The document discusses PID control, which combines proportional, integral and derivative control actions. It explains each control action and its effects on the system response and stability. Proportional control reduces steady-state error but can cause oscillation. Integral control eliminates steady-state error but also causes oscillation. Derivative control reduces overshoot and damping but increases sensitivity to noise. PID controllers combine these actions to achieve desired response without oscillations or steady-state error. The document provides examples of tuning the gains of each action.
This document discusses various models and terminology related to dependability in fault-tolerant computing systems. It presents hierarchical models that describe impairments from defects to failures at different abstraction levels. These include the fault-error-failure cycle, four-universe model, and multilevel model. Metrics for reliability, availability, maintainability, safety and integrity are defined. Common probability distributions for lifetimes and ways to compare reliability of systems are outlined.
This document provides an overview of PID controllers, including:
- The basic feedback loop and proportional, integral, and derivative algorithms
- Implementation issues like set-point weighing, windup, and digital implementation
- Practical operational aspects like bumpless transfer between manual and automatic modes
This document presents a comparative study of monotonic and non-monotonic phase linear time-invariant (LTI) systems using an improved analytical PID controller design. It discusses using gain crossover frequency and phase margin specifications to design controllers that ensure minimum phase margin inside the desired bandwidth. For the comparative study, it uses bode stability criterion, Nyquist stability criterion, and unit step response. It presents a case study comparing the design of controllers for a buck converter system, which exhibits a non-monotonic phase response, using both monotonic and non-monotonic design techniques. The results show that treating the non-monotonic system as monotonic leads to an overvalued proportional gain and undervalued derivative gain in the PID controller.
A machine consciousness approach to urban traffic signal controlAndré Paraense
In this work, we present a distributed cognitive architecture used to control the traffic
in a urban network. This architecture relies on a machine consciousness approach - Global
Workspace Theory - in order to use competition and broadcast, allowing a group of local traffic
controllers to interact, resulting in a better group performance. The main idea is that the local
controllers usually perform a purely reactive behavior, defining the times of red and green lights,
according just to local information. These local controllers compete in order to define which of
them is experiencing the most critical traffic situation. The controller in the worst condition
gains access to the global workspace, further broadcasting its condition (and its location) to all
other controllers, asking for their help in dealing with its situation. This call from the controller
accessing the global workspace will cause an interference in the reactive local behavior, for those
local controllers with some chance in helping the controller in a critical condition, by containing
traffic in its direction. This group behavior, coordinated by the global workspace strategy, turns
the once reactive behavior into a kind of deliberative one. We show that this strategy is capable
of improving the overall mean travel time of vehicles flowing through the urban network. A
consistent gain in performance with the “Artificial Consciousness” traffic signal controller during
all simulation time, throughout different simulated scenarios, could be observed, ranging from
around 13.8% to more than 21%.
This document describes the design of a type-III control loop using an explicit analytical PID tuning technique. It begins with definitions of closed-loop control systems and describes the characteristics of type-I, type-II, and type-III control loops. It then presents the conventional symmetrical optimum design criterion for PID tuning and derives equations for tuning PID controller parameters. The document proposes using a revised symmetrical optimum criterion to design a PID controller and compares it to the conventional criterion, claiming the proposed technique provides better control.
Study of Compensation of Variable Delay in Communication Link Using Communica...ijsrd.com
With growing technology, number of control system elements is increasing. So, it is not possible to place entire control system at a same place. Therefore, separate control elements connected by a communication link are required, it introduces delay. This delay is either constant or random in nature depending on communication link. This delay destabilizes the overall system and can be compensated using smith predictor. But smith predictor is only applicable to constant delay communication links. In this paper, communication disturbance observer (CDOB) and network disturbance (ND) have been introduced to compensate variable delay in communication link.
A new directional weighted median filter is proposed for removing random-valued impulse noise. It uses differences between pixel values and neighbors in four directions to detect impulse noise. Then, a weighted median filter is applied, which can preserve edges while removing noise. However, it works poorly for highly corrupted images.
A decision-based unsymmetrical trimmed median filter is introduced to remove high density salt and pepper noise. It uses a 3x3 window and checks for corrupted pixels values of 0 or 255. Pixels are sorted and trimmed means or medians are applied depending on the number of corrupted pixels to denoise while preserving textures and edges.
Design and Implementation of Low Ripple Low Power Digital Phase-Locked LoopCSCJournals
We propose a phase-locked loop (PLL) architecture, which reduces the double frequency ripple without increasing the order of loop filter. Proposed architecture uses quadrature numerically–controlled oscillator (NCO) to provide two output signals with phase difference of π/2. One of them is subtracted from the input signal before multiplying with the other output of NCO. The system also provides stability in case the input signal has noise in amplitude or phase. The proposed structure is implemented using field programmable gate array (FPGA), which dissipates 15.44mw and works at clock frequency of 155.8 MHz.
