What type of feedback signal does the closed loop industrial control typically uses?

2.1.4 Feedback Sensors

Feedback sensors provide the control system with measurements of physical quantities necessary to close control loops. The most common sensors are for motion states (position, velocity, acceleration, and mechanical strain), temperature states (temperature and heat flow), fluid states (pressure, flow, and level), and electromagnetic states (voltage, current, charge, light, and magnetic flux). The performance of most traditional (nonobserver) control systems depends, in large part, on the quality of the sensor. Control-system engineers often go to great effort to specify sensors that will provide responsive, accurate, and low-noise feedback signals. While the plant and power converter may include substantial imperfections (for example, distortion and noise), such characteristics are difficult to tolerate in feedback devices.

2.1.4.1 Errors in Feedback Sensors

Feedback sensors measure signals imperfectly. The three most common imperfections, as shown in Figure 2-5, are intrinsic filtering, noise, and cyclical error.

Figure 2-5. A practical sensor is a combination of an ideal sensor and error sources.

The intrinsic filtering of a sensor limits how quickly the feedback signal can follow the signal being measured. The most common effect of this type is low-pass filtering. For all sensors there is some frequency above which the sensor cannot fully respond. This may be caused by the physical structure of the sensor. For example, many thermal sensors have thermal mass; time is required for the object under measurementsto warm and cool the sensor's thermal mass. Filtering may also be explicit as in the case of electrical sensors where passive filters are connected to the sensor output to attenuate noise.

Whatever the source of the filtering, its primary effect on the control system is to add phase lag to the control loop. Phase lag reduces the stability margin of the control loop and makes the loop more difficult to stabilize. The result is often that system gains must be reduced to maintain stability in order to accommodate slow sensors. Reducing gains is usually undesirable because both command and disturbance response degrade.

Cyclical error is the repeatable error that is induced by sensor imperfections. For example, a strain gauge measures strain by monitoring the change in electrical parameters of the gauge material that is seen when the material is deformed. The behavior of these parameters for ideal materials is well known. However, there are slight differences between an ideal strain gauge and any sample. Those differences result in small, repeatable errors in measuring strain. Since cyclical errors are deterministic, they can be compensated out in a process where individual samples of sensors are characterized against a highly accurate sensor. However, in any practical sensor some cyclical error will remain. Because control systems are designed to follow the feedback signal as well as possible, in many cases the cyclical error will affect the control-system response.

Stochastic or nondeterministic errors are those errors that cannot be predicted. The most common example of stochastic error is high-frequency noise. High-frequency noise can be generated by electronic amplification of low-level signals and by conducted or transmitted electrical noise commonly known as electromagnetic interference (EMI). High-frequency noise in sensors can be attenuated by the use of electrical filters; however, such filters restrict the response rate of the sensor as discussed above. Designers usually work hard to minimize the presence of electrical noise, but as with cyclical error, some noise will always remain. Filtering is usually a practical cure for such noise; it can have minimal negative effect on the control system if the frequency content is high enough so that the filter affects only frequency ranges well above where phase lag is a concern in the application.

The end effect of sensor error on the control system depends on the error type. Limited responsiveness commonly introduces phase lag in the control system, reducing margins of stability. Noise makes the system unnecessarily active and may reduce the perceived value of the system or keep the system from meeting a specification. Deterministic errors corrupt the system output. Because control systems are designed to follow the feedback signal (including its deterministic errors) as well as possible, deterministic errors will carry through, at least in part, to the control-system response.

(b) Auto Stabilization

With sensor feedback fed into the vehicle control module, any number of parameters may be used in vehicle control through a system of closed-loop control routines. Just as dogs follow a scent to its source, ROVs can use sensor input for positive navigation. Advances are currently being made for tracking chemical plumes from environmental hazards or chemical spills. A much simpler version of this technique is the rudimentary auto depth/altitude/heading.

