Thursday, April 28, 2016

Fuzzy adaptive control system of a non-stationary plant with closed-loop passive identifier


Abstract

Typically chemical processes have significant nonlinear dynamics, but despite this, industry is conventionally still using PID-based regulatory control systems. Moreover, process units are interconnected, in terms of inlet and outlet material/energy flows, to other neighboring units, thus their dynamic behavior is strongly influenced by these connections and, as a consequence, conventional control systems performance often proves to be poor.
This paper proposes a hybrid fuzzy PID control logic, whose tuning parameters are provided in real time. The fuzzy controller tuning is made on the basis of Mamdani controller, also exploiting the results coming from an identification procedure that is carried on when an unmeasured step disturbance of any shape affects the process behavior.
In addition, this paper compares a fuzzy logic based PID with PID regulators whose tuning is performed by standard and well-known methods. In some cases the proposed tuning methodology ensures a control performance that is comparable to that guaranteed by simpler and more common tuning methods. However, in case of dynamic changes in the parameters of the controlled system, conventionally tuned PID controllers do not show to be robust enough, thus suggesting that fuzzy logic based PIDs are definitively more reliable and effective.

Keywords

  • PID-controller; 
  • Identification; 
  • Fuzzy controller; 
  • Closed-loop; 
  • Unknown disturbances;
  • Auto-tuning control

1. Introduction

Nowadays the conventional proportional-integral-derivative (PID) controllers are the most widely used for process control in most of the industrial plants. The success of PID control logic can be attributed to the achievement of simple structures of automatic control systems (ACS) and its effectiveness for linear systems [1], [2], [3], [4], [5],[6] and [7]. There is a wide variety of PID controllers tuning rules: the Ziegler-Nichols rule[8], [9] and [10], the magnitude optimum method [11], [12], [13], [14], [15] and [16], the direct synthesis methods [17] and [18], the Internal Model Control methods [9], [19],[20] and [21], the minimum error integral criteria [22], [23] and [24], the iterative feedback tuning method [25], the virtual reference feedback tuning method [26] and [27], the approximate M-constrained integral gain optimization method [28], AMIGO method [29]and others. The required quality of a PID control system can be achieved by means of a variety of tuning rules once a linear model of the controlled system and a criteria for the assessment of the control performance are chosen.
Usually the conventional PID controller is not effective for complex dynamic systems[30] and [31]. The complex dynamic systems are those systems with non-linear static characteristics, i.e. those systems that are described by differential equations with time-varying parameters. This feature essentially complicates the design and analysis of PID-based control systems and decreases their control performance.
A number of researchers have conducted studies to combine a conventional PID controller with a fuzzy logic controller (FLC) in order to achieve a better control quality in ACS rather than the one guaranteed by conventional PID controllers. The idea of using fuzzy sets [32] is successfully applied, for the first time, in the control of a dynamic plant developed by Mamdani and Assilian [33]. Currently, there are different types of FLC, but a PID-based FLC is the most common and practical for applications to ACS [34], [35],[36], [37] and [38]. Such FLC is equivalent to a conventional PID controller for the input-output structure [34] and [39]. PID-based FLC may be constructed by sequentially incorporating FLC and PID controllers or paralleling PID and FLC (PID with an adapter based on FLC). Moreover, the use of FLC logic makes it easy to add nonlinearities and additional input signals to the control law [1], that, in turn, allows to apply PID-based FLC to complex dynamic systems.
A priori information about the dynamics of the controlled plant is required for the synthesis of PID-based FLC. Hammerstein and Wiener models may be used to describe complex dynamics real-life processes [40], [41], [42] and [43]. Hammerstein and Wiener models are methodologies constituted by the combination of a static nonlinearity (N) and a linear system (L), respectively in the N-L and L-N form. The problem of identifying N and L from input-output data has attracted and attracts a lot of research interests and many methods are available for this problem in literature [40], [41], [42], [43], [44],[45] and [46]. The nonlinear dynamic system can be approximated by a linear dynamic system near the operating point, which is sufficient for PID tuning. It is not a simple task to define the parameters of the linear dynamic model approximation in the closed-loop system. In [47], [48] and [49] active methods of identification are proposed; here sine waves in input are used to excite the Wiener continuous-time system and frequency methods are used to determine the unknowns. Unknown additive disturbances create problems for closed-loop identification [50]. Good results can be obtained by using MATLAB system identification toolbox for the identification of the parameters of the process with the use of ARX, ARMAX, BJ state space, polynomial models and others[51].
Practically, in chemical and nuclear industries (i.e. integrated separations, extractions[52] and [53], crystallization processes to purify U and Pu from other fusion side-components) any processing step has a high level of automation but, in the contrary an insufficient automation in process control occurs. Moreover field operators need to work within the control loops of complex physicochemical processes. On the one hand, all processes are high responsibility technology (HRT), i.e. high performance technology with respect of safety level. On the other hand, they are also complex dynamic systems.
The purpose of the research is to develop a method of synthesis for low-level ACS (relative to HRT), which will provide the required control performance also in the presence of a significant change in the process parameters and several step disturbances with unknown amplitudes and durations. A Low-level ACS must fulfill the following limitations: control in the tight real-time mode should be performed with hot standby of the controllers; applied controllers have limited computation abilities which do not allow an extension of the mathematical support functions; for the purpose of control, conventional PID controllers should be employed.