This document discusses various models and terminology related to dependability in fault-tolerant computing systems. It presents hierarchical models that describe impairments from defects to failures at different abstraction levels. These include the fault-error-failure cycle, four-universe model, and multilevel model. Metrics for reliability, availability, maintainability, safety and integrity are defined. Common probability distributions for lifetimes and ways to compare reliability of systems are outlined.
This document provides an overview of PID controllers, including:
- The basic feedback loop and proportional, integral, and derivative algorithms
- Implementation issues like set-point weighing, windup, and digital implementation
- Practical operational aspects like bumpless transfer between manual and automatic modes
This document presents a comparative study of monotonic and non-monotonic phase linear time-invariant (LTI) systems using an improved analytical PID controller design. It discusses using gain crossover frequency and phase margin specifications to design controllers that ensure minimum phase margin inside the desired bandwidth. For the comparative study, it uses bode stability criterion, Nyquist stability criterion, and unit step response. It presents a case study comparing the design of controllers for a buck converter system, which exhibits a non-monotonic phase response, using both monotonic and non-monotonic design techniques. The results show that treating the non-monotonic system as monotonic leads to an overvalued proportional gain and undervalued derivative gain in the PID controller.
A machine consciousness approach to urban traffic signal controlAndré Paraense
In this work, we present a distributed cognitive architecture used to control the traffic
in a urban network. This architecture relies on a machine consciousness approach - Global
Workspace Theory - in order to use competition and broadcast, allowing a group of local traffic
controllers to interact, resulting in a better group performance. The main idea is that the local
controllers usually perform a purely reactive behavior, defining the times of red and green lights,
according just to local information. These local controllers compete in order to define which of
them is experiencing the most critical traffic situation. The controller in the worst condition
gains access to the global workspace, further broadcasting its condition (and its location) to all
other controllers, asking for their help in dealing with its situation. This call from the controller
accessing the global workspace will cause an interference in the reactive local behavior, for those
local controllers with some chance in helping the controller in a critical condition, by containing
traffic in its direction. This group behavior, coordinated by the global workspace strategy, turns
the once reactive behavior into a kind of deliberative one. We show that this strategy is capable
of improving the overall mean travel time of vehicles flowing through the urban network. A
consistent gain in performance with the “Artificial Consciousness” traffic signal controller during
all simulation time, throughout different simulated scenarios, could be observed, ranging from
around 13.8% to more than 21%.
This document describes the design of a type-III control loop using an explicit analytical PID tuning technique. It begins with definitions of closed-loop control systems and describes the characteristics of type-I, type-II, and type-III control loops. It then presents the conventional symmetrical optimum design criterion for PID tuning and derives equations for tuning PID controller parameters. The document proposes using a revised symmetrical optimum criterion to design a PID controller and compares it to the conventional criterion, claiming the proposed technique provides better control.
Study of Compensation of Variable Delay in Communication Link Using Communica...ijsrd.com
With growing technology, number of control system elements is increasing. So, it is not possible to place entire control system at a same place. Therefore, separate control elements connected by a communication link are required, it introduces delay. This delay is either constant or random in nature depending on communication link. This delay destabilizes the overall system and can be compensated using smith predictor. But smith predictor is only applicable to constant delay communication links. In this paper, communication disturbance observer (CDOB) and network disturbance (ND) have been introduced to compensate variable delay in communication link.
A new directional weighted median filter is proposed for removing random-valued impulse noise. It uses differences between pixel values and neighbors in four directions to detect impulse noise. Then, a weighted median filter is applied, which can preserve edges while removing noise. However, it works poorly for highly corrupted images.
A decision-based unsymmetrical trimmed median filter is introduced to remove high density salt and pepper noise. It uses a 3x3 window and checks for corrupted pixels values of 0 or 255. Pixels are sorted and trimmed means or medians are applied depending on the number of corrupted pixels to denoise while preserving textures and edges.
Design and Implementation of Low Ripple Low Power Digital Phase-Locked LoopCSCJournals
We propose a phase-locked loop (PLL) architecture, which reduces the double frequency ripple without increasing the order of loop filter. Proposed architecture uses quadrature numerically–controlled oscillator (NCO) to provide two output signals with phase difference of π/2. One of them is subtracted from the input signal before multiplying with the other output of NCO. The system also provides stability in case the input signal has noise in amplitude or phase. The proposed structure is implemented using field programmable gate array (FPGA), which dissipates 15.44mw and works at clock frequency of 155.8 MHz.
The PID controller is the most widely used type of feedback controller, making up over 95% of controllers used in industry. It uses proportional, integral, and derivative terms to calculate the control signal based on the error between the setpoint and process variable. The proportional term responds to current error, the integral term responds to accumulated past error to eliminate steady-state error, and the derivative term anticipates future error based on the current rate of change. Together these three terms allow PID controllers to provide stable and accurate control of processes while compensating for disturbances.
Sampling and Reconstruction (Online Learning).pptxHamzaJaved306957
1. Sampling and reconstruction of signals was analyzed using the impulse sampling math model.
2. The analysis showed that a bandlimited signal can be perfectly reconstructed from its samples as long as the sampling rate is at least twice the bandwidth of the signal.
