ME1402-Mechatronics-Unit-3

ME 1402 – MECHATRONICS (UNIT – III) SYSTEM MODELS This chapter determines how the systems behave with time when subjected to some disturbance E.g A microprocessor switches on a motor The speed will not attain immediately but it will take some time to attain full speed In order to understand the behavior of the systems, mathematical models are needed These models are equations which describe the relationship between the input and output of a system The basis for any mathematical model is provided by the fundamental physical laws that govern the behavior of the system In this chapter a range of systems will be considered including mechanical, electrical, thermal & fluid examples Systems can be made up from a range of building blocks from a number of basic building blocks MECHANICAL SYSTEM BUILDING BLOCKS The basic building blocks of the models used to represent mechanical systems are 1) Springs 2) dashpots 3) masses Springs Springs represents the stiffness of the system The fig shows a spring subjected to force F In case of spring the extension (or) compression is proportional to the applied forces F = K x F – Applied force x – extension k – a constant The spring when stretched stores energy, the energy being released when the spring back to its original length The energy stored, E= F2 K x = 2K Dash Pots Dashpots building blocks represent the types of forces experienced when we push the object through a fluid or move an object against frictional forces In ideal case damping or resisting force F is proportional to the velocity of the piston Thus F=Cv V – Velocity of piston F =C dx dt C – a constant (Since velocity is the rate of change of displacement x.) Masses Masses represent the inertia or resistance to acceleration According to Newton’s II law F = ma =m dv dt = m d 2x dt There is also energy stored in mass, when it is moving with velocity V1 The energy being referred to as kinetic energy, and released when it stops moving E= × mv 2 However there is no energy stored in the dashpot It does not return to the original position, when there is no force input The dashpot dissipates energy rather than spring The power dissipated depending on the velocity V and being given by P = C V2 ROTATIONAL SYSTEMS The spring, dashpot and mass are the basic building blocks for mechanical systems when forces and straight line displacements are involved without any rotation If there is rotation then the equivalent three building blocks are a torsional spring, a rotary damper and the moment of inertia, i.e, the inertia of a rotating mass With such building blocks the inputs are torque and the outputs angle rotated With a torsional spring the angle θ rotated is proportional to the toque T Hence With the rotary damper a disc is rotated in a fluid and the resistive toque T is proportional to the angular velocity ω, and since angular velocity is the rate at which angle changes i.e dθ dt The moment of inertia building block exhibits the property that the greater the moment of inertia I the greater the torque needed to produce an angular acceleration α Thus, since angular acceleration is the rate of change of angular velocity, i.e dω , dt and angular velocity is the rate of change of angular displacement, then The torsional spring and the rotating mass store energy; the rotary damper just dissipates energy The energy stored by a torsional spring when twisted through an angle θ is ½ kθ2 and since T = k θ this can be written as The energy stored by a mass rotating with an angular velocity ω is the kinetic energy E, where The power P dissipated by the rotary damper when rotating with an angular velocity ω is BUILDING UP A MECHANICAL SYSTEM TRANSLATIONAL MECHANICAL SYSTEM Spring mass damper system: A spring mass damper system is shown in fig The system is fixed at one end and the mass is supported by a spring and damper The mass is excited by force and free to oscillate The equation of motion related to horizontal motion x of mass to applied force can be developed with of a free body diagram Net force applied to mass m = F − k x − B.v = F − kx − B dx dt - (1) d 2x dt - Also net force applied to mass = mass x acceleration = m (2) Equation (1) = (2) Apply Newton’s II law of motion m dx d 2x = F − kx − B dt dt F =m d 2x dx + kx + B dt dt This equation is called as the differential equation that describes the relation between input and output ILLUSTRATIONS MATHEMATICAL MODEL FOR A MACHINE MOUNTED ON THE GROUND MATHEMATICAL MODEL OF A WHEEL OF A CAR MOVING ALONG A ROAD PROBLEMS ELECTRICAL SYSTEM BUILDING BLOCKS The basic building blocks of electrical building blocks are inductors, capacitors, and resisters Resistors: Resistance is an opposition to movement of flow of material or energy An electric resistor opposes the flow of current, the voltage V across the resistor is given by V= I R, Where R= resistance Capacitors Capacitors are used to stored charge to increase the voltage by iV A capacitor consists of two parallel plates separated by insulating material and capacitor act as a strong device of energy The voltage equation for a capacitor is V = ∫ idt C Where c = capacitor Inductors: It consists of a coil wire When current flows through the wire, a magnetic field surrounding the wire is produced Any attempt to change the density of this magnetic field leads to the induction of voltage The inductor equation is V =L di dt 10 3) The control system mode and parameters are automatically and continuously adjusted in order to minimize the difference between the desired and actual system performance Adaptive control system can take a number of forms The three commonly used forms are: Gain scheduling control Self – tuning control Model – reference adaptive control Gain scheduling control With gain scheduling control, present changes in the parameter of the controller are made on the basis of some auxiliary measurement of some