2. Material and methods for the fuzzy adaptive control of a generic plant

The proposed method employs algorisms for the plant identification coupled with fuzzy systems such as Mamdami controllers [54] and [55]. The layout of a generic ACS plant is presented in Fig. 1 while a scheme of an adaptive fuzzy controller is shown in Fig. 2.
Fuzzy adaptive control system. g : reference signal; f* : non-measurable ...
Fig. 1. 
Fuzzy adaptive control system. g : reference signal; f* : non-measurable disturbance; f : measurable disturbance; Pu : plant control channel; Pf : plant disturbance channel; Pf* : plant non-measurable disturbance channel; y: controlled variable; ε : control error is defined as ε = g – y.
Figure options
Adaptive fuzzy controller for an ACS.
Fig. 2. 
Adaptive fuzzy controller for an ACS.
Figure options
The optimization problem consists of maximizing or minimizing a functional which plays the key role from the viewpoint of the design of adaptive and optimal control systems. It is addressed here in the following form:
equation1
min(Jek+Juk+Jnk)
Turn MathJaxon
where
equation2
View the MathML source
equation3
View the MathML source
Jnk– the number of control error oscillations in the interval he, (2)
where k = 1,2, … ∞, εj – the control error, uj – the manipulated variable, he – the control error interval, hu – the control interval, j – the index of time sampling.
The adaptor-optimizer of the suggested ACS (see Fig. 2) includes the following blocks: an identifier, a fuzzy rules base generator, a Mamdani fuzzy output controller and Jn, Jeand Ju terms calculation engines. The identification is performed in the closed-loop system in those operating conditions where the edge of the transient is reached (seeFig. 4).
Parameters of control object, obtained as a result the identification transmitted into generator fuzzy rules and used to calculate parameters controller by the magnitude optimum method. Obtained controller parameters are used to optimize the algorithm, which is shown in Fig. 3.
The principle of operation of the generator fuzzy rules.
Fig. 3. 
The principle of operation of the generator fuzzy rules.
Figure options
The variation in the controlled variable, caused by the change of the non-measurable disturbance f*, is considered the initial signal for the identification procedure. The time instant t0 where the non-measurable step disturbance f* undergoes a step change is unknown. The time instant t1 is defined by the deviation threshold of y from g by Δy  >  yg, where yg is the required control accuracy, and t2 is the time instant of the y variable sign change. The parameters of the plant are defined by Levenberg-Marquardt optimization method. In this case, the measured disturbance f, the control action u and the controlled variable y (see Fig. 1, Fig. 2, Fig. 3 and Fig. 4) are supplied to the identifier input in the time interval whose lower and upper bounds are, respectively, t2 and t3.
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A semi autonomous home defense system will require a PLC