3. If the sampling rate is lower than the minimum required rate, aliasing error occurs where frequency components fold back into the baseband.
This document summarizes work done to upgrade a capillary pulling system at CHESS to reduce noise and improve tension control. It describes implementing a PID control algorithm using LabView to average tension readings and reduce noise, but finding this increased noise instead by slowing feedback. Tables show noise levels decreased with higher P values from 0.05 to 0.5 steps/g. Future work planned includes continuing PID tuning to optimize the I term and reprogramming feedback in a lower-level language to improve speed. The upgrades aimed to maintain constant tension and reduce noise during capillary pulling.
Multivariable Control System Design for Quadruple Tank Process using Quantita...IDES Editor
This paper focus on design of multivariable
controller for Quadruple Tank Process, a two input two
output system with large plant uncertainty using QFT
methodology. In the present work, a new approach using
Quantitative Feedback Theory (QFT) is formulated for
design of a robust two degree of freedom controller for
Quadruple Tank Process. The design is done in frequency
domain. This paper presents a design method for a 2 x 2
multiple input multiple output system. The plant
uncertainties are transformed into equivalent external
disturbance sets, and the design problem becomes one of
the external disturbance attenuation. The objective is to
find compensator functions which guarantee that the
system performance bounds are satisfied over the range
of plant uncertainty. The methodology is successfully
applied to design a two degree of freedom compensator
Quadruple Tank Process.
Approximate Dynamic Programming: A New Paradigm for Process Control & Optimiz...height
1. Approximate dynamic programming (ADP) is a computationally feasible approach for handling large-scale and uncertain systems like process industries more effectively than conventional tools.
2. ADP works by approximating the optimal "scores" or value functions for every system state and action offline through simulations, rather than computing them exactly. This allows for manageable online computation.
3. By handling uncertainties through simulations during offline learning, ADP can provide improved policies for decision making under uncertainty compared to approaches that ignore uncertainties.
This document provides an overview of the EL2450 Hybrid and Embedded Control course offered in Spring 2022. The course aims to teach students how to analyze, design, and implement sampled-data control systems and apply hybrid systems modeling techniques to embedded systems. Key topics covered include time-triggered and event-triggered control, real-time operating systems, and modeling and control of hybrid systems. An example of a vehicle dynamics control system is presented to illustrate an embedded control application. The course outline and topics are then reviewed, including modeling of sampled systems to be covered in the next lecture.
This document discusses a self-tuning predictive controller based on a step response model for real-time control frameworks. The predictive controller is tuned using a step response model of the process, which is easier to obtain than parameters for higher order process models. This approach helps improve control performance for higher order processes compared to traditional PID or predictive controllers. The document also describes challenges with noise and proposes methods to address stability issues for noisy processes.
New controllers efficient model based design methodAlexander Decker
This document proposes new methods for designing P, PI, PD, and PID controllers based on selecting the controller gains based on the plant's parameters. The goal is to achieve acceptable stability and medium fast response. Expressions are proposed for calculating the controller gains for first-order, second-order, and time-delay systems based on the plant's time constant, damping ratio, and natural frequency. The proposed controller design methods are tested on first, second, and first-order systems with time delay using MATLAB/Simulink. The results show the methods can achieve acceptable stability and medium fast response with minimum steady state error by selecting a single tuning parameter.
Multiple Sensors Soft-Failure Diagnosis Based on Kalman Filtersipij
Sensor is the necessary components of the engine control system. Therefore, more and more work must do for improving sensors reliability. Soft failures are small bias errors or drift errors that accumulate relatively slowly with time in the sensed values that it must be detected because of it can be very easy to be mistaken for the results of noise. Simultaneous multiple sensors failures are rare events and must be considered. In order to solve this problem, a revised multiple-failure-hypothesis based testing is investigated. This approach uses multiple Kalman filters, and each of Kalman filter is designed based on a specific hypothesis for detecting specific sensors fault, and then uses Weighted Sum of Squared Residual (WSSR) to deal with Kalman filter residuals, and residual signals are compared with threshold in order to make fault detection decisions. The simulation results show that the proposed method can be used to detect multiple sensors soft failures fast and accurately.
Robust PID Controller Design for Non-Minimum Phase Systems using Magnitude Op...IRJET Journal
This document discusses two approaches for designing a controller for non-minimum phase systems: 1) the magnitude optimum and multiple integration method, and 2) a numerical optimization approach. The magnitude optimum method uses areas calculated from the process step response to determine the PID controller parameters, eliminating the need to estimate process parameters directly. The numerical optimization approach formulates the controller design as an optimization problem to minimize sensitivity functions in the closed-loop system. Both approaches are presented as ways to design robust controllers for non-minimum phase systems.
ECG SIGNAL DENOISING USING EMPIRICAL MODE DECOMPOSITIONSarang Joshi
The document presents a method for denoising ECG signals corrupted with power line interference using empirical mode decomposition and thresholding. It provides background on sources of power line interference in ECG signals and existing approaches to remove it. The proposed approach decomposes noisy ECG signals into intrinsic mode functions using EMD, then applies various thresholding techniques to the IMFs to remove noise before reconstructing the signal. It tests the method on signals from the MIT-BIH Arrhythmia Database corrupted with 10-50% noise and evaluates performance based on correlation coefficient and SNR improvement. Results show Donoho’s thresholding and hard thresholding achieved the best denoising based on these metrics.
