Robust Control of Crane Crab - Report Example

PROJECT INTRODUCTION The main problem of the crane drive control is to keep almost zero burden deviation in the final crane crab or bridge position. The main variable parameters are the burden weight mG (detected by a tensometer) and hanging rope length l (measured by an incremental sensor). A robust design by Ackermann’s method is preferably used for changeable systems or systems with variable parameters. The range of robustness is checked and areas related to expected variation values are defined. Knowing the values of changing parameters, a robust switch table is configured for their whole range of variance that satisfies the condition of forbidden burden swinging. In the future, there will be work on eliminating the varying parameters by an observer of the burden weight and burden swinging. The real crane was completely designed and connected to the distributed control system (DSR). Communication interfaces between the technological, system operator and information levels were created. The bridge crane was identified by ARX model through experimental identification and we obtained the crab, bridge and uplift transfer functions and their transformation to the state description. OE model identified burden swinging in the direction of the crane crab and bridge. The crane position was scanned by incremental sensors. For scanning the burden swinging, first use Hall sensors. Because of interference and output error, eventually measured the swinging by rotary rheostats. The frequency converter NORDis used for the crab, bridge and uplift drive control. The burden weight, respecting the designed crane construction, ranges from 0 to 100 kg and the rope length from 0 to 2.5 m. When trying to keep zero burdens swinging, the worst situation occurs in the case of the shortest rope at the minimum weight because the frequency of periodical vibrations increases. Experimental Bridge Crane ROBUST CONTROL DESIGN The property of robust control is in system robustness and its correct control against variation of parameters. In formula (12) the polynomial a (p) includes a variable characteristic polynomial with robust controllers. Solutions are feedback parameters suitable for uncertain parameters and in this meaning required system robustness [1, 2, 3]. All poles of the characteristic polynomial have to be located in the left part of 􀀀-area (Fig. 5) and to distance −a from the imaginary axis and inside the sector assigned by the damping value d = sin . Then stability and desired damping are ensured. n−2 back-feed parameters have to be known for the design to be robust. A graphical computing method can locate the values of the rest two controllers r1 , r2 which are included in a(p) . Then curves A for the minimum and maximum values of variable parameters plot the possible selection of robust controllers [5]. We can solve the system robustness against the burden weight and the rope length. CRANE PARAMETERS MEASUREMENT The crane position and its recalculated speed are measured by two kinds of incremental sensors. Two sensors of IRC 120 type are assigned for measuring the bridge position, next two Hengstler type were used for crab and uplift measuring. Their function is to transform the rotary motion to electrical signals proportional to the passed trajectory. The cables from sensors have to be shielded otherwise interference and self-graduation of incremental sensors will be observed [7, 8]. The experimental crane was assembled with position switches that protect the crab, bridge and uplift from moving outside the allowed area. Swinging was scanned by four Hall probes (two for the crab and two for bridge direction). Because of a strong interference signal at the start of ac motors this sensor was replaced by rotary rheostats. All rheostats are located upright; one corresponds to swinging in crab direction and other one in bridge direction. Burden swinging is transmitted through the hanging rope so that chromo bars are installed on the rope and connected with the corresponding rheostat. For correct robust control it is necessary to know the burden weight and rope length. The load weight is gained from the strain-gauge sensor that corresponds to the resistance value at burden variation. RESULTS OF CRANE MEASUREMENTS The control program consists of these main parts: calibration and crab, bridge and uplift drive control, calculation block, setup parameters, identification. We deal firstly with crab and bridge motion but to reduce the time of transport it is very efficient to test simultaneously the motion of both components. Crab motion: mG = 50 kg; l = 2.5 m Crab Trajectory Figure here displays the actual rope length x5Z (m), reference w5 (m) and real x5 (m) crab position. Simulation of burden deviation x6 (m) is in Fig. 14 without robust control and shows forbidden periodical oscillation in the terminal position (x5 = 1.5 m and back to 0 m). Simulation presents robust control of burden swinging to the zero value with allowance of 0.5 cm over swinging. The burden is damped by the control system to zero oscillation. 1. We observe again damping of burden deviation x6M (m) in the direction of the bridge to the zero value. 