change time in hydraulic circuit and the response time of solenoid valve separately.

There are three shortcomings in real control application. Firstly another loop is regulated supposing that one loop achieves stable stage.Secondly, small disturb is exerted by another loop, regulation quantity become small and regulation time longer. Thirdly the matching degree of dual loop PID coefficient is not very good, the work of PID parameter tuning is heavy and complex. To solve the above shortcomings, a new method of dual PID parameter tuning is investigated in neural network, especially in PID parameter matching of two loops.

2 Model of Hydraulic Power System

2.1 Hydraulic pressure system

Hydraulic pressure system consists of variable pump and energy accumulator, variable pump is used to output flow rate, energy accumulator is connected to a hydraulic pressure circuit by switch valve, the pressure wavelet of system decreased and transient flow demand to compensate load is met.

Variable pump is made up of electromagnetic proportion valve, valve control cylinder, and variable plunge and serve valve, flow rate is regulated by control piston rod motion in fixed power based on load change, piston rod drives serve valve to change motion direction, and regulate motion direction, and finally output flow rate of variable pump is changed.

Mathematic model of each part in variable pump based on Ref.[12], transmission function of piston displacement in variable pump to input current of electromagnetic proportion valve is

where K is open loop gain, K =K2K1,K2=Ke/A0, K1is distance increase coefficient of serve valve, Keis flowed rate increase coefficient of serve valve, A0is big end area of variable piston; W0, W1is natural frequency of hydraulic cylinder and serve valve respectively; σ1, σ0is damping ratio of hydraulic cylinder and serve valve respectively.

Because hydraulic cylinder seriously affects transient performance, W1is largely greater than W0, transmission function of output flow rate in variable pump to input current of electromagnetic proportion valve is simplified. There exists a linear relation between piston rod displacement and output flow rate of variable pump, the linear relation is replaced by a proportion coefficient, the transmission function of output flow rate in variable pump to input current of electromagnetic proportion valve is

Flow continuity equation of variable pump is

Transmission function of output flow rate in variable pump is

where qpis the flow rate of variable pump; npis the rotation speed of variable pump; Kpis the griadient of bump displacement; Kais the increase coefficient of integrate amplifier; CLis the internal leakage coefficient; Pheis the oil pressure in high pressure end of variable pump.

Hydraulic accumulator is a kind of energy saving device in hydraulic pneumatic system, the common bladder accumulator is composed of charging valve, shell, air bag and lifting valve, it contains oil part and gas part with air tight seal,the fluid around the bladder is connected to the fluid circuit. Since the liquid is incompressible,the accumulator uses the compressibility of the gas to store the liquid, as the pressure increases,the fluid enters the accumulator and the gas is compressed, when the pressure drops, the compressed gas expands and the oil hydraulic pressure enters the circuit.

Flow continuity equation of energy accumulator is

According to Boyle’s law of thermodynamics, we have

Force balance relations of energy accumulator is

Transmission function of energy accumulator is

where qais the flow rate entering energy accumulator; pa, Vais the gas pressure and volume of energy accumulator; m is the polytropic index; p0,V0is the gas pressure and volume of energy accumulator in stable work point; Q is the input flow rate of variable pump torque; psis the output pressure of variable pump; Aais the conversion area of oil chamber; mais the conversion fluid quantity of oil chamber area; Bais the equivalent viscous damping coefficient; ωais the hydraulic natural frequency; ξais the hydraulic relative damping ratio.

2.2 Gasoline engine model

Intake air quantity is regulated by a throttle in gasoline engine, intake manifold fulfills mixture with fuel and air, finally rotation speed is gained by power assemble. Two-stroke gasoline engine is controlled by a throttle valve, its model is made up of throttle and intake line and power system, it is the throttle rotation–speed response model.

The throttle work results from control motor action to make throttle position change, the relation of throttle is

where Δθc[jT] is the change quantity of the throttle open; Δθ(jT) is real throttle position change.

Transmission function for intake manifold is

where p is the pressure increase of intake manifold; k0, knis two positive constants, dependent on engine speed and average pressure of manifold respectively; τf, Kfis the time constant and manifold transient increase respectively; n is the rotation speed of gasoline engine.

The change of engine output speed is decided by output torque and indicated torque and frication loss torque, its relation is existed as follows

where J is the rotation inertia quantity; ΔTcindicated torque increase; ΔTois the output torque increase; ΔTfis the frication loss torque increase;kfis a fixed constant.