process variable The term gain – scheduled control was used because the only parameter originally adjusted was to gain is kp Self tuning 57 With self tuning control system continuously tunes its own parameter based on monitoring the variable that the system is controlling Self- tuning is found in PID controllers It is generally refers to auto- tuning When the operator presses a button, the controller injects a small disturbance into the system and measures the response This response is compared to the desired response and the control parameters are adjusted Model – reference control Model reference system is an accurate model of the system is developed The set value is then used as input to both model systems and actual systems and the difference between the actual output and output from the model compared The difference in these signals is then used to adjust the parameters of the controller to minimize the difference 58 MICROPROCESSOR’S CONTROL A microprocessor is a programmable digital electronic component that incorporates the functions of a central processing unit (CPU) on a single semi conducting integrated circuit (IC) The microprocessor was born by reducing the word size of the CPU from 32 bits to bits, so that the transistors of its logic circuits would fit onto a single part One or more microprocessor typically serves as the CPU in a computer system, embedded system, or hand held device Microprocessors made possible the advent of the microcomputer in the mid- 1970s.Before this period, electronic CPUs were typically made from bulky discrete switching devices (and later small-scale integrated circuits) containing the equivalent of only a few transistors By integrating the processor onto one or a very few large-scale integrated circuit packages (containing the equivalent of thousands or millions of discrete transistors), the cost of processor power was greatly reduced Since the advent of the IC in the mid1970s, the microprocessor has become the most prevalent implementation of the CPU, nearly completely replacing all other forms Definition The microprocessor is a program controlled semiconductor device (IC), which fetches (from memory), decodes and executes instructions It is used as CPU (Central Processing Unit) in computers Microprocessors are now rapidly replacing the mechanical cam operated controllers and being used in general to carry out 59 control functions They have the great advantage that a greater variety of programs became feasible 60 REGISTERS 61 General purpose registers registers but access is not required, it is an internal operation Thus it provides an efficient way to store intermediate results and use them when required The efficient programmer prefers to use these registers to store intermediate results than the memory locations which require but access and hence more time to perform the operation Temporary Registers a) Temporary Data Register 62 The ALU has two inputs One input is supplied by the accumulator and other from temporary data register The programmer cannot access this temporary data register However, it is internally used for execution of most of the arithmetic and logical instructions For example, ADD B is the instruction in the arithmetic group of instructions which adds the contents of register A and register B and stores result in register A The addition operation is performed by ALU The ALU takes inputs from register A and temporary data register The contents of register B are transferred to temporary data register for applying second input to the ALU b) 'W and Z Registers W and Z registers are temporary registers These registers are used to hold 8-bit data during execution pf some instructions These registers are not available for programmer, since 8085 uses them internally Use of W and Z Registers The CALL instruction is used to transfer program control to a subprogram or subroutine This instruction pushes the current PC contents onto the stack and loads the given address into the PC The given address is temporarily stored in the W and Z registers and placed on the bus for the fetch cycle Thus the program control is transferred to the address given in the instruction XCHG instruction exchanges the contents of H with D and L with E At the time of exchange W and Z registers are used for temporary storage of data 63 Special Purpose Registers a) Register A (Accumulator) It is a tri-state eight bit register It is extensively used in arithmetic, logic, load, and store operations, as well as in, input/output (1/0) operations Most of the times the result of arithmetic and logical operations is stored in the register A Hence it is also identified as accumulator b) Flag Register It is an 8-bit register, in which five of the bits carry significant information in the form of flags: S (sign flag), Z (zero flag), AC (auxiliary carry flag), P (parity flag) and CY (carry flag), as shown in figure S-sign flag After the execution of arithmetic or logical operations, if bit D, of the result is 1, the Sign flag is set In a given byte if D, is 1, the number will be viewed as negative number If D is 0, the number will be considered as positive number The zero flag sets if the result of operation in ALU is zero and flag resets if result is non zero The zero flag is also set if a certain register content becomes zero following an increment or decrement operation of that register 64 AC-Auxiliary Carry Jag This flag is set if there is an overflow out of bit 3, i.e., carry from lower nibble to higher nibble (D, bit to D, bit) This flag is used for BCD operations and it is not available for the programmer P-Parity Flag Parity is defined by the number of ones present in the accumulator After an arithmetic or logical operation if the result has an even number of ones, i.e even parity, the flag is set If the parity is odd, flag is reset CY-carry flag This flag is set if there is an overflow out of bit