2. Bridge motion: mG = 50 kg; l = 2.5 m 3. Simultaneous crane crab and bridge motion: mG = 50 kg; l = 2.5 and 0.5 m Control system simultaneously adjusts burden deviation in the direction of the crane crab and also of the bridge. The reference position of both components is w5 = w5M = 1.5 m and backwards. The burden deviation x6 , x6M (m) with robust control. In the final position of motion the burden will be damped with the allowed tolerance 0.5 cm. The worst situation of control is met at the minimum rope length (Fig. 19) where correct designed controllers were employed to damp burden swinging. Let’s have a look on the mechanical side of the Crab crane. FACTORS AFFECTING MECHANICAL PROPERTIES Mechanical properties are those which define the behaviour of a material under applied loads. Mechanical properties of materials are affected due to: Alloy contents such as addition of W, Cr, etc., improve hard- ness and strength of materials. Fine grain size materials exhibit higher strengths and vice- versa. Crystal imperfections such as dislocations reduce the strength of the material. Excessive cold working produces strain-hardening and the material may crack. Manufacturing defects such as cracks, blowholes etc., reduce the strength of the material. EFFECT OF GRAIN SIZE ON PROPERTIES OF METALS —On the basis of grain size, materials may be classified as: 1. Coarse grained materials, (the grain size is large). 2. Fine grained materials, (the grain size is small).. Grain size is very important in deciding the properties of poly- crystalline materials because it affects the area and length of the grain boundaries. —Various effects of grain size on mechanical properties of metals are: 1. Fine grained materials possess higher strength, toughness, hardness and resistance to suddenly applied force. 2. Fine grained materials possess better fatigue resistance, and impact strength. 3. Fine grained materials are more crack-resistant and provide better finish in deep drawing unlike coarse grained ones which give rise to orange-peel effect. 4. Fine grained steel develops hardness faster in carburizing (heat treatment). 5. Fine grained materials are preferred for structural applications. 6. Fine grained materials generally exhibit greater yield stresses than coarse grained materials at low temperatures, whereas at high temperatures grain boundaries become weak and sliding occurs. 7. A coarse grained material is responsible for surface roughness. 8. A coarse grained material possesses more ductility, malleability (forging, rolling, etc.) and better mach inability. 9. Coarse grained metals are difficult to polish or plating (as rough surface is visible even after polish etc.). 10. Coarse grained steels have greater depth of hardening power as compared to fine grained ones. 11. At elevated temperatures, coarse grained materials show better creep strength than the fine grained ones. EFFECT OF HEAT TREATMENT ON PROPERTIES OF METALS Heat treatment is an operation or combination of operations involving heating and cooling of a metal/alloy in solid state to obtain desirable (/) Properties, e.g., better mach inability, improved ductility, homogeneous structure etc.; (ii) Conditions, e.g., that of relieved stresses. Some important heat-treatment processes are: Annealing, Normalising, Hardening, Tempering, Mar tempering, Aus tempering etc —One or the other heat-treatment processes produce the following effects on the properties of metals: 1. Hardens and strengthens the metals. 2. Improves mach inability. 3. Changes or refines grain size. 4. Softens metals for further working as in wire drawing. 5. Improves ductility and toughness. 6. Increases resistance of materials to heat, wear, shock and corrosion. 7. Improves electrical and magnetic properties. 8. Homogenises the metal structure. 9. Relieves internal stresses developed in metals/alloys during cold working, welding, casting, forging etc. 10. Produces a hard wear resistant surface on a ductile steel piece (as in case hardening). 11. Improves thermal properties such as conductivity. EFFECT OF ATMOSPHERIC EXPOSURE ON PROPERTIES OF METALS The atmosphere contains mainly nitrogen and oxygen and added to it are gaseous products such as sulphur dioxide, hydrogen sulphide, moisture, chlorine, fluorine etc., as industrial and other pollutants. On account of oxygen, an oxide film forms on the metals. (/) In the presence of humid air, an oxide film—rust —can be seen on the surface of mild steel which is not desirable. The oxide film on the metal surface absorbs moisture. Due to development of cracks or discontinuities on the oxide film, local cell formation takes place providing a fresh exposure of metal to the action of humid atmosphere. A flow of local corrosion current between the anodic areas of newly exposed metal surface and the large cathodic areas of the coated metal takes place resulting in corrosion of the exposed surface. (ii) The oxide film formed on aluminium, nickel, chromium or stainless steel acts as a protective coating and resists further oxidation. This is only because of chromium oxide film on stainless steel that it does not rust. But in industrialized areas in the presence of reducing agents, the surfaces of above mentioned metals become tarnished. When exposed to moist (and saline) atmosphere, the metals may corrode. Corrosion is a gradual chemical attack on a metal under the influence of a moist atmosphere, (or of a natural or artificial solution). Aluminium fins of the condenser of an air conditioner corrode when the air conditioner is used in coastal areas. Electro chemical and (chemical) corrosion may result due to alternate wetting and