Auto depth is easily maintained through input from the vehicle's pressure-sensitive depth transducer. Auto altitude is equally simple, but the vehicle manufacturer is seldom the same company as the sensor manufacturer (causing some issues with communication standards and protocols between sensor and vehicle). The most common compass modules used in observation-class ROV systems are the inexpensive flux gate-type. These flux gate-type compasses have a sampling rate (while accurate) slower than the yaw swing rate of most small vehicles, which cause the vehicle to ‘chase the heading’. Flux gate auto heading is better than no auto heading, but several manufacturers of small systems have countered this ‘heading chase’ problem by using a gyro.

Gyros for small ROVs come in two basic types, the slaved gyro and the rate gyro. The slaved gyro samples the magnetic compass to slave the gyro periodically to correspond with its magnetic counterpart. Since the auto heading function of an ROV is simply a heading hold function, some manufacturers have gotten away with using a simple rate gyro for ‘heading stabilization’. When the heading hold function is slaved to a gyro only, sensing a turn away from the initial setting and a rate at which the turn is progressing (i.e. the rate gyro has no reference to any magnetic heading), the vehicle is then only referenced to a given direction. Hence the term ‘heading stabilization’ due to the lack of any reference to a specific compass direction.

4.1.2 Autostabilization

With sensor feedback fed into the vehicle control module, any number of parameters may be used in vehicle control through a system of closed-loop control routines. Just as dogs follow a scent to its source, ROVs can use sensor input for positive navigation. Advances are currently being made for tracking chemical plumes from environmental hazards or chemical spills (although this is considered a higher, logic-driven control level). A much simpler version of this technique is the rudimentary auto-depth/altitude/heading.

Auto-depth is easily maintained through input from the vehicle’s pressure-sensitive depth transducer. Auto-altitude is equally simple, but the vehicle manufacturer is seldom the same company as the sensor manufacturer (causing some issues with communication standards and protocols between sensor and vehicle). The most common compass modules used in observation-class ROV systems are the inexpensive flux gate type. These flux gate type compasses have a sampling rate (while accurate) slower than the yaw swing rate of most small vehicles, which cause the vehicle to “chase the heading.” Flux gate auto-heading is better than no auto-heading, but several manufacturers of small systems have countered this “heading chase” problem by using a gyro.

As described in Chapter 11, gyros for ROVs come in two basic types, the slaved gyro and the rate gyro. The slaved gyro samples the magnetic compass to slave the gyro periodically to correspond with its magnetic counterpart. Since the auto-heading function of an ROV is simply a heading hold function, some manufacturers have gotten away with using a simple rate gyro for “heading stabilization.” When the heading hold function is slaved to a gyro only, sensing a turn away from the initial setting and a rate at which the turn is progressing (i.e., the rate gyro has no reference to any magnetic heading), the vehicle is then only referenced to a given direction. Hence the term “heading stabilization” due to the lack of any reference to a specific compass direction.

12.4.7 Deterministic Feedback Error

Errors in feedback sensors can cause nonlinear behavior. Repeatable errors can often be measured when the machine or process is commissioned and then canceled by the controller during normal operation. For example, many machines rely on motor feedback sensors to sense the position of a table that is driven by the motor through a transmission, typically a gearbox and lead screw. The motor feedback, after being scaled by the pitch of the lead screw and the gear ratio, provides the position of the table. This is shown in Figure 12.21.

One weakness of this structure is that the transmission has dimensional errors that degrade the accuracy of the motor feedback signal. However, this can be compensated for by measuring the table to high accuracy with an external measuring device such as a laser interferometer. During commissioning, the position of the motor (as measured by the motor feedback device) is compared with the presumed-accurate signal from the interferometer and the difference is stored in a table. This is shown in Figure 12.22. Many positions are measured to fill the table.

During normal operation, the error stored in the table is subtracted from the feedback sensor to compensate for the transmission inaccuracy. This amounts to using the error table for offset scheduling, as shown in Figure 12.23. Of course, the most straightforward cure to deterministic error is to use more accurate transmission components. However, more accurate transmission components are usually more expensive. Offset scheduling can bring great benefits in accuracy without significantly increasing the cost of the machine.