Laplacian transfer is made for Eq. (10).

where S is the complex frequency; τR, KRis the time constant of transmission system and the increase constant of transmission system respectively, KR=1/kf.

Torque of gasoline engine is determined by ignite time and air-combustion ratio and combustion process, due to OTTO cycle character, fresh air intake in the intake stroke is delayed to real making work in the power stroke, small variety of manifold pressure caused output torque change, the relation is showed in the transfer function

where Gpis the increase constant; dependent on steady intake pressure and ahead ignition angle and air-ratio; exp(-SτP) is indicated delay of making work stroke to intake stroke; τp=120/n is the time constant used by per stroke.

3 Mixed Neural Network PID

3.1 Mixed neural network PID

The integral and differential terms of digital PID formula is discrete, sample period T and sample sequence number k are set, substitute summation for integral and replacing differentiation with increment are made, discrete digital PID is

where Kpis the proportional coefficient; TIis the integral time coefficient; Tdis the differential time coefficient; ukis the output computing value of kth sampling; ek, ek–1is the input deviation value of k-th and (k-1)-th sampling respectively; KIis the integral constant, KI=KpT/TI, KDis the differential constant, KD=KpTd/T.

A simplified neural network structure in which a digital PID control algorithm combined with neural network[13], PID control algorithm is made by forward algorithm of network, a PID coefficient self-adapt adjustment is made by backward algorithm of network, PID coefficient is automatically adjusted, well-training neural network can quickly finish multi-target approaching and need not compute PID coefficient. it can simplify PID coefficient self-tuning.

Mixed neural network PID(MNN PID) adopts two simplified neural networks PID, the two neural networks are independent and parallel connected, every network consists of input layer,implicit layer and output layer and different neural units, as shown in Fig.3. The weight of two implicit layer not only connects with its owns output, but also links with the other network output, thus influences of the two disturbs are included in each other, and two PID control coefficients can correspond in the same time.

The four neural units of input layer are control target r1, r2and output values y1, y2, r1, r2are a control target of engine speed and pump pressure, y1, y2are a output variable of engine speed and pump pressure, fitted nonlinear relation of Eq. (17) is integrated into an implicit layer of neural network, there are three neural units in the implicit layer, different activation functions are used to these neural units corresponding to the proportional part, integral part,and differential part, there is only two neural units in the output layer, that is output u1, u2of PID, w′jhand w′jkare the network weight of implicit layer respectively, the PID parameters on two control loop are made by reviewing network weights of implicit layer.

Fig.3 Neural network structure of dual PID

The output in the input layer is

The implicit layer is made up of two groups.In each group, there are three neural units, which is proportional, integral and differential neural unit, respectively. The input is

The output is

Proportional

Integral

Differential

The output in output layer is

3.2 Neural network PID calculation

The physical variables of BP network input joint are different from each other, its numbers are very large, in order to prevent small values from being inundated by large ones, input data is normalized to [0, 1], the normalization treatment is

where a,b are the two constants to make all sample input data enter [0,1]; Xmax,Xminare the maximum and minimum of each group data respectively; X,X′are the value of each group data before and after normalization respectively.

Weight vector from input layer to implicit layer is

The indicates minimal square errors J between the ideal target r and the actual output y is[14]

The steepest decent is a simple and typical method of learning process in BP neural network,when learning step is set as η, after n step learning, weight value of implicit layer to output layer is

Suitable learning step is very important to the improvement of convergence speed and learning times, a self-adapted learning step is introduced, in order to make learning step change to much, the variation of learning step is

where ξ is the increase constant, 0.01 ≤ξ ＜0.1; λ is the symbol constant, α is momentum item parameter, 0≤α≤1.

When λ ＞0, learning step is increased, if target and learning error is given, neural network PID can automatically modify network weight value, and meditate controlled object to approach target value.

Flow frame of MNN PID algorithm is as follows.

① Initial condition e=r –y, weighty value w1j(0),w2j(0) are set.

② Initial learning step η and learning error ε are given, the range of increase constant and momentum item is set as (0.1).

③ System control target is given, learn error ε is set.

④ When J ＞ε, network weight value w can be modified.

⑤ When J ＜ε, output value u of PID is determined.

4 Simulation and Test Control

4.1 Simulation control

In the Matlab/simulink simulation environment, MNN PID model is found in M language,due to the limited page, the speed control is taken as an example to illustrate the network calculation and control effect, engine transfer function model of throttle-rotation speed response is shown in Fig.4. In the condition of sample time 1 ms, target speed 10 000 r/min, different steps and learn error is selected in the MNN PID model, control effect of different step is shown in Tab. 2, with the learning error decreasing, learning steps become more, control time needed is longer, but speed vibration range is small, whenlearning error is less in 0.06, speed vibration range is in 100 r/min. Meanwhile, Tab. 2 shows vibration range of pressure is in 1.8 MPa when target pressure is 18.5 MPa.