drying of metals by condensation of moisture. Carbon dioxide, sulphur dioxide and hydrogen sulphide gases from industrial atmosphere are absorbed by the condensed moisture and the dilute acids thus formed serve as electrolytes that start electro-chemical corrosion. The most important factor promoting atmospheric corrosion is the relative humidity. It has been noticed that corrosion of ferrous metals is almost arrested in atmosphere containing less than 30% humidity. Corrosion adversely affects the life and performance of a component in service. When exposed to very cold atmosphere, even ductile metals may behave like brittle metals. Water pipes in very cold countries normally burst and this is the effect of atmospheric exposure. —When the metals are subjected to a very hot atmosphere there is (i) Accelerated oxidation and/or corrosion. (ii) Creep. (iii) Grain boundary weakening. (iv) Allotropic and other phase changes, (v) Change of conventional properties, (vi) Reduction in tensile strength and yield point. EFFECT OF LOW TEMPERATURE ON THE PROPERTIES OF METALS —Cryogenics is the study of the behaviour of matter at temperatures below -200°C. —Food processing, liquefaction of gases, synthetic rubber manufacture, hydrocarbon polymerization, high altitude air crafts (-50°C), refrigeration applications (~60°C), de waxing of petroleum (-100°C), ships travelling in cold waters, are a few of the examples where metals are subjected to low temperature conditions. The low temperatures affect the properties of metals in the following ways: (i) As the temperature lowers, there is an increase in yield strength, tensile strength modulus and hardness and a decrease in ductility. At lower temperatures, an otherwise ductile material also becomes brittle. {Hi) Unlike high temperatures, there are no changes in the microstructure of a material as the temperature is lowered, (iv) Creep strength improves at lower temperatures, (v) Metals such as tin, lead, zinc and aluminium show phenomenon of superconductivity at lower temperatures (within a few degrees of absolute zero temperature). (vi). Copper, nickel, aluminium and austenitic alloys retain their much of tensile ductility and resistance to shock at low temperatures in spite of the increase in strength. (vii) F.C.C. metals and alloys retain their ductility substantially unimpaired upto - 24°C. (viii) A tendency for B.C.C. metals (e.g., steels) to (become sensitive to multiaxial stresses under shock load conditions and this is manifested by the sharp decline in the value of the absorbed energy in the notch impact test thereby indicating that the materials) behave in a brittle manner, at lower temperatures. THERMAL PROPERTY By thermal property is meant the response of a material to the application of heat. As a solid, absorbs energy in the form of heat, its temperature rises and its dimensions increase. The energy may be transported to cooler regions of the specimen if temperature gradients exist and ultimately, the specimen may melt. The study of thermal properties of materials is essential in order to evaluate the thermal behaviour of solids, i.e., their response to thermal changes — the lowering or rising of temperature. It is very necessary to know the thermal behaviour of those materials which are to be used in making component parts of furnaces, ovens or boilers that have to withstand steady high or fluctuating temperatures. Thermal properties such as (1) Heat capacity (3) Thermal expansion (5) Thermal conductivity (7) Thermal stability are important to be determined for the materials. (2) Specific heat (4) Melting point (6) Thermal shock resistance 1) Heat Capacity A solid material, when heated, experiences an increase in temperature signifying that some energy has been absorbed. Heat capacity is a property that is indicative of a material's ability to absorb heat from the external surroundings; it represents the amount of energy required to produce a unit temperature rise. In mathematical terms, the heat capacity C is expressed as follows: C=dQ dt where dQ is the energy required to produce a dT temperature change.Ordinarily, heat capacity is specified per mol of material (e.g., J/mol -K, or cal/mol -K). Specific heat (often denoted by a lowercase c) is sometimes used; this represents the heat capacity per unit mass, and has various units (J/kg -K, cal/g -K, Btu/lbm -°F). (2) Specific heat Specific heat is the quantity of heat that must be added to a unit mass of the solid to raise its temperature by one degree. When measured in Metric system specific heat is expressed as, (cal/g)/°K (or °C) and in British system as, (Btu/lb)/°F, i.e., the amount of heat energy, measured in Btu's, that will raise the temperature of 1 lb of the material by 1°F. Specific heat, though it is assumed to remain constant, usually increases with temperature. Mach inability- The ease of machining depends upon (i) the design of tools, (ii) method of lubrication, and (iii) the microstructure and properties of the metal. — Mach inability is an important property of a metal used in manufacturing operations. It may be measured as the quantity of chips that can be removed in a given time, as the weight of chips per hour. Since the behaviour of tool is important also, one may choose to determine mach inability in terms of useful life of the tool used or in terms of energy absorbed in machining one kg of chips. Taylor' measured the cutting qualities of a tool