Programmable logic controllers provide dependable, high-speed control and monitoring demanded by a wide variety of automated applications.
Programmable logic controllers(PLCs) have gained a substantial hold in the industrial manufacturing arena, and we would be remiss if this technology were not given the due attention it has earned. As such, we are featuring a series of articles based on the fundamentals of PLCs in this new EC&M department covering the technology of solid-state industrial automation. Throughout this series on PLC fundamentals, we'll cover PLC hardware modules; software capabilities; current applications; installation parameters; testing and troubleshooting; and hardware/software maintenance.
What is a PLC?
The National Electrical Manufacturers Association (NEMA) defines a PLC as a "digitally operating electronic apparatus which uses a programmable memory for the internal storage of instructions by implementing specific functions, such as logic, sequencing, timing, counting, and arithmetic to control through digital or analog I/O modules various types of machines or processes."
One PLC manufacturer defines it as a "solid-state industrial control device which receives signals from user supplied controlled devices, such as senors and switches, implements them in a precise pattern determined by ladder-diagram-based application progress stored in user memory, and provides outputs for control of processes or user-supplied devices, such as relays or motor starters."
Basically, it's a solid-state, programmable electrical/electronic interface that can manipulate, execute, and/or monitor, at a very fast rate, the state of a process or communication system. It operates on the basis of programmable data contained in an integral microprocessor-based system.
A PLC is able to receive (input) and transmit (output) various types of electrical and electronic signals and can control and monitor practically any kind of mechanical and/or electrical system. Therefore, it has enormous flexibility in interfacing with computers, machines, and many other peripheral systems or devices.
It's usually programmed in relay ladder logic and is designed to operate in an industrial environment.
What's it look like?
PLCs come in various sizes. Generally, the space or size that a PLC occupies is in direct relation to the user systems and input/output requirements as well as the chosen manufacturer's design/packaging capabilities.
Image result for PLC pic
The chassis of a PLC may be of the open or enclosed type. The individual modules plug into the back plane of the chassis.
The electronic components are mounted on printed circuit boards (PCBs) that are contained within a module.
Where did it come from?
The first PLC was introduced in the late 1960s and was an outgrowth of the programmable controller or PC (not to be confused with the notation as used for the personal computer). PCs have been around the industry since the early 60s.
The need for better and faster control relays that fit into less space as well as the frustration over program inflexibility (hard-wired relays, stepping switches, and drum programmers) gave birth to the PC.
Although the PC and PLC have been interchanged in speech, the difference between them is that a PC is dedicated to control functions in a fixed program, similar in a sense to the past problem of limited ability. A PLC, on the other hand, only requires that its software logic be rewritten to meet any new demands of the system being controlled. Thus, a PLC can adapt to changes in many processes or monitoring application requirements.
How does a PLC work?
Image result for I/O pic
To know how the PLC works, it is essential that we have an understanding of its central processing unit's (CPU's) scan sequence. The methodology basically is the same for all PLCs. However, as special hardware modules are added into the system, additional scanning cycles are required.
Here's one simple scanning process that involves every PLC. First, the I/O hardware modules are scanned by the ladder logic software program as follows.
Upon power-up, the processor scans the input module and transfers the data contents to the input's image table or register. Data from the output image table is transferred to the output module.
Next, the software program is scanned, and each statement is checked to see if the condition has been met. If the conditions are met, the processor writes a digital bit "1" into the output image table, and a peripheral device will be energized. If the conditions are not met, the processor writes a "0" into the output image table, and a peripheral device (using "positive logic") remains deenergized.
A PLC interfaces numerous types of external electrical and electronic signals. These signals can be AC or DC currents or voltages. Typically, they range from 4 to 20 milliamperes (mA) or 0 to 120VAC, and 0 to 48VDC. These signals are referred to as I/O (input/output) points. Their total is called the PLC's I/O capability. From an electronic point-of-view, this number is based on how many points the PLC's CPU is able to look at, or scan, in a specified amount of time. This performance characteristic is called scan time. From the practical perspective of the user, however, the number of I/O modules needed as well as the number of I/O points contained on each I/O module will drive what the system's I/O capability should be.
It's important to have sufficient I/O capability in your PLC system. It's better to have more than less so that, when more I/O points are required at a future time, it's easier to write the existing spare I/O points into the software (since the hardware is already there). There's no harm to the operating system in having spare I/O points; the software can be programmed to ignore them, and these points will have a negligible effect on the PLC's scan time.
The PLC's software program
The software program is the heart of a PLC and is written by a programmer who uses elements, functions, and instructions to design the system that the PLC is to control or monitor. These elements are placed on individually numbered rungs in the relay ladder logic (RLL). The software's RLL is executed by the processor in the CPU module or controller module (same module, different name).