14.2 Encoders

The position feedback sensor in modern motion controllers is usually either an incremental encoder, a sine encoder, or a resolver coupled with a resolver-to-digital converter, or RDC. In all cases, the servo controller knows the position only to within a specified resolution. For the two-channel incremental encoders used in most servo applications, the resolution is four times the line count; encoder interface circuitry uses a technique called quadrature decoding to generate four pulses for each encoder line. Figure 14.3 shows the technique, which is based on having two encoder signals, named Channel A and Channel B, separated by 90°. Because of quadrature, there are four edges for each encoder line — one positive and one negative for each channel. Thus a 1000-line encoder will generate 4000 counts for each encoder revolution. It should be noted that single-channel encoders are used occasionally in servo applications. This is rare because two channels are necessary to determine the direction of motion.

6.2.1 Transfer Function of Disturbance Response for Traditional Systems

Disturbance response of a control system both with sensor feedback and with observed-state feedback can be evaluated using transfer functions. The transfer function of the disturbance response of the traditional system shown in Figure 6-9 is easily calculated since there is only one loop.

L1=−GC(s)×G PC(s)×GP(s)×GS(s)

There is a single path from D(S) to C(S):GP(S). The transfer function is then:

(6.8)C(s)D( s)=GP(s)11+GC(s)×GPC(s)×GP(s)×GS(s)⋅

An algebraic manipulation yields

(6.9)C(s)D(s)=GP(s)(1−GC(s)×GPC(s)×GP(s)×GS(s)1+GC(s)×GPC(s)×GP(s)×GS(s)).

Equation 6.9 can be rewritten in terms of the control-law closed-loop transfer function, GCL(S) =Y(S)/R(S):

(6.10)C(s)D(s)=GP(s)(1−GCL(s)).

Understanding that the ideal disturbance response is 0, the closer that GCL(S), the closed-loop response, is to unity, the better the disturbance response. The closed-loop response will be closest to one at low frequency and, correspondingly, the disturbance response will be the best. Raising the control-system bandwidth improves disturbance by keeping GCL(S) approximately unity for a wider range of frequencies; the disturbance response of Equation 6.10 will be lower over a wider frequency range, rejecting more of the disturbance input.

Well above the control-loop bandwidth, the closed-loop response will be near zero and the disturbance response will be GP(S); that is, the disturbances will be limited only by the plant gain. At high frequencies, disturbance response is passive as, for example, when a large capacitor in a power supply prevents high-frequency voltage ripple or when a large inertia prevents high-frequency velocity ripple.

29.5.4 Synchronous Driving Using Open-Loop Control

Many inexpensive brushless motors do not provide Hall sensor feedback.3 These motors have only three wires, for the phases A, B, and C. Such motors are often used in quadcopters, for example. It is possible to drive these motors to achieve a desired angular velocity by commutating open-loop (no Hall sensor feedback).

To understand how a BLDC motor can run without sensing, consider that if we kept a constant voltage at A, ground at B, and left C floating, the rotor might first experience a positive torque, accelerating in the positive direction until it reaches the point where the magnetic poles at α,α¯,β, and β¯ provide zero torque. Then, after overshooting the zero torque position, it would experience a negative torque, decelerating it. With damping, the rotor would eventually rest at a position where it experiences zero torque, much like the operation of a stepper motor.

The eventual negative torque that comes from not commutating can be viewed as a type of built-in stabilizing feedback. In the extreme stepper-like case above, the feedback causes the rotor to stop. Instead, consider what happens when the commutation cycles through the steps 1-6 at a fixed frequency. If the frequency is slightly too low for the voltage (or PWM level) used, the rotor may experience deceleration before the next commutation step occurs and it begins to accelerate it again. Although somewhat inefficient, this deceleration acts as negative feedback, causing the rotor to slow its travel around its mechanical revolution to better match the speed of the electrical revolution imposed by the commutation.