by measuring the fastest speed of turning that permitted the tool to hold its edge for 20 minutes. If surface finish appears to be of prime importance, one may like to determine mach inability in terms of surface finish of the work piece. One may, thus, conclude that mach inability involves several properties of a material, each of varying importance. Hence, mach inability of a metal may be considered very good if the greatest amount of material can be removed in the shortest time for each grind of a given tool, while obtaining satisfactory surface finish, with the ultimate objective being low overall cost. Good mach inability is associated with: (/) the removal of material with moderate forces, (ii) the formation of rather small chips, (///) medium degree of tool abrasion, and (iv) good surface finish. — All machinable metals are compared to a basic standard, and the comparison yields a percentage of rating which indicates the ease of cutting each metal. The standard metal used for the 100% mach inability rating is steel, coded by the American Iron and Steel Institute (AISI) Index as B 1112 steel. It is free machining steel. When compared to this steel, different metals have their mach inability rating as follows: Metals Mach inability Rating (%>) Aluminium 300-2000 Ni-steels 40-50 C-steels 40-60 Cast Iron 50-80 Chipless Machining — The metal is removed either by Chemical, or Electrochemical, or Erosion of the metal work piece by the action of a high voltage spark. Extremely hard materials can be cut. Very accurate work can be done on delicate parts. Examples of chip less machining processes are, Electrical discharge machining, Electrochemical machining, Chemical milling, etc. 3. Heat Cutting — Heat cutting is done either (i) by heating metal to a sufficiently high temperature so that it can be oxidized very rapidly by a stream of oxygen (i.e., oxyacetylene cutting), or (ii) by heating it to its melting temperature so that it can be blown away by a stream of air (i.e., carbon arc-air process). Thermal expansion — When thermal energy is added to a material, a change in its dimensions occurs. For example, if a 10 cm long rod of mild steel is heated (and it is free to expand) it increases in length. This phenomenon is thermal expansion and the property of a material responsible for this is known as coefficient of thermal expansion. The coefficient of (linear) thermal expansion is the amount of expansion in a unit length of a solid material as a result of a temperature rise of 1°. — Coefficient of thermal expansion, a = 1 di I ' Dt ...(in)(vi) Copper, nickel, aluminum and austenitic alloys retain their much of tensile ductility and resistance to shock at low temperatures in spite of the increase in strength, (v/i) F.C.C. metals and alloys retain their ductility substantially unimpaired up to - 24°C. (viii) A tendency for B.C.C. metals (e.g., steels) to (become sensitive to multi axial stresses under shock load conditions and this is manifested by the sharp decline in the value of the absorbed energy in the notch impact test thereby indicating that the materials) behave in a brittle manner, at lower temperatures. THERMAL PROPERTIES By thermal property is meant the response of a material to the application of heat. As a solid absorbs energy in the form of heat, its temperature rises and its dimensions increase. The energy may be transported to cooler regions of the specimen if temperature gradients exist and ultimately, the specimen may melt. The study of thermal properties of materials is essential in order to evaluate the thermal behaviour of solids, i.e., their response to thermal changes — the lowering or raising of temperature. It is very necessary to know the thermal behaviour of those materials which are to be used in making component parts of furnaces, ovens or boilers that have to withstand steady high or fluctuating temperatures. Thermal properties such as (1) Heat capacity (3) Thermal expansion (5) Thermal conductivity (7) Thermal stability are important to be determined for the materials. Heat Capacity - A solid material, when heated, experiences an increase in temperature signifying that some energy has been absorbed. Heat capacity is a property that is indicative of a material's ability to absorb heat from the external soundings; it represents the amount of energy required to produce a unit temperature rise. In mathematical terms, the heat capacity C is expressed as follows: dQ is the energy required to produce a dT temperature change. Ordinarily, heat capacity is specified per mol of material {e.g., J/mol -K, or cal/mol ~K). Specific heat (often denoted by a lowercase c) is sometimes used; this represents the heat capacity per unit mass, and has various units (J/kg -K, cal/g -K, Bt,u/lbm -°F). (2) Specific heat Specific heat is the quantity of heat that must be added to a unit mass of the solid to raise its temperature by one degree.When measured in Metric system specific heat is expressed as, (cal/g)/°K (or °C) and in British system as, (Btu/lb)/°F, i.e., the amount of h eat energy, measured in Btu's, that will raise the temperature of 1 lb of the material by 1°F. Specific heat, though it is assumed to remain constant, usually increases with temperature. When mathematically expressed, m dT m is the mass E is the total energy content T is the temperature. where, Coefficient of thermal expansion, though it may be assumed to be constant, for most