Proportional integral and derivative PID controller Mostafa Ragab
The document discusses PID controllers and their origins. It provides information on:
1) The basic components and functions of PID controllers, including proportional, integral and derivative terms that react to error, accumulated error over time, and rate of change of error respectively.
2) The benefits and limitations of proportional, integral and derivative control modes individually and in combination. PID controllers can reduce rise time, settling time and steady state error.
3) Applications of different PID variations and guidelines for controller design depending on process characteristics like temperature, flow or liquid level control.
4) Tips for designing PID controllers including obtaining an open-loop response and adjusting gains to achieve desired closed-loop performance.
This document discusses a high performance dense linear system solver that is resilient to soft errors. It presents an LU factorization based approach that uses checksums to detect and recover from soft errors. Checksums are generated and stored for the input matrix and L factor to detect errors. A fault tolerant algorithm is described that can locate the error column and recover the solution vector x using the Sherman-Morrison formula. Performance evaluations on the Kraken supercomputer show the approach maintains high performance even when checkpointing is added for soft error resilience.
This document contains lecture notes on signals and systems for a course at Chadalawada Ramanamma Engineering College. It includes:
1. An introduction to signals, systems, and some common elementary signals like the unit step, unit impulse, ramp, sinusoid, and exponential signals.
2. A classification of signals as continuous/discrete, deterministic/non-deterministic, even/odd, periodic/aperiodic, energy/power, and real/imaginary.
3. A discussion of basic operations on signals like amplitude scaling, addition, and subtraction.
The document discusses automatic control systems. It defines automatic control as a methodology for analyzing and designing systems that can self-regulate operating conditions with minimal human intervention. It describes the basic functions, elements, components, and types of feedback in automatic control systems. It provides examples of a first order and second order control system's time response to a unit step input function. It also discusses transfer functions and types 0, 1, and 2 control systems. Finally, it demonstrates modeling automatic control systems using MATLAB/Simulink.
4 ijaems nov-2015-4-fsk demodulator- case study of pll applicationINFOGAIN PUBLICATION
FSK Demodulator, one of the applications of PLL has been implemented using both hardware and software. Results are found to be similar and based on these results it is believed that this will contribute for the improvement in performance and reliability for future communication systems. Hence this will also contribute to the development of higher reliability of the systems.
The document discusses machine learning techniques for multivariate data analysis using the TMVA toolkit. It describes several common classification problems in high energy physics (HEP) and summarizes several machine learning algorithms implemented in TMVA for supervised learning, including rectangular cut optimization, likelihood methods, neural networks, boosted decision trees, support vector machines and rule ensembles. It also discusses challenges like nonlinear correlations between input variables and techniques for data preprocessing and decorrelation.
1. The document discusses the integration of system identification (SYSID) methods with model predictive control (MPC).
2. It describes how SYSID can be used to estimate process models, which are then used for prediction in MPC. The model estimates are also regularly updated using new process data to adapt the MPC predictions over time.
3. However, the document notes that while the components of SYSID and MPC are established individually, fully integrating them in software in a systematic way remains a challenge, particularly for complex multi-variable systems.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
The PID controller is the most widely used type of feedback controller, making up over 95% of controllers used in industry. It uses proportional, integral, and derivative terms to calculate the control signal based on the error between the setpoint and process variable. The proportional term responds to current error, the integral term responds to accumulated past error to eliminate steady-state error, and the derivative term anticipates future error based on the current rate of change. Together these three terms allow PID controllers to provide stable and accurate control of processes while compensating for disturbances.
Sampling and Reconstruction (Online Learning).pptxHamzaJaved306957
1. Sampling and reconstruction of signals was analyzed using the impulse sampling math model.
2. The analysis showed that a bandlimited signal can be perfectly reconstructed from its samples as long as the sampling rate is at least twice the bandwidth of the signal.
3. If the sampling rate is lower than the minimum required rate, aliasing error occurs where frequency components fold back into the baseband.
This document summarizes work done to upgrade a capillary pulling system at CHESS to reduce noise and improve tension control. It describes implementing a PID control algorithm using LabView to average tension readings and reduce noise, but finding this increased noise instead by slowing feedback. Tables show noise levels decreased with higher P values from 0.05 to 0.5 steps/g. Future work planned includes continuing PID tuning to optimize the I term and reprogramming feedback in a lower-level language to improve speed. The upgrades aimed to maintain constant tension and reduce noise during capillary pulling.