There are many types of PLC software design packages available. One frequently selected software package is of the RLL format and includes contacts, coils, timers, counters, registers, digital comparison blocks, and other types of special data handling functions. Using these elements, the programmer designs the control system. The external devices and components are then wired into the system identical to that of the programmer's software ladder logic. Not all of the software elements will have a hard-wired, physical counterpart, however.
As the PLC's processor scans (topdown) through the software program (rung-by-rung), each rung of RLL is executed. The hard-wired device that the software is mirroring then becomes active. The software is thus the controlling device and provides the programmer or technician the flexibility to either "force a state" or "block a device" from the system operation. For example, a coil or contact can be made to operate directly from the software (independent of the control cabinet's hard-wiring to source or field input devices). Or, a device can be made to appear invisible (removed from the system's operation), even though it's electrically hard-wired and physically in place.
Individual PLC sections
Common to all PLCs are four sections, each of which can be subdivided into smaller but equally important sections. These primary sections include the power supply section, which provides the operating DC power to the PLC and I/O base modules and includes battery backup; the program software section; the CPU module, which contains the processor and holds the memory; and the I/O section, which controls peripheral devices and contains the input and output modules.
Power supply section. The power supply (PS) section gets its input power from an external 120VAC or 240VAC source (line voltage), which is usually fused and fed through a control relay and filter external to the PS. In addition, the PS has its own integral AC input fuse.
This line voltage is then stepped-down, rectified, filtered, regulated, voltage- and current-protected, and status-monitored, with status indication displayed on the front of the PS in the form of several LEDs (light-emitting diodes). The PS can have a key switch for protecting the memory or selecting a particular programming mode.
The output of the PS provides low DC voltage(s) to the PLC's various modules (typically, with a total current capability of 20A or 50A) as well as to its integral lithium battery, which is used for the memory backup. Should the PS fail or its input line voltage drop below a specific value, the memory contents will not change from what they were prior to the failure.
The PS output provides power to every module in the PLC; however, it does not provide the DC voltages to the PLC's peripheral I/O devices.
CPU module. "CPU," "controller," or "processor" are all terms used by different manufacturers to denote the same module that performs basically the same functions. The CPU module can be divided into two sections: the processor section and the memory section.
The processor section makes the decisions needed by the PLC so that it can operate and communicate with other modules. It communicates along either a serial or parallel data-bus. An I/O base interface module or individual on-board interface I/O circuitry provides the signal conditioning required to communicate with the processor. The processor section also executes the programmer's RLL software program.
The memory section stores (electronically) retrievable digital information in three dedicated locations of the memory. These memory locations are routinely scanned by the processor. The memory will receive ("write" mode) digital information or have digital information accessed ("read" mode) by the processor. This read/write (R/W) capability provides an easy way to make program changes.
The memory contains data for several types of information. Usually, the data tables, or image registers, and the software program RLL are in the CPU module's memory. The program messages may or may not be resident with the other memory data.
A battery backup is used by some manufacturers to protect the memory contents from being lost should there be a power or memory module failure. Still others use various integrated circuit (IC) memory technologies and design schemes that will protect the memory contents without the use of a battery backup.
A typical memory section of the CPU module has a memory size of 96,000 (96K) bytes. This size tells us how many locations are available in the memory for storage. Additional memory modules can be added to your PLC system as the need arises for greater memory size. These expansion modules are added to the PLC system as the quantity of I/O modules are added or the software program becomes larger. When this is done, the memory size can be as high as 1,024,000 (1024K) bytes.
Manufacturers will state memory size in either "bytes" or "words." A byte is eight bits, and a bit is the smallest digit in the binary code. It's either a logic "1" or a logic "0." A word is equal in length to two bytes or 16 bits. Not all manufacturers use 16-bit words, so be aware of what your PLC manufacturer has defined as its memory word bit size.
Software program. The PLC not only requires electronic components to operate, it also needs a software program. The PLC programmer is not limited to writing software in one format. There are many types available, each lending itself more readily to one application over and above another. Typical is the RLL type previously discussed. Other S/W programs include "C," State Language, and SFC (Sequential Function Charts).
Regardless of which software is chosen, it will be executed by the PLC's CPU module. The software can be written and executed with the processor in an online state (while the PLC is actually running) or in the off-line state (whereby the S/W execution does not affect current operation of the I/O base).
In the RLL software program, we find several types of programming elements and functions to control processes both internal to the PLC (memory and register) as well as external (field) devices. Listed below are some of the more common types of elements, functions, and instructions:
* Contacts (can be either normally opened or closed; highlighted on the monitor means they are active).
