# Projects:2014s2-80 Swinging Crane Project

**Project aim:** Swinging Crane project is aim to transporting a payload from one place to another and reducing the consuming time as much as possible. Using the software of Simulink and ControlDesk on computer to create and simulate a system model. Through the hardware of dSPACE board, amplifier and simulator to realize practical control, which is move the trolley for 0.5 meters and count the consuming time from starting movement to fully settled. The outcomes are supposed to realize multiple control methods, which includes automatic and manual control. The system performance should be improved compared with last year results. This project also could be used for helping high school student to understand the principle of control systems.

## Contents

## Project introduction

### Technical introduction

Gantry cranes are wildly used in industry, for lifting heavy objects by a hoist which is fitted in a hoist trolley and can move horizontally on a rail or pair of rails fitted under a beam.

There are two examples on the above shows 2 worst case in controlling the system. First example uses a large force applied on the trolley, leads the residual swinging angle at the end is very large and the system cost much time to settle. Second example uses small force to drive the trolley from start, but the trolley movement is too slow, which costs a lot of time either. In this project, we will concentrate on designing appropriate feed forward input to the system, and add controllers to help control the system motion, further improve the system performance.

Figure 1 demonstrates the model of swinging crane, the DC motor controls the trolley to horizontally move a load in a short distance. There are two encoders to record the data, one is the moving distance, and another is sway angle of the load. By giving a signal from operation control system, it will generate a DC current from a current source, then injecting it into a motor, which would drive the conveyor belt. There is a trolley placed on one side of the belt, and start moving towards another side. At the bottom of the trolley, using a rod stand for the hoist, connect with a load. At the start of transporting the loads, it will cause accelerated, corresponds to a traction force, effect on the trolley. There occur an angle between the rod and vertical. After the trolley stops, the loads may turn to oscillate. If the initial angle large, the oscillation duration roses, which is a potential risk to the people on the ground.

The system is operated inside a flow, shown as Figure 2. Input signal is generated from Simulink, goes into the plant through dSPACE and amplifier. The outputs of the plant are measured by two encoders, and send back to dSPACE, finally transfer to the computer. The dSPACE and amplifier components will introduce later. The plant is the real model of the system, the transfer relationship is shown in Figure 3. The current flows into DC motor, which drives the belt on the grid. The trolley is bind on the belt, thus it has the same acceleration with the belt. There are two outputs from the, the trolley position and the swinging angle of the pendulum.

### Motivation

The gantry crane system could be identified into separate sections: linear motion and swinging pendulum. The goal is to minimum the time used to transport loads and reduce the swinging oscillation as minimize as possible. The pendulum was studied by Galileo, Huygens, Newton, Hooke and all the leading figures of 17th-century science. Since the long history on the study, pendulum theory has been almost perfect, but still exist imperfection in applied to practical. In this project, the basic model is simple gravity pendulum. To analyze the motion parameters of pendulum, Newton’s classical mechanics Laws are applied. In traditional education, Newton’s lows are taught in high-school physics lecture. The theorem is abstract to student, and divorced from the practical application. The gantry crane system is a representative application, and easy to understand, thus it is suitable for demonstration teaching purpose.

### Objectives

The aim of swinging crane project is to demonstrate research component of project, examine and improve last year’s project, perform analysis, show understanding of theoretical principles, simulations and experiments, then improve system robustness, calculating instantaneous energy and optimize system motion trajectories. The 5 objectives of this project are shown as bellow:

1.Modelling of system – physical principles, approximates which can be used to simplify model (e.g. linearized model).

2.Selection of reference trajectories-trade-offs, constraints, optimization.

3.Calculation and control of “energy” stored in pendulum-means for damping energy.

4.Simulation of system- investigates and checks performance.

5.Experimental demonstration- interfacing operation, model verification.

## Background

### Crane system

The crane system model can be dismantled into 2 parts: a pendulum subsystem with fixed trolley position and a free trolley position while there is no pendulum oscillation drive by a DC motor. The system control methods including feed forward control and feedback control.

### Feed forward/open-loop control

Feed forward control can change the system output directly through a per-defined path. Feed forward control is usually used with feedback control since a feedback control system is required to track set point changes and to suppress unmeasured disturbances in system response. In system theory, reference input is necessary to control the plant, and how to set an appropriate input signal is difficult. Moreover, there exists a lot of methods for optimal input-shaping, which is aim to improve system performance through system input, instead of controller. This usually has more obvious effect than the feedback control.

### Feedback/closed-loop control

## Previous work

The swinging crane real system is designed by the workshop of University of Adelaide. Some analysis has been done by previous group, a simple PID control and current manual control have also been developed. Thus some data of the model could use by directly looking up their reports.