Multivariable Control System Design for Quadruple Tank Process using Quantita...IDES Editor
This paper focus on design of multivariable
controller for Quadruple Tank Process, a two input two
output system with large plant uncertainty using QFT
methodology. In the present work, a new approach using
Quantitative Feedback Theory (QFT) is formulated for
design of a robust two degree of freedom controller for
Quadruple Tank Process. The design is done in frequency
domain. This paper presents a design method for a 2 x 2
multiple input multiple output system. The plant
uncertainties are transformed into equivalent external
disturbance sets, and the design problem becomes one of
the external disturbance attenuation. The objective is to
find compensator functions which guarantee that the
system performance bounds are satisfied over the range
of plant uncertainty. The methodology is successfully
applied to design a two degree of freedom compensator
Quadruple Tank Process.
Approximate Dynamic Programming: A New Paradigm for Process Control & Optimiz...height
1. Approximate dynamic programming (ADP) is a computationally feasible approach for handling large-scale and uncertain systems like process industries more effectively than conventional tools.
2. ADP works by approximating the optimal "scores" or value functions for every system state and action offline through simulations, rather than computing them exactly. This allows for manageable online computation.
3. By handling uncertainties through simulations during offline learning, ADP can provide improved policies for decision making under uncertainty compared to approaches that ignore uncertainties.
This document provides an overview of the EL2450 Hybrid and Embedded Control course offered in Spring 2022. The course aims to teach students how to analyze, design, and implement sampled-data control systems and apply hybrid systems modeling techniques to embedded systems. Key topics covered include time-triggered and event-triggered control, real-time operating systems, and modeling and control of hybrid systems. An example of a vehicle dynamics control system is presented to illustrate an embedded control application. The course outline and topics are then reviewed, including modeling of sampled systems to be covered in the next lecture.
This document discusses a self-tuning predictive controller based on a step response model for real-time control frameworks. The predictive controller is tuned using a step response model of the process, which is easier to obtain than parameters for higher order process models. This approach helps improve control performance for higher order processes compared to traditional PID or predictive controllers. The document also describes challenges with noise and proposes methods to address stability issues for noisy processes.
New controllers efficient model based design methodAlexander Decker
This document proposes new methods for designing P, PI, PD, and PID controllers based on selecting the controller gains based on the plant's parameters. The goal is to achieve acceptable stability and medium fast response. Expressions are proposed for calculating the controller gains for first-order, second-order, and time-delay systems based on the plant's time constant, damping ratio, and natural frequency. The proposed controller design methods are tested on first, second, and first-order systems with time delay using MATLAB/Simulink. The results show the methods can achieve acceptable stability and medium fast response with minimum steady state error by selecting a single tuning parameter.
Multiple Sensors Soft-Failure Diagnosis Based on Kalman Filtersipij
Sensor is the necessary components of the engine control system. Therefore, more and more work must do for improving sensors reliability. Soft failures are small bias errors or drift errors that accumulate relatively slowly with time in the sensed values that it must be detected because of it can be very easy to be mistaken for the results of noise. Simultaneous multiple sensors failures are rare events and must be considered. In order to solve this problem, a revised multiple-failure-hypothesis based testing is investigated. This approach uses multiple Kalman filters, and each of Kalman filter is designed based on a specific hypothesis for detecting specific sensors fault, and then uses Weighted Sum of Squared Residual (WSSR) to deal with Kalman filter residuals, and residual signals are compared with threshold in order to make fault detection decisions. The simulation results show that the proposed method can be used to detect multiple sensors soft failures fast and accurately.
Robust PID Controller Design for Non-Minimum Phase Systems using Magnitude Op...IRJET Journal
This document discusses two approaches for designing a controller for non-minimum phase systems: 1) the magnitude optimum and multiple integration method, and 2) a numerical optimization approach. The magnitude optimum method uses areas calculated from the process step response to determine the PID controller parameters, eliminating the need to estimate process parameters directly. The numerical optimization approach formulates the controller design as an optimization problem to minimize sensitivity functions in the closed-loop system. Both approaches are presented as ways to design robust controllers for non-minimum phase systems.
ECG SIGNAL DENOISING USING EMPIRICAL MODE DECOMPOSITIONSarang Joshi
The document presents a method for denoising ECG signals corrupted with power line interference using empirical mode decomposition and thresholding. It provides background on sources of power line interference in ECG signals and existing approaches to remove it. The proposed approach decomposes noisy ECG signals into intrinsic mode functions using EMD, then applies various thresholding techniques to the IMFs to remove noise before reconstructing the signal. It tests the method on signals from the MIT-BIH Arrhythmia Database corrupted with 10-50% noise and evaluates performance based on correlation coefficient and SNR improvement. Results show Donoho’s thresholding and hard thresholding achieved the best denoising based on these metrics.
Proportional integral and derivative PID controller Mostafa Ragab
The document discusses PID controllers and their origins. It provides information on:
1) The basic components and functions of PID controllers, including proportional, integral and derivative terms that react to error, accumulated error over time, and rate of change of error respectively.
2) The benefits and limitations of proportional, integral and derivative control modes individually and in combination. PID controllers can reduce rise time, settling time and steady state error.
3) Applications of different PID variations and guidelines for controller design depending on process characteristics like temperature, flow or liquid level control.