materials, it increases slightly with temperature and changes with any phase change in the material. Melting point It is the temperature at which a pure metal, compound, or eutectic changes from solid to liquid; the temperature at which the liquid and the solid are in equilibrium. The melting point of the material is related to the bonding forces in solids. Materials having stronger bonds tend to have higher melting points. Thus, materials having covalent, ionic, metallic and molecular bonds possess melting points in decreasing order. For example, diamond having perfect covalent bond possesses highest melting point. Melting points of mild steel, copper and aluminum, for example, are about 1500,1080, and 650°C respectively. Thermal shock resistance Thermal shock defines the conditions of a body when it is subject- ed to sudden and severe changes in temperature caused either by a change in external environment or by internal heat generation. The ability of a body to withstand such temperature changes without failure is called thermal shock resistance. A ductile material will withstand severe thermal shock much better than brittle materials of comparable strength and thermal properties. In ductile materials any excessive thermal stress developed can be dissipated as the result of plastic deformation whereas, in brittle materials, the stress at a point of stress concentration is usually the governing stress tending toward failure. Thus, in ductile materials, even a very severe thermal shock may not result in fracture, but it can cause distortion or excessive deformation. However, low ductility and notch sensitivity will enhance thermal crack formation. - Thermal fatigue also may occur in systems subjected to cycles of many sudden changes of temperature. Repeated cycles of rapid heating or drastic cooling tend to reduce the capacity of the will be either larger or smaller in diameter as compared to the solvent atom. For example, steel contains iron as solvent and carbon as solute atoms, having large difference in their diameters. Since, solvent and solute atoms have different sizes, when solute is added to solvent, distortion in lattice takes place. If the solute atom is larger than the solvent atoms, compressive strain fields are set up, and if it is smaller, tensile fields. In both the cases, the stress field of a moving dislocation interacts with the stress field of the solute atom, thereby increasing the stress required to move the dislocation through the crystal. This impedes dislocation motion. The more the difference between atomic sizes of solvent and solute atoms, the higher is the stress field around solute atoms. This provides more resistance to the motion of dislocations and hence increases the tensile strength and hardness of the material. If the amount of solute or the number of solute atoms is more, greater will be the local distortion in the lattice and hence more will be the resistance to the moving dislocations. This will increase the hardness and strength of the material. Solute atoms (such as carbon and nitrogen) forming interstitial solid solutions with iron produce tetragonal distortion in the lattice and effectively increase the yield strength of iron. Solute atoms (such as silicon, manganese, molybdenum, etc.) forming substitution solid solutions with iron produce spherical distortion in the lattice and are much less effective in increasing the yield strength of iron, Moreover, disordered solid solutions are less harder and stronger than ordered solid solutions. CONCLUSION The main aim of the control design of the experimental crane was to ensure crane robustness against the burden weight and rope length variations. The designed drive control of the crane crab, bridge and uplift warrants sharp burden positioning and avoids burden swinging in the final position. These conditions improve precision and transport speed of the load. We have verified a correct selection of robust controllers by poles movement at changing variable parameters, which demonstrated stability and system damping. The distributed control system gives transparent information on the control of separate components. The technological level is intended for elaboration of process data and full information about the system state. The second level is used for monitoring and controlling the lower level. Project crane is integrated into the information level by computer nets, which allows controlling the object from a further station. Measuring of necessary parameters is realized mostly by incremental sensors and for measuring of swinging a rotary rheostat was effectively used. Simulation results obtained suggest profitable using of the robust crane control with guaranteed forbidden swinging. Stability and correct damping were kept at different burden weight and rope length. Simultaneous crab and bridge motion has increased the effectiveness of transport, where individual control systems controlled burden swinging in specific directions. The next trend in upgrading the experimental crane control will be made by a weight and deviation observer, which eliminates sensor measuring of parameters. References 1. ACKERMANN, J. : Parameter Space Design of Robust Control Systems, IEEE Trans. on Automatic Control, 1980. 2. LEONHARD, W. : Control of Electrical Drives Springer Verlag, Berlin, 1985. 3. R, M.: Written Work to the Dissertation Exam, Robust Control of Crane Crab, Koˇsice, 2001. Read More