Mechatronics Book Notes

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Open Closed Loop

The real-time control software can be divided into two groups, ,The foreground program is the one that is executed every time the sampling clock generates an interrupt. background program handling operator input/output operations, checks error and alarm conditions, and checks other process inputs and outputs (I/O) not used in closing the control loop but used for other logic and sequencing functions 1. Disturbances (w(s)): there are always disturbances which are not under our control. They exist and cause error in the system response. For instance, the wind acts as a disturbance on an airplane changing its flight direction. Low outside temperature and the heat loss due to it from the walls of a heated house acts as a disturbance on the control system since the outside temperature is not under our control, yet it affects the temperature of the house. 2. Variations in process dynamics (?G(s)): the dynamics of the process may change structurally or parametrically. Structural changes in the dynamics imply drastic significant changes, such as the change in the dynamics of an aircraft due to loss of an engine or a wing. Whereas parametric changes imply less significant, more smooth, non-drastic changes, such as the change in the weight of an aircraft as the fuel is being consumed, or due to opening of the wing control surfaces. 3. Sensor noise (v(s)): closed loop control requires the measurement of the actual response (the controlled variable). The sensor signals always have some noise in the measurement. The noise is included in the control decisions and hence affects the overall performance of the system. Three major groups of events which are not under our control and affect the system performance are: 1. variations in the process parameters and dynamics, 2. disturbances, 3. sensor noise. A desired performance specification for any CLS includes specifications regarding 1. stability, 2. response quality (transient and steady state), 3. robustness of stability and response quality despite real-world imperfections, that is variations in the process dynamics, disturbances, and sensor noise. The main advantage of feedback control over open loop control is that it increases the robustness of the system against the disturbances and variations in the process dynamics. The general characteristics of control systems are discussed in terms of the shape of the loop transfer function in order to provide good robustness against these undesirable real-world problems of control systems. However, sensor noise or sensor failure can make a closed loop system unstable. If the process dynamics does not vary much and the disturbances are well known, open loop control may be a better choice than closed loop control. Open loop control does not suffer from the potential stability problems associated with sensor failures. The issue with closed loop is the disturbance (low frequency) and sensor noise (usually high frequency)

BASIC FEEDBACK CONTROL TYPES -PID

Proportional: � action is generated based on the current error
Integral:�action is generated based on the past error
Derivative: �action is generated based on the anticipated future error

MECHANISMS FOR MOTION TRANSMISSION

.In general, it is not practical to place the actuator exactly at the location where the motion of a tool is needed. Therefore, a motion transmision mechanism is needed between the actuator and the tool. Motion transmission mechanisms perform two different roles, 1. they transmit motion from actuator to tool when the actuator cannot be designed into the same location as the tool with the desired motion type, 2. they increase or reduce torque and speed between input and output shafts while maintaining the power conservation between input and output (output power is input power minus the power losses).

The most common motion transmission mechanisms fit into one of three major categories:

1. rotary to rotary motion transmission mechanisms (gears, belts, and pulleys)

2. rotary to translational motion transmission mechanisms (lead-screw, rack-pinion, belt-pulley),

3. cyclic motion transmission mechanisms (linkages and cams).

ROTARY TO ROTARY MOTION TRANSMISSION MECHANISMS

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Gears are used to increase or decrease the speed ratio between the input and output shaft. The effective gear ratio is obvious (Figure 3.1). Assuming that the gears do not slip, the MECHANISMS FOR MOTION TRANSMISSION 137 linear distance traveled by each gear at the contact point is same,

The gear ratio of a belt-pulley mechanism is the ratio between the input and output diameters. Assuming no slip between the belt and pulleys on both shafts, the linear displacement along the belt and both pulleys should be equal

ROTARY TO TRANSLATIONAL MOTION TRANSMISSION MECHANISMS

Lead-screw and ball-screw mechanisms are the most widely used precision motion conversion mechanisms which transfer rotary motion to linear motion. Ball-screw design uses precision ground spherical balls in the groove between the screw and nut threads to reduce backlash and friction in the motion transmission mechanism. Any lead-screw has a finite backlash typically in the order of micrometer range. By using preloaded springs, a set of spherical bearing-type balls are used to reduce the backlash.

The advantage of the rack and pinion mechanism over the lead-screw mechanism is that the translational motion range can be very long. The lead-screw length is limited by the torsional stiffness.