4) Tips for designing PID controllers including obtaining an open-loop response and adjusting gains to achieve desired closed-loop performance.
This document discusses a high performance dense linear system solver that is resilient to soft errors. It presents an LU factorization based approach that uses checksums to detect and recover from soft errors. Checksums are generated and stored for the input matrix and L factor to detect errors. A fault tolerant algorithm is described that can locate the error column and recover the solution vector x using the Sherman-Morrison formula. Performance evaluations on the Kraken supercomputer show the approach maintains high performance even when checkpointing is added for soft error resilience.
This document contains lecture notes on signals and systems for a course at Chadalawada Ramanamma Engineering College. It includes:
1. An introduction to signals, systems, and some common elementary signals like the unit step, unit impulse, ramp, sinusoid, and exponential signals.
2. A classification of signals as continuous/discrete, deterministic/non-deterministic, even/odd, periodic/aperiodic, energy/power, and real/imaginary.
3. A discussion of basic operations on signals like amplitude scaling, addition, and subtraction.
The document discusses automatic control systems. It defines automatic control as a methodology for analyzing and designing systems that can self-regulate operating conditions with minimal human intervention. It describes the basic functions, elements, components, and types of feedback in automatic control systems. It provides examples of a first order and second order control system's time response to a unit step input function. It also discusses transfer functions and types 0, 1, and 2 control systems. Finally, it demonstrates modeling automatic control systems using MATLAB/Simulink.
4 ijaems nov-2015-4-fsk demodulator- case study of pll applicationINFOGAIN PUBLICATION
FSK Demodulator, one of the applications of PLL has been implemented using both hardware and software. Results are found to be similar and based on these results it is believed that this will contribute for the improvement in performance and reliability for future communication systems. Hence this will also contribute to the development of higher reliability of the systems.
The document discusses machine learning techniques for multivariate data analysis using the TMVA toolkit. It describes several common classification problems in high energy physics (HEP) and summarizes several machine learning algorithms implemented in TMVA for supervised learning, including rectangular cut optimization, likelihood methods, neural networks, boosted decision trees, support vector machines and rule ensembles. It also discusses challenges like nonlinear correlations between input variables and techniques for data preprocessing and decorrelation.
1. The document discusses the integration of system identification (SYSID) methods with model predictive control (MPC).
2. It describes how SYSID can be used to estimate process models, which are then used for prediction in MPC. The model estimates are also regularly updated using new process data to adapt the MPC predictions over time.
3. However, the document notes that while the components of SYSID and MPC are established individually, fully integrating them in software in a systematic way remains a challenge, particularly for complex multi-variable systems.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
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1. Control Systems I
Lecture 12: PID Control
Readings: A&M, Ch. 10, Guzzella, Chapter 11.2,
Jacopo Tani
Institute for Dynamic Systems and Control
D-MAVT
ETH Zürich
December 7, 2018
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 1 / 31
2. Tentative schedule
# Date Topic
1 Sept. 21 Introduction, Signals and Systems
2 Sept. 28 Modeling, Linearization
3 Oct. 5 Analysis 1: Time response, Stability
4 Oct. 12 Analysis 2: Diagonalization, Modal coordinates
5 Oct. 19 Transfer functions 1: Definition and properties
6 Oct. 26 Transfer functions 2: Poles and Zeros
7 Nov. 2 Analysis of feedback systems: internal stability,
root locus
8 Nov. 9 Frequency response
9 Nov. 16 Analysis of feedback systems 2: the Nyquist
condition
10 Nov. 23 Frequency response II
11 Nov. 30 Specifications for feedback systems
12 Dec. 7 PID control
13 Dec. 14 Loop Shaping
14 Dec. 21 State feedback and Luenberger observers
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 2 / 31
3. Today’s learning objectives
Learn what a PID control is and how to design one:
Proportional control: what it is, pro’s and con’s
Derivative control: what it is, pro’s and con’s
Integral control: what it is, pro’s and con’t
Tuning strategies for PID controllers.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 3 / 31
4. A nice intro to PID control
https://www.youtube.com/watch?v=4Y7zG48uHRo
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 4 / 31
5. Recall: Control Specifications
Type of the system (order of ramp to track with zero steady-state error):
Number of integrators in L(s)
Time domain specifications (max overshoot, settling time, rise time, ...):
Location of dominant closed-loop poles (damping ratio and real part)
Frequency domain specifications (command tracking, disturbance/noise
rejection, closed-loop bandwidth):
Bode obstacle course (low/high frequency)
Crossover frequency
Control synthesis: how do we choose a feedback control system that
achieves these objectives?
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 5 / 31
6. Controller design methods
What other methods do exist to design controllers C(s) that meet design
specifications? Many approaches, among them:
PID, Loop Shaping, LQR, LQG-LTR, H∞, Discrete-time optimal control,
continuous-time optimal control, model predictive control,...
Today we look at the most widely used approach for SISO systems: PID
control.
