Review of PI and PID Controllers

Review of PI and PID Controllers Supriya V. Narvekar 1 Vasantkumar K. Upadhye 2 Assistant Professor 1,2 Angadi Institute of Technology and Management, Belagavi. Karnataka, India Abstract: This paper presents a literature review of available PI and PID controllers. A self tuning PID controller, PID type fuzzy controller and PI type fuzzy controller are reviewed. In this review a low power self-tuning analog proportional-integral-derivative controller model can be studied. By using a model-free tuning method, it overcomes problems associated with reconfigurable analog arrays. In comparison to a self-tuning digital PID controller, it combines the advantages of low power, no quantization noise, high bandwidth and high speed. Time domain techniques for the identification and tracking of plant and controller parameters, both explicit and implicit self-tuning controllers have been employed. The use of the frequency domain provides concise information on the dynamics of the process which has led to its wide acceptance as a domain for controller design. By relating to the conventional PID control theory, a new fuzzy controller structure is proposed, namely PID type fuzzy controller. In order to improve further the performance of the transient state and the steady state of the PID type controller, method is discussed to tune the scaling factors of the PID type fuzzy controller on- line. Ziegler-Nichols tuned PI or PID controller performs well around normal working conditions, but its tolerance to process parameter variations are severely affected. The Self-tuning Fuzzy PI controller (STFPIC) is used by to overcome these shortcomings. Keywords: Self-tuning controllers; Scaling factors; PID type fuzzy controller; Self-tuning Fuzzy PI controller. I. INTRODUCTION A controller is a device, historically using mechanical, hydraulic, pneumatic or electronic techniques often in combination, but more recently in the form of a microprocessor or computer, which monitors and physically alters the operating conditions of a given dynamical system. Typical applications of controllers are to hold settings for temperature, pressure, flow or speed. Basic Controller Types: PID controllers use a 3 basic types or modes: P - proportional, I - integrative and D - derivative. While proportional and integrative modes are also used as single control modes, a derivative mode is rarely used on it s own in control systems. Combinations such as PI and PD control are very often in practical systems. 1.1. P Controller: In general it can be said that P controller cannot stabilize higher order processes. For the 1 st order processes, meaning the processes with one energy storage, a large increase in gain can be tolerated. Proportional controller can stabilize only 1 st order unstable process. Changing controller gain K can change closed loop dynamics. A large controller gain will result in control system with: a) Smaller steady state error, i.e. better reference following b) Faster dynamics, i.e. broader signal frequency band of the closed loop system and larger sensitivity with respect to measuring noise c) Smaller amplitude and phase margin @IJRTER-2016, All Rights Reserved 381

When P controller is used, large gain is needed to improve steady state error. Stable systems do not have problems when large gain is used. Such systems are systems with one energy storage (1 st order capacitive systems). If constant steady state error can be accepted with such processes, than P controller can be used. Small steady state errors can be accepted if sensor will give measured value with error or if importance of measured value is not too great anyway. 1.2. PI Controller: PI controller will eliminate forced oscillations and steady state error resulting in operation of on-off controller and P controller respectively. However, introducing integral mode has a negative effect on speed of the response and overall stability of the system. Thus, PI controller will not increase the speed of response. It can be expected since PI controller does not have means to predict what will happen with the error in near future. This problem can be solved by introducing derivative mode which has ability to predict what will happen with the error in near future and thus to decrease a reaction time of the controller. PI controllers are very often used in industry, especially when speed of the response is not an issue. A control without D mode is used when: a) fast response of the system is not required b) large disturbances and noise are present during operation of the process c) there is only one energy storage in process (capacitive or inductive) d) there are large transport delays in the system. 1.3. PID Controller: PID controller has all the necessary dynamics: fast reaction on change of the controller input (D mode), increase in control signal to lead error towards zero (I mode) and suitable action inside control error area to eliminate oscillations (P mode). Derivative mode improves stability of the system and enables increase in gain K and decrease in integral time constant Ti, which increases speed of the controller response. PID controller is used when dealing with higher order capacitive processes (processes with more than one energy storage) when their dynamic is not similar to the dynamics of an integrator (like in many thermal processes). PID controller is often used in industry, but also in the control of mobile objects when stability and precise reference following are required. Conventional autopilot is for the most part PID type controllers. Tuning Tuning is adjustment of control parameters to the optimum values for the desired control response. Stability is a basic requirement. However, different systems have different behavior, different applications have different requirements, and requirements may conflict with one another. II. ANALOG PID CONTROLLER Varun Aggarwal, Meng Mao and Una-May O Reilly [1] discusses a low power self-tuning analog proportional-integral-derivative controller model. By using a model-free tuning method, it overcomes problems associated with reconfigurable analog arrays. In comparison to a self-tuning digital PID controller, it combines the advantages of low power, no quantization noise, high bandwidth and high speed. Prototype hardware used is a commercially available field programmable analog array (FPAA) and Particle Swarm Optimization (PSO) as the tuning method. The developed scheme is to correct the variance in measurement and shows that a self-tuned controller can outperform a hand tuned solution and demonstrate adaptability to plant drift. Framework for a self-tuning analog PID controller is shown in Figure 1. It uses a reconfigurable analog block as the controller and a microprocessor to run the tuning algorithm. The switches are used to put the system into control or tuning mode. In control mode, the FPAA takes the user input @IJRTER-2016, All Rights Reserved 382