CYCLIC MOTION TRANSMISSION MECHANISMS

Linkages are generally one degree of freedom, kinematically closed chain, robotic manipulators. The motion of one member (output link) of the linkage is a periodic function of the motion of another linkage member (input link). The most common linkages include 1. slider-crank mechanism (i.e., used in internal combustion engines (Figure 3.6)), 2. four-bar mechanism (see

Cams convert the rotary motion of a shaft into translational motion of a follower. It is common to design rise and fall periods of the cam as symmetric. During the dwell periods, the follower is stationary. Therefore, during dwell period the follower position is constant, and speed and acceleration are zero. If symmetric cam functions are used for rise and fall periods, then we are only concerned with the cam function design for the rise period. 1. Pressure angle: measured as the angle between the follower motion axis and the axis perpendicular to the common tangent line at the contact point between cam and follower (Figure 3.7). A cam should be machined such that the pressure angle stays less than about 30? in order to make sure the side loading force on the follower is not too high. 2. Eccentricity: the offset distance between the follower axis and cam rotation axis in the direction perpendicular to the cam motion. By increasing eccentricity, we can reduce the effective pressure angle, and hence the side loading forces on the follower. However, as the eccentricity increases, the cam gets larger and less compact. 3. Radius of curvature: the radius of the cam function curvature along its periphery. The radius of curvature should be a continuous function of the angular position of the cam input shaft. Any discontinuity in the radius of curvature is essentially reflected as a non-smooth cam surface. In general, the radius of curvature should be at least 2 to 3 times larger than the radius of the follower. The main considerations are the continuity and ability of the follower to maintain contact on the cam at all times

SHAFT MISALIGNMENTS AND FLEXIBLE COUPLINGS

Mechanical systems always involve two or more shafts to transfer motion. There is always a finite accuracy with which the two shafts can be aligned in the axial direction. Any shaft misalignments will result in loads on the bearings and cause vibration, and hence reduce the life of the machinery. In order to reduce the vibration and life reducing effects of shaft misalignment, flexible couplings are used between shafts There are two main categories of flexible shaft couplings: 1. couplings for large power transfer between shafts and motors, 2. couplings for precision motion transfer at low powers between shafts and motors High precision motion systems include motors with very low friction and yet very delicate bearings. Such motors are very sensitive to shaft misalignments. The bearing failure of the motor as a result of excessive shaft misalignment is a very common reliablity problem. Therefore, in most high performance servo motor applications, the motor shaft is coupled to the load via a flexible coupling. The flexible couplings provide the ability to make the system more tolerant to shaft misalignments. However, it comes at the cost of reduced stiffness of the mechanical system. Therefore, designers must make sure that the stiffness of the coupling does not interfere with the desired motion bandwidth (especially in variable speed and cyclic positioning applications). Couplings are rated by the following parameters: 1. maximum and rated torque capacity, 2. torsional stiffness, 3. maximum allowed axial misalignment, 4. rotary inertia and mass of the coupling,

HOMOGENEOUS TRANSFORMATION MATRICES

The geometric relationships in simple one degree of freedom mechanisms can be derived using basic vector algebra. The derivation of geometric relations for multi degrees of freedom mechanisms, such as robotic mechanisms, is rather difficult using three-dimensional vector algebra. The so called 4�4 homogeneous transformation matrices are very powerful matrix methods to describe the geometric relations

MICROCONTROLLERS

Analog to Digital Converter (ADC)

The analog to digital converter (A/D or ADC) allows conversion of an analog input signal to a digital number. The ADC on the PIC 18F452 has a 10-bit range and eight multiplexed input channels. Unused analog input channel pins can be configured as digital I/O pins.

Timers and Counters

In real-time applications, there are many cases when different tasks need to be performed at different periodic intervals. For instance, in an industrial control application, the status of doors in a building may need to be checked every minute, the parking lot gate status may need to be checked every hour. The best way to generate such periodic interrupts with different frequencies is to use a programmable timer/counter chip. A timer/counter chip operates as a timer or as a counter. In the timer mode of operation, it counts the number of clock cycles, hence it can be used as a time measurement peripheral. The clock source can be an internal clock or external clock.

Watch Dog Timers

A watch dog timer (WDT) is a hardware timer, which is used to reboot or take a predefined action if it expires. The watch dog timer keeps a �watch eye� on the system performance. If something gets stuck, the watch dog timer can be used to reset everything. A watch dog timer is essential in embedded controllers. The WDT counts down from a programmable preset value. If it reaches zero before the software resets the counter to preset value, it is assumed that something is stuck. Then the processor�s reset line is asserted. The time-out period can be programmed to a value between 4 ms to 131.072 s

INTERRUPTS

An interrupt is an event which stops the current task the microprocessor is executing, and directs it to do something else. And when that task is done, the microprocessor resumes the original task. An interrupt can be generated by two different sources: 1. hardware interrupts (external), 2. software (internal) generated interrupt with an instruction in assembly. In a given computer control system, there can be more than one interrupt source and they may happen at the same time. Therefore, different interrupts need to be assigned different priority levels to determine which one is more important. language, such as INT n.