Figure 4 gantry crane system is studied by last year project group. This model is based on lumped-mass model, which ignore the mass and the elongation of the rod caused by the tension force. Both of the trolley and payload are considered as point mass and moving in two-dimensional x-y plane.

The system total settling time from last year is 4.566s. The system input signal is as Figure 5. The system response and ControlDesk results are shown in Figure 6.

## System modelling

### Simple pendulum model

System total energy is the summation of kinetic energy of the trolley, the potential energy and kinetic energy of pendulum load. The animation on the left shows a free-trolley-position movement demonstration without friction or air-drag. It shows the energy conservation law, which means the total energy is constant all over the time, and in this particular case the system kinetic energy is complementary to potential energy. Consider a trail of total energy in a system process, shows as Figure 5, in where T1 is the acceleration time period, T2 is the deceleration period and T3 is the remain oscillation period. The magnitude of system total energy in T3 is a constant value with frictionless assumption. The left animation illustrates the system remaining oscillation relationship in T3.

### System equations

According to Figure 6, the system total energy could be expressed as:

Taking the force relation, the system transfer function is , if the pendulum swing a small angle(i.e.less than 10 degrees), the above equations could be reduced to .

By taking the Laplace transform, the system transfer function is 200px.

The above equations could also write as state-space model form. Assume the state variable , and state equation the state matrices are ,and.

## Control methods designing

### PID control

In this project the Figure 7 block structure is used. There are two PID controllers used to control the two state variables feedback. The PID controller parameters are designed by selecting appropriate , and gains through analysing the root-locus diagrams and considering the system robustness.

#### Inner-loop controller design

Observing from the above root-locus diagrams, PD controller has simple construction and enough to insure the stability of open-loop system.To ensure control system robustness, i.e. system is not sensitive to connector length l and load mass m changing, a robustness designing for inner-loop controller parameters is essential. The inner-loop system robustness with above parameters will have the tolerance of connector length changing 10% (from 0.389m to 0.475m), mass of load changing 44% (0.308kg to 0.792kg).

#### Outer-loop controller design

The outer loop is designed using the Simulink built-in function, PID self tuning with considering the following conditions: • Overshoot ≤ 5% • Settling time ≤ 5s • Steady state error ≤ ±1%

The outer loop PID controller response tuning design is shown as Figure 10. The tuning Bode diagram is shown as Figure 11.

### Fuzzy-logic control

Fuzzy logic control is a rule-based control method. The controller is designed with a set of fuzzy rules for both input and output sides. Figure 12 shows the basic structure of a fuzzy control system.

In classic control field, the precision of a control system modelling effects the system behaviour most. The dynamic information of the system state could help achieve the goal of accuracy control. However, the number of the state variables are too much for a complex system, and they may have influence to each other, thus it is difficult to describe the system state correctly. Fuzzy logic control uses the idea and theory of fuzzy algorithms to describe the system state. Fuzzy control is a nonlinear control method, and it also belongs to intelligent control branch. In general, a control engineer will use classic algorithms (of the classic PD type, for example) if the system can be modelled and fuzzy algorithms (of the fuzzy PD type, for example) if the system cannot be modeled (or can only be partly modeled).

In this project, there are 4 state variables, which defined in previous. Based these variables, two fuzzy controllers are used. The system simulation diagram shows as Figure 13.

#### Fuzzification design

The fuzzyfication process uses fuzzy state variables to describe the system. Assume the state variables and control variable are:

The state variables considered can be positive, zero or negative, also can be large and small. Presume there are 5 quantified intervals set for input variables, in which are “negative large” (NL), “negative small” (NS), “zero” (ZR), “positive small” (PS) and “positive large” (PL). While there are 5 quantified regions set for output, in which are “large acceleration” (LA), “slight acceleration” (SA), “zero acceleration” (ZA), “slight braking” (SB) and “large braking” (LB), illustrates as the fuzzy rules bar.

#### Fuzzy rules define

The fuzzy rules are defined as term of Θ (ZR, PS; AS) for example. Table 7 presents the corresponding relationship of the angular error, the angular acceleration error and the correction output acceleration. Table 8 is the position rule matrix, similar as Table 7. The example rule could be interpreted with the following implication: If the angular error εθ is NS and the variation of the angular error is NL, then the trolley acceleration Γ is LB.

#### Defuzzification design

The process of selecting the output from the two fuzzy controllers is called defuzzification. There are several methods to achieve defuzzification: the method of the center of gravity, the method of the maximum, and the method of the mean value of the maxima. In this project, the simplest one, maximum method, is used. In Simulink, this selection is realized through switch function, shown as Figure 12, and the result in scope is 1 in this case.