PID - control (proportional-integral-derivative control) is the most widely
applied controller design because it is able to cope well with the majority of
cases encountered in practice.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 6 / 31
7. Proportional Control
1
s+1
Transfer Fcn
Step
Scope
Band-Limited
White Noise
Step1
5
Gain
output
noise
measurement
reference error control
disturbance
The control input tries to move the system in a direction that is opposite to
the error, and is proportional to the error in magnitude.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 7 / 31
8. Proportional gain selection
0 1 2 3 4 5 6 7 8 9 10
t
0
0.2
0.4
0.6
0.8
1
1.2
y
k=2
k=5
k=10
k=50
As the proportional gain increases,
The closed-loop system remains stable;
The steady-state error decreases;
The response becomes faster;
The sensitivity to noise increases.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 8 / 31
9. Proportional gain selection
-60 -50 -40 -30 -20 -10 0 10
-3
-2
-1
0
1
2
3
60 50 40 30 20
0.88
0.975
0.989
0.995
0.997
0.999
1
1
10
0.88
0.975
0.989
0.995
0.997
0.999
1
1
Root Locus
Real Axis (seconds-1
)
Imaginary
Axis
(seconds
-1
)
Closed-loop transfer function
T(s) =
kL(s)
1 + kL(s)
=
1
s + 1 + k
,
i.e., the closed-loop pole is at s = −1 − k (see root locus above).
Steady-state error to a unit step: ess = lims→0
1
1+kL(s) = 1
1+k
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 9 / 31
11. Introducing an integrator
1
s+1
Transfer Fcn
Step
Band-Limited
White Noise
Step1
2
P Gain
simout
To Workspace
1
s
Integrator
5
I Gain
output
noise
measurement
reference error
disturbance
control
control
Integrating the error allows one to detect potential ”biases” in the system
behavior.
An integral control action tries to move the response in order to reduce the
detected biases.
PI control:
u(t) = kP e(t) + kI
Z t
0
e(τ)dτ,
C(s) = kP +
kI
s
=
kP s + kI
s
= kI
kP /kI · s + 1
s
.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 11 / 31
12. Integral gain selection
0 1 2 3 4 5 6 7 8 9 10
t
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
y
kP
=2, kI
= 2
kP
=2, kI
= 2
kP
=2, kI
= 5
kP
=10, kI
= 50
As the integral gain increases,
The steady-state error is zero (as long as kI is not zero)
The response becomes more oscillatory (warning!)
The sensitivity to noise does not change!
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 12 / 31
13. Integral gain selection
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10
-30
-20
-10
0
10
20
30
Root Locus
Real Axis (seconds-1
)
Imaginary
Axis
(seconds
-1
)
Steady-state error to a unit step: ess = lims→0
1
1+C(s)L(s) = 0
The root locus shows us that as the integral gain increases, the closed-loop
poles go from being “slow” and overdamped to being “fast” but with low
damping!
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 13 / 31
15. Proportional Control — Higher order systems
2
s +2s+2
2
Transfer Fcn
Step
Band-Limited
White Noise
Step1
50
P Gain
simout
To Workspace
output
noise
measurement
reference error
disturbance
control
control
How do the previous consideration extend to higher-order systems, e.g., 2nd
order?
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 15 / 31
16. Proportional gain selection
0 1 2 3 4 5 6 7 8 9 10
t
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
y
As the proportional gain increases,
The closed-loop system become more oscillatory (warning!);
The steady-state error decreases;
The response becomes faster;
The sensitivity to noise increases.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 16 / 31
17. Proportional gain selection
-2.5 -2 -1.5 -1 -0.5 0 0.5
-15
-10
-5
0
5
10
15
14
12
10
8
6
4
2
14
12
10
8
6
4
2
0.5
0.26
0.17 0.115 0.085 0.056 0.036 0.016
0.5
0.26
0.17 0.115 0.085 0.056 0.036 0.016
Root Locus
Real Axis (seconds-1
)
Imaginary
Axis
(seconds
-1
)
The root locus shows that as the proportional gain increases, the closed-loop
poles have decreasing damping ratio.
Steady-state error to a unit step: ess = lims→0
1
1+kL(s) = 1
1+k
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 17 / 31
19. Introducing a differentiator
2
s +2s+2
2
Transfer Fcn
Step
Band-Limited
White Noise
Step1
50
P Gain
simout
To Workspace
Derivative
50
D Gain
output
noise
measurement
reference error
disturbance
control
control
Differentiating the error allows one to “predict” what the error will do in the
near future.
An derivative control action tries to avoid overshooting, hence damping the
system.
PD control:
u(t) = kP e(t) + kDė(t)
C(s) = kP + kDs.
Note that this is not a causal transfer function (not physically realizable in
general). This is typically fixed by approximating the derivative as s ≈ s
cs+1
for some small c.)
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 19 / 31
20. Derivative gain selection
0 1 2 3 4 5 6 7 8 9 10
t
0
0.2
0.4
0.6
0.8
1
1.2
1.4
y
kP
=50, kD
=2
kP
=50, kD
=5
kP
=50, kD
=10
kP
=50, kD
=50
As the derivative gain increases,
The steady-state error not affected;
The response becomes less oscillatory, but potentially slower
The sensitivity to noise increases!