* Coils (can be normal or latched; highlighted means they are energized).
* Timers (coil can either be ON or OFF for the specified delay).
* Counters (can count by increments either up or down).
* Bit shift registers (can shift data by one bit when active).
* One-shot (meaning active for one scan time; useful for pulse timer).
* Drums (can be sequenced based on a time or event).
* Data manipulation instructions (enable movement, comparison of digital values).
* Arithmetic instructions (enable addition, subtraction, multiplication, and division of digital values).
Peripheral devices
Peripheral devices to the PLC and its I/O base(s) can be anything from a host computer and control console to a motor drive unit or field limit switch. Printers and industrial terminals used for programming are also peripheral devices.
Peripheral devices can generate or receive AC or DC voltages and currents as well as digital pulse trains or single pulses of quick length (pulse width).
These external operating devices, with their sometimes harsh and/or fast signal characteristics, must be able to interface with the PLC's sensitive microprocessor. Various types of I/O modules (using the proper shielded cabling) are available to do this job.
Input module
The input module has two functions: reception of an external signal and status display of that input point. In other words, it receives the peripheral sensing unit's signal and provides signal conditioning, termination, isolation and/or indication for that signal's state.
The input to an input module is in either a discrete or analog form. If the input is an ON-OFF type, such as with a push button or limit switch, the signal is considered to be of a discrete nature. If, on the other hand, the input varies, such as with temperature, pressure, or level, the signal is analog in nature.
Peripheral devices sending signals to input modules that describe external conditions can be switches (limit, proximity, pressure, or temperature), push buttons, or logic, binary coded decimal (BCD) or analog-to-digital (A/D) circuits. These input signal points are scanned, and their status is communicated through the interface module or circuitry within each individual PLC and I/O base. Some typical types of input modules are listed below.
* DC voltage (110, 220, 14, 24, 48, 15-30V) or current (4-20 mA).
* AC voltage (110, 240, 24, 48V) or current (4-20 mA).
* TTL (transistor transistor logic) input (3-15VDC).
* Analog input (12-bit).
* Word input (16-bit/parallel).
* Thermocouple input.
* Resistance temperature detector.
* High current relay.
* Low current relay.
* Latching input (24VDC/110VAC).
* Isolated input (24VDC/85-132VAC).
* Intelligent input (contains a microprocessor).
* Positioning input.
* PID (proportional, intregal, differentiation) input.
* High-speed pulse.
Output module
The output module transmits discrete or analog signals to activate various devices such as hydraulic actuators, solenoids, motor starters, and displays the status (through the use of LEDs) of the connected output points. Signal conditioning, termination, and isolation are also part of the output module's functions. The output module is treated in the same manner as the input module by the processor.
Some typical output modules available today include the following:
* DC voltage (24, 48,110V) or current (4-20 mA).
* AC voltage (110, 240v) or current (4-20 mA).
* Isolated (24VDC).
* Analog output (12-bit).
* Word output (16-bit/parallel).
* Intelligent output.
* ASCII output.
* Dual communication port.
TERMS TO KNOW
A/D: A device or module that transforms an analog signal into a digital word.
Address: A numbered location (storage number) in the PLC's memory to store information.
Analog input: A varying signal supplying process change information to the analog input module.
Analog output: A varying signal transmitting process change information from the analog output module.
Baud rate: The number of bits per second that is either transmitted or received; also the speed of digital transmission acceptable by a device.
BCD: Binary coded decimal. A method used to express the 0-thru-9 (base 10) numbering system as a binary (base 2) equivalent.
Bit: A single binary digit.
Byte: Eight bits.
Central Processing Unit (CPU): An integrated circuit (IC) that interprets, decides, and executes instructions.
D/A: A device or module that transforms a digital word into an analog signal
Electrically Erasable Programmable Read-Only Memory (EEPROM): Same as EPROM but can be erased electrically.
Erasable Programmable Read-Only Memory (EPROM): A memory that a user can erase and load with new data many times, but when used in application, it functions as a ROM. EPROMs will not lose data during the loss of electrical power. They are nanvolatile memories.
Image register/image table: A dedicated memory location reserved for I/O bit status.
Input module: Processes digital or analog signals from field devices.
I/O points: Terminal points on I/O modules that connect the input and output field devices.
Millisecond: One thousandth of a second (1/1000 sec, 0.001 sec).
Modem: Modem is an acronym for modulator/demodulator. This is a device that modulates (mixes) and demodulates (separates) signals.
Operator interface: Devices that allow the system operators to have access to PLC and I/O base conditions.
Output module: Controls field devices.
Parallel data: Data whose bytes or words are transmitted or received with all their bits present at the same time.
Program: One or more instructions or statements that accomplish a task.
Programming device: A device used to tell a PLC what to do and when it should be done.
Random Access Memory (RAM): A memory where data can be accessed at any address without having to read a number of sequential addresses. Data can be read from and written to storage locations. RAM has volatile memory, meaning a loss of power will cause the contents in the RAM to be lost.
Read-Only Memory (ROM): A memory from which data can be read but not written. ROMs are often used to keep programs or data from being destroyed due to user intervention.
Software: One or more programs that control a process.
Robert B. Hee is an electronic/electrical engineer in private practice in Virginia Beach, Va.
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