and controls the plant accordingly. In the self-tuning mode, the input is generated by a function generator controlled by the microprocessor. The system uses a model-free method, i.e. on the microprocessor it executes an optimization algorithm that minimizes a cost function defined on the characteristics of the closed-loop system. To get data for optimization, a 2-channel ADC is used to digitize and send the input and output signal to the processor. Figure 1. Proposed self tuning analog PID controller model Figure 2. The GRACE system A framework for a self-tuning analog PID controller overcomes traditional problems associated with FPAAs such as poor characterization and limited or coupled component parameter ranges. The framework overcomes these by using a model-free tuning method. It combines the advantages of low power, no quantization noise, high bandwidth and high speed in comparison to a self-tuning digital PID controller. A prototype of this PID controller is implemented using a state-of-art commercially available FPAA, Anadigm s AN221E04 and used Particle Swarm Optimization as the tuning method. A scheme to correct the variance in measurement and incorporated it into PSO. It is shown that a self-tuned controller can outperform a hand tuned solution. The optimization algorithm worked well despite the system offset and coupled ranges for different gain values. Future work is directed toward both prototype and framework. In terms of prototype, it is likely to incorporate search for the best ranges of gains into software so the search can be informed by closed loop characteristics. This would improve upon the manual method of finding ZN coefficients which must be done in open loop and which does not support adaptation of a highly varying plant. In terms of framework, one issue to address is the limitations of current prototype in which a very versatile FPAA is employed at the unfortunate cost of power consumption. III. A FREQUENCY DOMAIN BASED SELF TUNING PID CONTROLLER J.V. Ringwood and A. O Dwyer [2] discuss, both explicit and implicit self-tuning controllers which employed time domain techniques for the identification and tracking of plant and controller parameters. The use of the frequency domain provides concise information on the dynamics of the process which has led to its wide acceptance as a domain for controller design. They demonstrated a method employing recursive, on-line measurement of the process frequency response, with a straight @IJRTER-2016, All Rights Reserved 383

forward calculation of PID controller parameters. The computational effort involved is comparable with that of a time domain technique. A self-tuning controller has been presented, based on frequency domain calculations. One advantage of this is that no process parameterization is required. The computational effort, summarized is comparable with that of a time-domain self-tuner. In addition, the algorithm contains design parameters not dissimilar to a time-domain algorithm. These generally involve a trade-off between speed of tuning and noise immunity. One feature of this technique was the easy addition of caution control, since a direct measure of the tuning error (i.e. phase error) is available. The algorithm also extended to include explicit time delay estimation, since this effect (linear phase shift with frequency) can be resolved from the overall phase measurement. Such an extension is not possible with parametric time-domain schemes. IV. A PID TYPE FUZZY CONTROLLER WITH SELF TUNING SCALING FACTORS Zhi-Wei Woo, Hung-Yuan Chung, Jin-Jye Lin [3], proposed a new fuzzy controller structure by relating to the conventional PID control theory, namely PID type fuzzy controller. In order to improve further the performance of the transient state and the steady state of the PID type controller, a method was developed to tune the scaling factors of the PID type fuzzy controller on line. Simulation of the PID type fuzzy controller with the self-tuning scaling factors showed a better performance in the transient and steady state response. Figure 3. The PID Type Fuzzy Control System Fuzzy PI type control is known to be more practical than fuzzy PD type, since it is difficult for the fuzzy PD to remove the steady state error. The fuzzy PI type control is, however, known to give poor performance in the transient response for higher order process due to the internal integration operation. To improve the performance of the fuzzy PI type and fuzzy PD type at the same time a fuzzy controller is designed that processes the fine characteristics of the PID controller only by using the error and the rate of change of error as its inputs. A PID type fuzzy controller structure that simply connects the PD type and the PI type fuzzy controllers together in parallel is shown in Figure 3. These rules are expressed as: If {e is ZR and e is ZR}, then {u is ZR}. The membership functions of error, change rate of the error and u are shown in Figure 4. @IJRTER-2016, All Rights Reserved 384

