**7. References**

244 Introduction to PID Controllers – Theory, Tuning and Application to Frontier Areas

exhibited negative values). This indicates that, selecting the criterion of the most negative of the risk factors, the DSR, (that is the returns inferior to the risk free rate) the new model is

The following chart allows the visualization of the comparison of the two portfolios. It is to be remembered that when a column is missing, it indicates that its corresponding value is negative. In year 2001-2002, the column of portfolio A since its value is negligible. However,

Fig. 5. Sortino ratio of portfolios "A" and "B". The chart represents per each year of observation, Sortino values for the two portfolios. In particular, in black the results for Portfolio "A" are represented. In grey, the results of Portfolio "B" are illustrated. The absence of a column indicates that the indicator value is negative, hence non-interpretable. If Sortino and Sharpe Ratio results are compared it is evident the ability of Portfolio "A" to better perform in comparison of Portfolio "B". Since the difference between Sortino and Sharpe resides in the definition of the denominator portion of the formula, it is apparent that Portfolio "A" acts more efficiently on the DSR than on the total volatility. Hence, this selectivity capability of the model is a good feature. The PID control action on financial portfolios seems to function as a stabilizer of returns. Above all, it diminishes the worst

2004-2005

Portfolio "A" Sortino Portfolio "B" Sortino

2005-2006

2006-2007

2007-2008

2008-2009

2009-2010

2010-2011

2003-2004

This work illustrates a portfolio management model with the aim to obtain good returns and decrease portfolio risk through stabilization of returns, by means of the PID control applied to pure returns. As demonstrated in the previous sections, the new model is able to obtain returns that are satisfactory in the observation period. In addition, it is able, in about half of the analyzed cases, to diminish the volatility relative to the benchmark. In particular, the best results are exhibited when the Down Side Risk is considered instead of the whole volatility. The results illustrated herein relative to the Down Side Risk are of a good quality. The new model, through asset rebalancing, in the observation period, successfully reduces the negative volatility factor in 5 cases out of 11 more than the negative volatility of the benchmark. This research work furthers the analysis of two indicators of risk adjusted returns: Sharpe and Sortino. Confirming and reiterating what just said, Sortino, which uses

component of the returns, namely the ones inferior to the risk free rate.

the DSR in its denominator, obtained the best performances.

bale to guarantee a better performance in comparison to the benchmark.

Sortino's value in that year is relevant.

**6. Conclusion** 

0,00 0,30 0,60 0,90 1,20 1,50 1,80 2,10 2,40 2,70 3,00 3,30

1999-2000

2000-2001

2001-2002

2002-2003


**Part 8** 

**Practical Applications** 


**Part 8** 

**Practical Applications** 

246 Introduction to PID Controllers – Theory, Tuning and Application to Frontier Areas

Gold, L. M. (2004). Investing in pseudo-science: the active versus passive debate. *Journal of* 

Gruber, J. M. (1996). Another puzzle: the growth in actively managed funds. *The Journal of* 

MacBeth, J. & Emanuel, C. D. (1993) Tactical Asset Allocation: Pros and Cons. *Financial* 

Markowitz, H. (1952). Portfolio Selection. *The Journal of Finance*, Vol. 7, No. 1, (March, 1952),

Qian, E. (2003). Tactical Asset Allocation with Pairwise Strategies. Using pairwise

Sampagnaro, G. (Ed.). (2006). Asset Management: tecniche e stile di gestione di portafoglio,

Samuelson, A. P. (1974). Challenge to Judgment. *The Journal of Portfolio Management*, Vol. 1,

Samuelson, A. P. (2004). The Backward Art of Investing Money. *The Journal of Portfolio Management*, Vol. 30, No. 5, (30th anniversary, 2004), pp- 30-33, ISSN 00954918. Sharpe, F. W. (1991). The arithmetic of active management. *Financial Analyst Journal*, Vol. 47,

Shen, P. (2003). Market Timing Strategies That Worked. Based on the E/P Ratio of the

Skogestad, S. (2010) Feedback: still the simplest and best solution. Paper presented at

S&P500 and interest rates. *The Journal of Portfolio Management*, Vol. 29, No. 2,

International Conference Cybernetics and Informatics, 10 February, Bratislava,

*Finance*, Vol. 51, No. 3, (July, 1996), pp.783-810, ISSN 0022-1082.

0313-5934.

0015-198X.

pp. 77-91, ISSN 0022-1082.

(Fall, 2003), pp. 39-48, ISSN 00954918.

Franco Angeli, ISBN 8846472829, Milan.

(Winter, 2003), pp. 57-68, ISSN 00954918.

Slovac Republic.

No. 1, (Fall, 1974), pp.17-19, ISSN 00954918.

No. 1, (January-February, 1991), pp. 7-9, ISSN 0015-198X.

*the Securities Institute of Australia,* Vol.3, No. 3, (Summer 2004), pp. 2-6, ISSN

*Analysts Journal*, Vol. 49, No. 6, (November-December, 1993), pp. 30-43, ISSN

information to influence weights. *The Journal of Portfolio Management*, Vol.30, No.1,

**11** 

*Brazil* 

**Practical Applications** 

*Tiradentes University (UNIT), Aracaju,* 

Manuela Souza Leite and Paulo Jardel P. Araújo

**Relay Methods and Process Reaction Curves:** 

Proportional–integral–derivative (PID) controllers are the most adopted controllers in industrial settings because of the advantageous cost/benefit ratio they are able to provide (Astrom & Hanglund, 2006). Its function is very to explain and in most cases it is the easiest controller to adjust. Tuning controllers can significantly improve control performance. PID controller is to be applied in practical cases. It is seen that many PID variants have been developed in order to improve transient performance, such as biotechnological processes

Automation and process control can significantly influence the yield and final quality of products. However, there are few studies on the application of automatic controllers in the experimental plants. Most works focus on results obtained from computational simulations, that indeed do not represent these processes in all their complexity. The transient behavior and nonlinearities of these processes make the design of classical control dependent on trial-

In this context, this topic concerns in show some practical applications of use PID Controller. The development of a design and tuning method for use with PID controllers in

The primary function of a close-loop system is to make the controlled variable a desired value established by the set-point. Whenever the controlled variable becomes different then the set-point, the objective of the closed-loop system is to make then the same as quickly as possible. The controlled variable becomes different than the set-point under

One of the traditional ways to design a PID controller was to use empirical tuning rules based on measurements made on the real plant. Today is preferable for the PID designer to employ model based techniques. There is a large number of tuning methods, but in this chapter we describes for calculating proper values of the PID parameters (kc, ti, td) two

**1. Introduction** 

and chemical processes.

and-error methodology.

tree conditions: Set-point change; Disturbance;

Load demand change.

experimental processes for temperature control.

methods: Relay Methods and Process Reaction Curve.

**2. Tuning methods for pid controller** 