### Position manual control

To achieve the interactive demonstration purpose, a position manual control system is designed. This system is aim at synchronous moving the trolley according to user’s operation through a slider in ControlDesk. The minimum current to drive the motor is tested around 1.2A, thus to make the trolley motion more accurate compared with slider position, an extra current with the value of 1.2A is added to the output, shown as Figure 15, which is amplify and adjust part.

The function of above part could be explained by Figure 16 and Figure 17. Before amplify the current, trolley does not move much, after adjusting with friction implement, the trolley will move as expected.

## Hardware test and interfacing

The verified model is the precise nonlinear model. The verification process is taken by giving an initial angle to both simulation model and practical model, comparing their angular response. From Figure 18, the angle decay curves are similar according to the envelope and time period. Thus the simulated model is considered to be correct, and enough close to the practical model. However, the large friction along grid is varied, hence it is difficult to add this parameter to the simulation model. The friction implemented is achieved through an independent module. The tested dumping factor D=9, and at same point, to compensate the friction, the equivalent mass of trolley used is M*=7kg.

## Results comparison

Figure 19 to Figure 21 show the results comparison between last year and this year, PID feedback control and PD type fuzzy logic feedback control. The system position response and angular response are analysed and organized into Table 10. The data is analysed and calculated according to Figure 22 and Figure 23. Note that the period of oscillation T should be same if considering frictionless residual oscillation. In this case the value of T is used the angular oscillation period, since the friction on grid is large and the motor is under current control all the time. The system performance is mainly determined by the total consuming time, which from system start until settled. The requirement of project is to move the trolley for 0.5m along grid, and find optimal solution for overall consuming time without considering other limitations. According to Table 2, the steady state position errors are all under 5%, which is acceptable. The PID control result yield a large rising time, which means the system has a lower responding speed. Both of the two methods developed in this project has improved the system consuming time. Moreover, comparing with the position over shoot and maximum angle, it could be seen that the result from last year is much worse than this year.

## Conclusion

### Designing summarize

During the modeling process, the system parameters and assumptions are proofed to important, since one parameters could change the system performance totally different, and the assumptions should be made appropriately. The friction in this project is significant large compared with motor traction, thus friction implement is enssential, and cannot be ignored. In interfacing part, initially the system was built up without testing, as a consequence, the system behaves non-expected. For instance, the motor drives the trolley very fast for every time, it is hard to select a suitable current input only rely on experience. Also, the system model verification process is necessary, since the model reflects understanding from the designer, and it could help checking the accuracy of parameters. An appropriate designing process with logical order that learned from this project is as Figure 24.

### Project completion

Generally the project is completed and reached the aims and requirements in proposal. At this stage, the project achievements are as following aspects:

•Nonlinear and linear system model are derivate and successful simulated.

•According to the feedback, the system instantaneous energy is calculated and presented.

•A timer function with system “fully stooped” criteria is constructed in Simulink.

•In PID controller designing, the robustness is designed through sensitivity, and then the theoretical parameter variance is length 10% and load 10%.

•3 different controller methods are developed: PID, fuzzy-logic and hybrid PD-type fuzzy logic.

•The system performance is determined mainly through settling time, thus the best result is achieved by PID controlling. Last year group’s best result is 4.6 seconds, and this year is 3.2 seconds, which is 30% percent improvement.

•The demonstration ability is also enhanced since the position manual control is designed instead of current control.

•Visualize animation programs are developed to demonstrate the system results.

•System emergency break is realized in simulation, contrast with physical break of last year group.

### Skills training and professional development

Among the simulation state, the required skills include analysis and modelling physic model, Matlab simulation programming, dSPACE using method, and encoder and sensor devices using knowledge. During the project period, the team cooperation ability, the ability to communicate or negotiate with supervisor, the capability of literature review, time management and project management skill and other professional skills would be developed. All of the skills are essential for further research activities and could be apply to career.

### Future work

Gantry crane controlling is a large research area in control field. There still exists lot of work could be done.

The model used in this project to simulation is lumped mass model, in which the mass of the rod is neglect, but for practical device the connector is 0.5 kilo grams, which is the same weight as trolley. A distributed mass model could be studied in future.

There are other controllers that could research on. For instance, adaptive control is a method that widely applied in modern industrial, especially for changing conditions case. Fuzzy-tuned PID control is another type of hybrid controller, also there is an algorithm called particle swarm optimizations could help increase system controlling precision.

The practical model in lab is built together, hard to separate. In future could use a variable mass of payload and an extension-type of connector, which are more close to the actual application.

The model now is a planar model, but in real world the payload is mostly moving in a 3 dimension space. In future the system model could increase the dimension, which could coordinate with different payload shape or transport line.

## Group members

Liyan Yi

Xianghui Ma

## Supervisors

Dr.Wen Soong [1]

Dr Braden Phillips [2]

## References

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[21] dSPACE_guide_encoder

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