In summary, if the commutation frequency is neither too fast nor too slow for the given PWM level, the rotor will synchronize with the commutation due to the built-in negative feedback. If the commutation frequency is too fast, then, much like a stepper, the rotor will fall behind, become desynchronized, and likely end up vibrating. Similarly, if the acceleration or deceleration of the commutation is too high, the inertia of the BLDC and its load will prevent the rotor from following the commutation. To achieve open-loop control of a BLDC from rest, to a high velocity, and back to rest, the acceleration, deceleration, and maximum velocity must be limited.

Open-loop driving of a BLDC only works when the loads on the BLDC are relatively well known. If a large torque is suddenly applied to the BLDC rotor, the rotor is likely to desynchronize with the commutation.

Code Sample 29.4 open_loop.c demonstrates open-loop control of the unloaded Pittman ELCOM SL 4443S013 using the 9 V motor supply in Figure 29.12. The user specifies the desired PWM duty cycle as a signed percentage (−100 to 100). Using information from the motor’s data sheet, the relationship between the average voltage (and therefore PWM duty cycle) and the unloaded motor’s speed is derived. Knowing the motor speed corresponding to the user’s requested PWM, the duration of each commutation segment is calculated. For example, since there are 12 commutation phases per mechanical revolution, at 500 RPM, there are 500 × 12 = 6000 commutation phases per minute, or 100 commutation phases per second, so each commutation phase lasts 1 s/100 = 10 ms.

The duration of each commutation phase is counted in increments of 50 μs by using the ISR of Timer2, which is generating the 20 kHz (= 1/50 μs) PWM. When the duration of the commutation phase is exceeded, bldc_commutate (in the bldc library, above) is called with the virtual Hall sensor state of the next commutation segment.

Finally, when the user asks to change the PWM duty cycle, the code ramps up or ramps down the PWM in increments of 1%, which yields an acceleration rate found empirically to prevent desynchronization.

Code Sample 29.4

open_loop.c. Driving a BLDC Without Hall Effect Sensors.

#include "NU32.h" // constants, funcs for startup and UART

#include "bldc.h"

// Open-loop control of the Pittman ELCOM SL 4443S013 BLDC operating at no load and 9 V.

// Pins E0, E1, E2 correspond to the connected state of

// phase A, B, C. When low, the respective phase is floating,

// and when high, the voltage on the phase is determined by

// the value of pins D0 (OC1), D1 (OC2), and D2 (OC3), respectively.

// Some values below have been tuned experimentally for the Pittman motor.

#define MAX_RPM 1800 // the max speed of the motor (no load speed), in RPM, for 9 V

#define MIN_PWM 3 // the min PWM required to overcome friction, as a percentage

#define SLOPE (MAX_RPM/(100 - MIN_PWM)) // slope of the RPM vs PWM curve

#define OFFSET (-SLOPE*MIN_PWM) // RPM where the RPM vs PWM curve intersects the RPM axis

 // NOTE: RPM = SLOPE * PWM + OFFSET

#define TICKS_MIN 1200000 // number of 20 kHz (50 us) timer ticks in a minute

#define EMREV 2 // number of electrical revs per mechanical revs (erev/mrev)

#define PHASE_REV 6 // the number of phases per electrical revolution (phase/erev)

// convert minutes/mechanical revolution into ticks/phase (divide TP_PER_MPR by the rpm)

#define TP_PER_MPR (TICKS_MIN/(PHASE_REV *EMREV))

#define ACCEL_PERIOD 200000 // Time in 40 MHz ticks to wait before accelerating to next

 // PWM level (i.e., the higher this value, the slower

 // the acceleration). When doing open-loop control, you

 // must accel/decel slowly enough, otherwise you lose sync.