Figure 4. The Membership Function of e, e and u The fuzzy PID type control rule is shown in Table 1. Table 1. A General Fuzzy PID Type Rule Base To improve the performance of the proposed PID type fuzzy controller, a method of self-tuning scaling factors of fuzzy controller is designed. The PID type fuzzy controller can be decomposed into the equivalent proportional control, integral control and the derivative control components. This method decreases the equivalent integral control component of the fuzzy controller gradually with the system response process time so as to increase the damping of the system when the system is about to settle down, meanwhile keeping the proportional control component not to change too much so as to guarantee quick reaction against the error. With the self-tuning fuzzy controller, the oscillation of the system is strongly restrained and the settling time is shortened greatly. V. SELF TUNING FUZZY PI CONTROLLER AND IT S APPLICATIONS TO HVAC SYSTEM K. Pal and R. K. Mudi [4] discuss a Self-tuning Fuzzy PI controller for the supply air pressure control loop for Heating, Ventilation and Air-Conditioning (HVAC) system. The self-tuning Fuzzy PI controller (STFPIC) adjusts the output scaling factor on-line by fuzzy rules according to the current trend of the controlled process. The rule-base for tuning the output-scaling factor is defined on error and change of error of the controlled variable. Ziegler-Nichols tuned PI or PID controller performs well around normal working conditions, but its tolerance to process parameter variations are severely affected. The STFPIC is used here to overcome these shortcomings. Comparing with PID and Adaptive Neuro-Fuzzy (ANF) Controllers, simulations results show that STFPIC performances are better under normal conditions as well as when the HVAC system encounters large parameter variations. Heating, Ventilation and Air-Conditioning (HVAC) systems require control of environmental variables such as pressure, temperature, humidity etc. In the HVAC system, the supply air pressure is regulated by the speed of a supply air fan. Increasing the fan speed will increase supply air pressure, and vice versa. The dynamics from the fan variable speed drive to the supply air pressure can model as a second order plus dead time. The basic function of the rule base is to represent in a structured @IJRTER-2016, All Rights Reserved 385

way the control policy of an experienced process operator and/or control engineer in the form of a set of production rules such as If {process state} then {control output}. Figure 5. Block Diagram of the PI Type STFC Figure 5 shows that the output scaling-factor (SF) of the fuzzy controller is modified by a self-tuning mechanism, which is marked by bold rectangular portion in the figure. Then based on the knowledge of process control or by trial and error method choose suitable SF s for inputs and output. The relationship as follows for PI type self-tuning fuzzy controller scheme. en = Nee, ΔeN = NΔeΔe and Δu = (βnu) ΔuN Where Ne and NΔe are input scaling factor of error and change of error respectively and Nu is output scaling factor. Thereafter apart from fuzzy PI controller rule determination, also determines the rule base for gain updating factor, in the similar way like If e is E and Δe is ΔE then β is β. As shown in Figure 5, when this β is multiplied with the fuzzy controller gain Nu, gives the overall gain of STFPIC. It is very important to note that the rule base for computation of β will always be dependent on the choice of the rule base for the controller. Choice of Scaling Factor (gain): The scaling factors also known as gains, which describe the particular input normalization and output denormalization, plays an important role similar to that of the gain coefficients in a conventional controller. The STFPIC method used here is rather simple to understand by the control engineer. The results showed that the STFPI controller does not hamper the HVAC process performance. This scheme differs from others as it attempts to implement the operator s strategy while running a plant. The operators / control engineers can design the fuzzy rule base for fuzzy controller and as well as the fuzzy rule base for gain updating factor according to their knowledge. @IJRTER-2016, All Rights Reserved 386

VI. CONCLUSION A self-tuning analog PID controller overcomes traditional problems associated with FPAAs such as poor characterization and limited or coupled component parameter ranges. The framework overcomes these by using a model-free tuning method. It combines the advantages of low power, no quantization noise, high bandwidth and high speed in comparison to a self-tuning digital PID controller. A frequency domain based self-tuning PID controller requires no process parameterization. A PID type fuzzy controller with self-tuning scaling factors, decreases the equivalent integral control component of the fuzzy controller gradually with the system response process time so as to increase the damping of the system when the system is about to settle down, meanwhile keeping the proportional control component not to change too much so as to guarantee quick reaction against the error. Self-Tuning Fuzzy PI Controller and its Application to HVAC Systems does not hamper the HVAC process performance REFERENCES 1. Varun Aggarwal, Meng Mao and Una-May O Reilly, A Self-Tuning Analog Proportional- Integral-Derivative (PID) Controller in Prc. IEEE, Adaptive Hardware and Systems conference on 15-18 June 2006, pp. 12 19. 2. J.V. Ringwood and A. O Dwyer, A Frequency Domain Based Self-Tuning PID Controller proceedings of the Asian Control Conference, Tokyo, Japan, July 1994, pp. 331-334. 3. Zhi-Wei Woo, Hung-Yuan Chung, Jin-Jye Lin, A PID Type Fuzzy Controller With Self-Tuning Scaling Factors Published in journal Fuzzy Sets and Systems, volume 115 issue 2,oct. 16, 2000, pp. 321 326. 4. A. K. Pal and R. K. Mudi, Self-Tuning Fuzzy PI Controller and its Application to HVAC Systems International Journal of Computational Cognition Http://www.ijcc.us, Vol. 6, No. 1, March 2008. @IJRTER-2016, All Rights Reserved 387