The carry flag also serves as a borrow flag for subtraction In both the examples show below, the carry flag is set c) Instruction Register In a typical processor operation, the processor first fetches the opcode of instruction from memory (i.e it places an address on the address bus and memory responds by placing the data stored at the specified address on the data bus) 65 The CPU stores this opcode in a register called the instruction register This opcode is further sent to the instruction decoder to select one of-the 256 alternatives Sixteen Bit Registers a) Program Counter (PC) Program is a sequence of instructions As mentioned earlier, microprocessor fetches these instructions from the memory and executes them sequentially The program counter is a special purpose register which, at a given time, stores the address of the next instruction to be fetched Program counter acts as a pointer to the next instruction How processor increments program counter depends on the nature of the instruction; for one byte instruction it increments program counter by one, for two byte instruction it increments program counter by two and for three byte instruction it increments program counter by three such that program counter always points to the address of the next instruction In case of JUMP and CALL instructions, address followed by JUMP and CALL instructions is placed in the program counter The processor then fetches the next instruction from the new address specified by JUMP or CALL instruction In conditional JUMP and conditional CALL instructions, if the condition is not satisfied, the processor increments program counter by three so that it points the instruction followed by conditional JUMP or CALL instruction; otherwise processor fetches the next instruction from the new address specified by JUMP or CALL instruction 66 b) Stack Pointer (SP) The stack is a reserved area of the memory in the RAM where temporary information may be stored A 16-bit stack pointer is used to hold the address of the most recent stack entry ARITHMETIC LOGIC UNIT (ALU) The 8085'sALU performs arithmetic and logical functions on eight bit variables The arithmetic unit bitwise fundamental arithmetic operations such as addition and subtraction The logic unit performs logical operations such as complement, AND, OR and EX-OR, as well as rotate and clear The ALU also looks after the branching decisions Instruction Decoder As mentioned earlier, the processor first fetches the opcode of instruction from memory and stores this opcode in the instruction register It is then sent to the instruction decoder The instruction decoder decodes it and accordingly gives the timing and control signals which control the register, the data buffers, ALU and external peripheral signals (explained in later sections) depending on the nature of the instruction The 8085 executes seven different types of machine cycles It gives the information about which machine cycle is currently 67 executing in the encoded form on the So, S, and 10 IM lines This task is done by machine cycle encoder Address Buffer This is a 8-bit unidirectional buffer It is used to drive external high order address bus (A15, -A8,) It is also used to tristate the high order address bus under certain conditions such as reset, hold, and halt and when address lines are not in use Address/Data Buffer This is an 8-bit bi-directional buffer It is used to drive multiplexed address/data bus, i.e., low order address bus (A7, -A0,) and data bus (D7, - Do) It is also used to tristate the multiplexed address/data bus under certain conditions such as reset, hold, and halt and when the bus is not in use The address and data buffers are used to drive external address and data buses respectively Due to these buffers the address and data buses can be tri-stated when they are not in use Incrementer/Decrementer Address Latch This 16-bit register is used to increment or decrement the contents of program counter or stack pointer as a part of execution of instructions related to them Interrupt Control The processor fetches, decodes and executes instructions in a sequence Sometimes it is necessary to have processor the automatically execute one of a collection of special routines 68 whenever special condition exists within a program or the microcomputer system The most important thing is that, after execution of the special routine, the program control must be transferred to the program which processor was executing before the occurrence of the special condition The occurrence of this special condition is referred as interrupt The interrupt control block has five interrupt inputs RST 5.5, RST 6.5, RST 7.5, TRAP and INTR and one acknowledge signal INTA Serial I/0 Control In situations like, data transmission over long distance and communication with cassette tapes or a CRT terminal, it is necessary to transmit data bit by bit to reduce the cost of cabling In serial communication one bit is transferred at a time over a signal line The 8085's serial I/0 controls provide two lines, SOD and SID for serial communication The serial output data (SOD) line is used Timing and Control Circuitry The control circuitry in processor 8085 is responsible for all the operations The control circuitry and hence the operations in 8085 are synchronized with the help of clock signal Along with the control of fetching and decoding operations and generating appropriate signals for instruction execution, control circuitry also generates signals required to interface external devices to the processor, 8085 Pin Configuration of 8085 69 Figure shows 8085 pin configuration and functional pin diagram of 8085 respectively The signals of 8085 can be classified into seven groups according to their functions a) Power supply and frequency signals b) Data bus and address bus c) Control bus d) Interrupt signals e) Serial L/O signals f) DMA signals g) Reset signals 70 71