Fig.4 Transfer function model of throttle-rotation speed response

Tab. 2 Control parameter change range in different learning errors

According to set learning error, PID coefficient is given after learning in MNN PID model,speed control effect is shown in Fig.5. In Fig.5,curve 1 and curve 2 are corresponding to 160 steps and 50 steps respectively, curve 3 is corresponding to traditional PID with Kp=45, KI=8,KD=0.8. Curve 1 corresponding to 160 steps is better than that of curve 2 in 50 steps. Control time of curve 1 approaching to different target is shorter than that of curve 3 with traditional PID.

According to set learning error, PID coefficient is given after learning in MNN PID model,the control effect of system pressure is shown in Fig.6. In Fig.6, pressure wavelet under different target is less and stable time approaching target pressure is in 100 ms, control effect of system pressure for different target is ideal in simulation condition.

4.2 Test control

Fig.5 Control effect of variable rotation speed target

Fig.6 Control effect of variable pressure target

In order to verify the effect of mixed neural network PID algorithm, test system is designed based on real dynamic system for hydraulic walking platform, test system consists of gasoline,transmission box with gear ratio 4 : 1, variable pump, energy accumulator, electronic control unit, electronic throttle and electronic servo valve, pressure gauge, displacement sensor, pressure sensor and rotation speed sensor.

Rotation speed of gasoline engine in hydraulic walking platform is varied with four walking gaits: standing, stepping, slow walking and fast walking, maximum burden and minimum burden is set in gait of slow walking and fast walking respectively, the target of system pressure and is set in each walking gait, as shown in Tab. 3.

Because the speed response time of the gasoline engine is much faster than that of the hydraulic circuit, and the throttle is controlled by the stepping motor, its feedback loop is the firstorder inertia plus pure lag link, and the transmission link is less, the response time is fast. Firstly,the influence of hydraulic circuit is not taken into account, it decouples as a separate system, thespeed of gasoline engine is controlled using the calculated throttle position. Then, duty time of the PWM control signal of the electromagnetic proportional valve is calculated for the hydraulic circuit, and output of variable pump is adjusted to make the system pressure approach the target value.

Tab. 3 Target rotation speed and pressure of engine in different gaits

Electronic controlled unit is developed with digital signal microprocessor DSP56F807, MNN PID model procedure is downloaded in DSP56F807 to fulfill MNN PID algorithm, different speed target is input and control effect is displayed in a monitor computer. The PID coefficients are automatically calculated by the neural network structure PID algorithm, 50 ms sample period is given, the speed mediation effect by control system is shown in Fig.7 after 450 ms sample time, dashed line indicated the rotation speed target, and real line is the real measurement speed. Fig.7 shows that real rotation speed is well traced to the target value, the transitional change time is short, the super regulation value is small, all these results show that control effect of variable target in rotational speed is good.

Power system load varies with walking gesture and burden condition of unmanned hydraulic walking platform, in order to keep hydraulic system pressure to a fixed range, gasoline rotation speed is required to control in real time by ECU and change in a given range. When hydraulic system pressure is fixed to 15– 20 MPa and gasoline rotation speed target is 10 500 r/min,real control effect of bump pressure and rotation speed under variable target is shown in Fig.8.Fig.8 shows that real bump outlet pressure varies with the different pressure target when hydraulic system pressure target is changed, wavelet range of bump pressure is less 2 MPa in 100 ms,in the same time, real speed is stable near the set target speed, the change amplitude of rotation speed is about ±100 r/min, and there is no oscillation speed to appear.

Fig.7 Control effect of variable rotation speed target

Fig.8 Control effect of bump pressure and rotation speed under variable target

5 Conclusions

① By means of the relation on torque-flow for hydraulic pressure system and throttle-rotation speed response for gasoline engine, the transfer function of hydraulic power system is founded, and a dual loop PID control method of coupled parameter is presented.

② A mixed neural network PID is formed using neural network PID, the PID coefficient relation is embedded into the structure with three layers, it can simplify PID coefficient self-tuning.

③ Test results showed that rotation speed and pressure of control effect by MNN PID algorithm are stable, and MNN PID can meet the design requirement in control parameter adjusting.