 // The PWM is adjusted by 1 percent in each accel period,

 // but the deadband where the motor does not move is skipped.

static volatile int pwm = 0; // current PWM as a percentage

static volatile int period = 0; // commutation period, in 50 us (1/20 kHz) ticks

void __ISR(_TIMER_2_VECTOR, IPL6SRS) timer2_ISR(void) { // entered every 50 us (1/20 kHz)

 // the states, in the order of rotation through the phases (what we’d expect to read)

 static unsigned int state_table[] = {0b101,0b001,0b011,0b010,0b110,0b100};

 static int phase = 0;

 static int count = 0; // used to commutate when necessary

 if(count >= period) {

 count = 0;

 if(pwm > MIN_PWM) {

 ++phase;

 } else if (pwm < -MIN_PWM){

 --phase;

 }

 if(phase == 6) {

 phase = 0;

 } else if (phase == -1) {

 phase = 5;

 }

 bldc_commutate(pwm, state_table[phase]);

 } else {

 ++count;

 }

 IFS0bits.T2IF = 0;

}

// return true if the PWM percentage is in the deadband region

int in_deadband(int pwm) {

 return -MIN_PWM <= pwm && pwm <= MIN_PWM;

}

int main(void) {

 char msg[100];

 NU32_Startup(); // cache on, interrupts on, LED/button init, UART init

 bldc_setup();

 // Set up Timer2 interrupts (the bldc already uses Timer2 for the PWM).

 // We just reuse it for our timer here.

 IPC2bits.T2IP = 6;

 IFS0bits.T2IF = 0;

 IEC0bits.T2IE = 1;

 while(1) {

 int newpwm = bldc_get_pwm(); // get new PWM from user

 if(in_deadband(newpwm)) { // if PWM is in deadband where motor doesn’t move, pwm=0

 __builtin_disable_interrupts();

 period = 0;

 pwm = 0;

 __builtin_enable_interrupts();

 } else {

 // newpwm is not in the deadband

 int curr_pwm = pwm;

 _CP0_SET_COUNT(0);

 while(curr_pwm != newpwm) { // ramp the PWM up or down, respecting accel limits

 int comm_period;

 if(curr_pwm > newpwm) {

 --curr_pwm;

 // skip the deadband

 if(in_deadband(curr_pwm)) {

 curr_pwm = - MIN_PWM - 1;

 }

 } else if(curr_pwm < newpwm) {

 ++curr_pwm;

 if(in_deadband(curr_pwm)) {

 curr_pwm = MIN_PWM + 1;

 }

 }

 // divide T_PER_MPR by the RPM to get the commutation period

 // We compute the RPM based on the RPM vs pwm curve RPM = SLOPE pwm + OFFSET

 comm_period = (TP_PER_MPR/(SLOPE*abs(curr_pwm)+ OFFSET));

 while(_CP0_GET_COUNT() < ACCEL_PERIOD) { ; } // delay until accel period over

 __builtin_disable_interrupts();

 period = comm_period;

 pwm = curr_pwm;

 __builtin_enable_interrupts();

 _CP0_SET_COUNT(0); // we just moved to a new pwm, reset the acceleration period

 }

 sprintf(msg,"PWM Percent: %d, PERIOD: %d∖r∖n",pwm,period);

 NU32_WriteUART3(msg);

 }

 }

}

Another method for estimating the angle of a BLDC without Hall sensors involves monitoring the back-emf of the windings, but we do not pursue this method in this chapter.

13.1.3.3 Identifying the Feedback

Feedback identification may require measured results. If you purchase the feedback sensor, the vendor should be able to provide you with a measured transfer function. As with the power converter, expect a scaling constant and a one- or two-pole low-pass filter over the frequency range of interest. Don’t forget to add the scaling constant to convert the units of the feedback device to SI. For example, a rotary encoder with 4000 counts per revolution would have an implicit DC scale of 4000/2π counts/rad.