Sensors

Intro

1./ The change in the measured physical variable (i.e., pressure, temperature, displacement) is translated into a change in the property (resistance, capacitance, magnetic coupling) of the sensor. This is called the transduction. The change of the measured variable is converted to an equivalent property change in the sensor. The transduction relationship, that is the relationship between the measured variable and the change in the sensor material property, is the fundamental physical principle of the sensor operation. It is desirable that this relationship is repeatable and does not vary with other environmental variables. For instance, a pressure sensor output voltage as a function of pressure should not change much due to changes in the ambient temperature. 2. The change in the property of the sensor is translated into a low power level electrical signal in the form of voltage or current. 3. This low power sensor signal is amplified, conditioned (filtered), and transmitted to an intelligent device for processing, for example to a display for monitoring purposes or use in a closed loop control algorithm.

Accuracy, Repeatablity, and Resolution.

Resolution refers to the smallest change in the measured variable that can be detected by the sensor. Accuracy refers to the difference between the actual value and the measured value. Accuracy of a measurement can be determined only if there is another way of more accurately measuring the variable so that the sensor measurement can be compared with it. Repeatability refers to the average error in between consecutive measurements of the same value. The same definitions apply to the accuracy of a control system as well. In a measurement system, repeatability can be at best as good as the resolution.

Sensor Issues

1. gain changes, 2. offset (bias or zero-shift) changes, 3. saturation, 4. hysteresis, 5. deadband, 6. drift in time Remedies: If the nonlinearities are known to be repeatable, then they can be compensated for in software in order to obtain accurate measurement. In general, a sensor needs to be calibrated to customize it for an application. In any control system application such as an automated machine in an assembly line or a mobile equipment, which may involve hundreds of sensors, one of the first steps in implementing a control system is the sensor calibration.

MEASUREMENT DEVICE LOADING ERRORS

There are two types of loading errors: 1. mechanical loading error, 2. electrical loading error. Consider that we want to measure the temperature of a liquid in a container. If we insert a mercury-in-glass thermometer in the container, there will be a finite amount of heat transfer between the liquid and the thermometer. This is the loading error where measuring the item also changes its temp. The electrical loading error issue exists in electrical circuits used in measurement systems. Once the measurement device is connected to the circuit at points A and B, it changes the the electrical circuit and can cause a loading error. Therefore, in order to minimize the effect of electrical loading errors due to the circuits used for the measurement, the measurement device should have a large input resistance (input impedance). The larger the input impedance, the smaller the electrical loading error in the voltage measurement.

POSITION SENSORS

There are two kinds of length measurements of interest: (i) absolute position (the distance between two points), (ii) incremental position (the change in the position). If a sensor can measure the position of an object on power-up relative to a reference (the distance of the object from a reference point on power-up), we call it an absolute position sensor. If the sensor cannot tell the distance of the object from a reference on power-up, but can keep track of the change in position from that point on, we call it an incremental position sensor. Examples of absolute position sensors include a calibrated potentiometer, absolute optical encoder, linear variable differential transformer, resolver, and capacitive gap sensor. Examples of incremental position sensors include incremental optical encoder and laser interferometer. Most of the position sensors have rotary and translational (linear) position sensor versions.

Potentiometer

A potentiometer relates the absolute position (linear or rotary) into the resistance (Figures 6.9 and 6.10). The resistance change is converted to a proportional voltage change in the electrical circuit portion of the sensor

LVDT, Resolver, and Syncro

The linear variable differential transformer (LVDT), resolver, and syncro are sensors which operate based on the transformer principle of electromagnetism.

Advantages: The LVDT has low power consumption. It has higher sensitive. It has ruggedness. It has wide range. It has low hysteresis. Disadvantages: It has large primary voltage produce distortion in output. Temperature affects the performance. Sensitive to stray magnetic field.

Encoders

There are two main groups of encoders: absolute encoders and incremental encoders. Absolute encoders can measure the position of an object relative to a reference position at any time. The output signal of the absolute encoder presents the absolute position in a digital code format. An incremental encoder can measure the change in position, not the absolute position. Therefore, the incremental encoder cannot tell the position relative to a known reference. If absolute position information is needed from incremental encoder measurement, the device must perform a so called �home-ing� motion sequence in order to establish its reference position after the power up. From that point on, the absolute position can be kept track of by digital counting. Encoders can also be classified based on the type of position they measure: translational or rotary. Rotary two main types of rotary encoder: absolute and incremental.

Absolute encoder maintains position information when power is removed from the encoder.[3] The position of the encoder is available immediately on applying power. It can maintain absolute position of the encoder within one revolution. An incremental encoder will immediately report changes in position, which is an essential capability in some applications. However, it does not report or keep track of absolute position.

Linear Encoder

Linear encoders sense and digitize linear position and movement. A linear encoder is a sensor linked to a scale. The sensor reads the scale and converts position into an analog or digital signal that informs a digital readout. Movement is determined from changes in position with time

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