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 20 / 31
21. Derivative gain selection
-120 -100 -80 -60 -40 -20 0 20
-30
-20
-10
0
10
20
30
Root Locus
Real Axis (seconds-1
)
Imaginary
Axis
(seconds
-1
)
Steady-state error to a unit step: ess = lims→0
1
1+C(s)L(s) = 1
1+kP L(0)
The root locus shows us that as the derivative gain increases, the closed-loop
poles are “pulled” into the left half plane!
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 21 / 31
22. Derivative gain selection
-60
-40
-20
0
20
40
Magnitude
(dB)
k_P=50, k_D=2
k_P=50, k_D=5
k_P=50, k_D=10
k_P=50, k_D=50
10-2
10-1
100
101
102
103
-180
-135
-90
-45
0
Phase
(deg)
Bode Diagram
Frequency (rad/s)
As the derivative gain increases,
Phase margin increases;
The crossover frequency increases;
The low-frequency gain does not change;
The high-frequency gain increases.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 22 / 31
23. Proportional-Integral-Derivative Control
2
s +2s+2
2
Transfer Fcn
Step
Band-Limited
White Noise
Step1
10
P Gain
simout
To Workspace
Derivative
5
D Gain
1
s
Integrator
10
D Gain1
output
noise
measurement
reference error
disturbance
control
control
One can also combine the effects of an integrator and of a differentiator with
the basic proportional controller.
PID control:
u(t) = kP e(t) + kI
Z t
0
e(τ)dτ + kDė(t),
C(s) = kP +
kI
s
+ kDs =
kDs2
+ kP s + kI
s
.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 23 / 31
24. PID Tuning
PID tuning corresponds to choosing the parameters kp, ki and kd to reach the
feedback control design specifications.
PID tuning can be done with tuning rules by hand or numerically using
MATLAB or other tools (the latter requires a system model).
There exist heuristic methods to tune a PID controller without a model of
the plant P(s), e.g. the tuning rules proposed by Ziegler and Nichols.
My recommendation: think of a PID as
C(s) = kRL
(s − z1)(s − z2)
s
i.e., as two zeros and one pole at the origin. Decide where you want these
zeros (in the complex plane, or in terms of natural frequency and damping
ratio on the Bode plot), and what you want the (root-locus) gain to be.
Finally, compute the corresponding kP , kI , kD.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 24 / 31
25. Summary
Proportional control
Decrease the steady-state error;
Increase the closed-loop bandwidth;
Increase sensitivity to noise;
Can reduce stability margins for higher-order systems (2nd order or more).
Integral control
Eliminates the steady-state error to a step (if the closed-loop is stable);
Reduces stability margins, can make a higher-order system unstable.
Derivative control
Reduce overshooting, increase damping;
Improves stability margins;
Increase sensitivity to noise.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 25 / 31
26. Today’s learning objectives
Learn what a PID control is and how to design one:
Proportional control: what it is, what it does, pro’s and con’s
Derivative control: what it is, what it does, pro’s and con’s
Integral control: what it is, what it does, pro’s and con’s
Tuning strategies for PID controllers.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 26 / 31
27. Ziegler Nichols Tuning Rules
Assumption: Plant can be approximated by the transfer function
P(s) =
k
τs + 1
e−Ts
with T/(T + τ) small.
Apply the controller C(s) = kp to the system starting at kp = 0 and increase
kp until the system is in a steady-state oscillation, then note the ”critical kp”
called k∗
p and the corresponding critical oscillation period T∗
.
Use k∗
p and T∗
to calculate the control gains:
type kp Ti Td
P 0.5 · k∗
p ∞ · T∗
0 · T∗
PI 0.45 · k∗
p 0.85 · T∗
0 · T∗
PD 0.55 · k∗
p ∞ · T∗
0.15 · T∗
PID 0.6 · k∗
p 0.5 · T∗
0.125 · T∗
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 27 / 31
28. Ziegler Nichols Tuning Rules
Graphically:
1
1(Lino Guzzella ”Analysis and Synthesis of Single-Input Single-Output Control Systems)
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 28 / 31
29. Ziegler Nichols Tuning Example
Plant: P(s) =
1
(s + 1) · (s2 + 2s + 2)
Approximation: Papprox =
0.5
0.5 · s + 1
· e−0.01s
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 29 / 31
30. Ziegler Nichols Tuning Example
Set Ti = ∞, Td = 0, τ = 0 and increase gain kp.
Critical gain k∗
p = 10 with critical oscillation period T∗
= 2π
ω∗ = 2π
2 = π
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 30 / 31
31. Ziegler Nichols Tuning Example
P, PI, PD, PID controller according to Ziegler and Nichols tuning rules.
PID controller derived with MATLAB sisotool.
Ziegler Nichols tuning rules can be useful when no model of the plant is
available but generally other tuning rules provide better results.
J. Tani, E. Frazzoli (ETH) Lecture 12: Control Systems I 7/12/2018 31 / 31