10.3.2 Smart vision

In addition to the development of audio- and haptic-feedback sensors and actuators, visual feedback is important for completing the entire human–robot interaction within TP2. Therefore strong collaboration of the Chair of Acoustic and Haptic Engineering and Fraunhofer FEP is required. In this respect, wearables (such as near-to-eye displays), also referred to as eyeables or smart glasses, as given in Fig. 10.6, are developed at Fraunhofer FEP. A typical OLED-on-silicon microdisplay architecture is schematically shown in Fig. 10.7. The microdisplay consists of a silicon wafer with integrated Complementary Metal Oxide Semiconductor (CMOS) electronics and the patterned anode. Different OLED layers are deposited by thermal evaporation in ultrahigh vacuum. Finally, color filters and encapsulation are put on top. Typically, OLED microdisplays consist of a white emission layer and lithographically etched color filters. Within the last years, several micropattering approaches (e.g., fine metal masks, lithography, e-beam direct writing) have been investigated to realize red, green, and blue OLED pixels instead of the white OLED in order to increase efficiency, color gamut, and contrast. However, all these techniques came along with new challenges, such as resolution limitations or yield issues.

Increasing pixel density for high-resolution, reducing latency and power consumption, and the application of multicolor displays are the key challenges for OLED microdisplays nowadays. Therefore new OLED-on-silicon display backplane architectures are required and need to be implemented in a deep-submicron process node. Besides new backplane circuitry concepts (see Section 10.4.2), the OLED structure itself needs to be highly efficient and stable. This requires a careful design of the electronic, optical, and excitonic properties. To meet the criterion of long lifetime, typically fluorescent emitters are used in OLED microdisplays, which allow only for maximum 25% internal quantum efficiency due to spin statistics. Phosphorescent emitters allow for 100% internal quantum efficiency, but they are expensive and the lifetime, especially of blue emitters, do not meet industry requirements.

2.3.3 Transfer Functions of Physical Elements

Physical elements are made up of the plant— the mechanism or device being controlled— and the feedback sensor(s). Examples of plants include electrical elements, such as inductors, and mechanical elements, such as springs and inertias. Table 2.2 provides a list of ideal elements in five categories.32 Consider the first category, electrical. A voltage force is applied to an impedance to produce a current flow. There are three types of impedance: inductance, capacitance, and resistance. Resistance is proportional to the current flow, inductive impedance is in proportion to the derivative of current flow, and capacitive impedance is in proportion to the integral of flow.

Table 2.2. Transfer Functions of Plant Elements

The pattern of force, impedance, and flow is repeated for many physical elements. In Table 2.2, the close parallels between the categories of linear and rotational force, fluid mechanics, and heat flow are evident. In each case, a forcing function (voltage, force, torque, pressure or temperature difference) applied to an impedance produces a flow (current, velocity, or fluid/thermal flow). The impedance takes three forms: resistance to the integral of flow (capacitance or mass), resistance to the derivative of flow (spring or inductance), and resistance to the flow rate (resistance or damping).

Table 2.2 reveals a central concept of controls. Controllers for these elements apply a force to control a flow. For example, a heating system applies heat to control a room’s temperature. When the flow must be controlled with accuracy, a feedback sensor can be added to measure the flow; control laws are required to combine the feedback and command signals to generate the force. This results in the structure shown in Figure 2.2; it is this structure that sets control systems apart from other disciplines of engineering.

The plant usually contains the most nonlinear elements in the control system. The plant is often too large and expensive to allow engineers the luxury of designing it for LTI operation. For example, an iron-core inductor in a power supply usually saturates; that is, its inductance declines as the current approaches its peak. The inductor could be designed so that saturation during normal operation is eliminated, but this requires more iron, which makes the power supply larger and more expensive.

Most of the impedances in Table 2.2 can be expected to vary over normal operating conditions. The question naturally arises as to how much they can vary. The answer depends on the application, but most control systems are designed with enough margin that variation of 20–30% in the plant should have little impact on system performance. However, plant parameters sometimes vary by much more than 30%. For example, consider the inertia in rotational motion. An application that winds plastic onto a roll may see the inertia vary by orders of magnitude, an amount too large for ordinary control laws to accommodate simply by adding margin. We will deal with variations in gain of this magnitude in Chapter 12.