University of Tehran School of Electrical and Computer

University of Tehran School of Electrical and Computer Engineering Center of Excellence for Control and Intelligent Processing Designing MIMO PID Controller using Colonial Competitive Algorithm: Applied to Distillation Column Process By: Esmaeil Atashpaz Gargari Farzad Hashemzadeh Caro Lucas Control and Intelligent Processing Center of Excellence, University of Tehran, Iran

Introduction Outline Main objective PID Controller for Multivariable Process Problem Statement What is Colonial Competitive Algorithm (CCA)? ¡ Simulation Results ¡ Conclusion ¡ ¡ 2 IEEE WCCI 2008

Introduction Main objective § To show an industrial application of a novel evolutionary optimization algorithm. § To design a MIMO PID controller for a distillation column process § The design objective in PID controller design is to track the system outputs by the inputs. § A colonial competitive Algorithm is used for this purpose. 3 IEEE WCCI 2008

PID Controller for Multivariable Process 4 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Introduction ¡ Colonial Competitive Algorithm (CCA) is novel sociopolitically motivated optimization strategy. ¡ Proposed by Atashpaz-gargari and Lucas in the papers“Imperialist Competitive Algorithm: An Algorithm for Optimization Inspired by Imperialistic Competition”. IEEE CEC 2007, Singapore ¡ Is inspired by sociopolitical process of Imperialism !! ¡ Since in late inception, it has been used in many applications. ¡ Has shown good convergence and global minimum achievement. ¡ Has a lot to do with. 5 IEEE WCCI 2008

Colonial Competitive Algorithm!? Is it useful? A short list of CCA applications 6 ¡ SISO PID Controller Design ¡ MIMO PID Controller design for Distillation Column Process ¡ Intelligent Recommender Systems ¡ Adaptive Antenna Design ¡ Optimal Layout design ¡ Nash Equilibrium point achievement ¡ Gershgorin Bands Narrowing ¡ Automated Guided Vehicle ¡ Materials property characterization through sharp and spherical indentation tests. ¡ … IEEE WCCI 2008

What is Colonial Competitive Algorithm? Basic Idea of CCA ¡ GAs use the biological evolution of human as a source of inspiration. ¡ Why most of evolutionary algorithms such as GA and SA are computer simulation of natural processes? Colonial Competitive ¡ Is human evolution limmited to biological evolution? Algorithm (CCA) ¡ No!! ¡ Are there. Is one ofkinds of evolution? question another the answers to this ¡ Yes. ! ¡ Is there any way to use these kind evolutions as a sourse of inspiration for an optimization algorithm? ¡ Yes. 7 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Basic Idea of CCA ¡ Imperialism is the policy of extending the power and rule of a government beyond its own boundaries. ¡ A country may attempt to dominate others by direct rule or by less obvious means such as a control of markets for goods or raw materials. The latter is often called neocolonialism. ¡ Imperialism changed the public attitude toward civilization of the West during 19 th and 20 th century. ¡ Social Darwinists interpreted imperialism and supported the idea that the culture of West is superior to the East’s culture. ! 8 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Basic idea of CCA ¡ According to the assimilation policy, some countries like France intended to construct a new France in Indochina through building French speaking schools and expanding its language and culture. ¡ In the proposed algorithm, the imperialists do the same for their colonies. !!! ¡ All the imperialists compete for taking possession of colonies of each other. ¡ Also assimilation policy is modeled by moving the colonies toward the imperialists. 9 IEEE WCCI 2008

What is Colonial Competitive Algorithm? A big picture 10 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Creating Initial Empires ¡ We form an array of variable values to be optimized. ¡ In GA terminology, this array is called “chromosome”, but here the term “country” is used for this array. Culture Economical Policy Language …. . Religion ¡ We are looking for the best country. That is a country with best Culture, Language, … ! 11 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Generating Initial Empires (Cont. ) 12 IEEE WCCI 2008

What is Colonial Competitive Algorithm? A big picture 13 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Assimilation Policy! Imperialist states started to spread their culture in their colonies through making the schools with their own language and. . . Language Culture 14 IEEE WCCI 2008

Revolution A sudden change in socio-political characteristics of a country 15 IEEE WCCI 2008

What is Colonial Competitive Algorithm? A big picture 16 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Exchanging Positions of the Imperialist and a Colony ¡ While moving toward the imperialist, a colony may reach to a position with lower cost than that of imperialist. ¡ In such a case, the imperialist moves to the position of that colony and vise versa. 17 IEEE WCCI 2008

What is Colonial Competitive Algorithm? A big picture 18 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Total Power of an Empire ¡ Total power of an empire is mainly affected by the power of imperialist country. ¡ But the power of the colonies of an empire has an effect, albeit negligible, on the total power of that empire. ¡ This fact is modeled by defining the total cost as 19 IEEE WCCI 2008

What is Colonial Competitive Algorithm? A big picture 20 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Imperialistic Competition ¡ all empires try to take possession of colonies of other empires and control them. 21 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Imperialistic Competition (Cont. ) Roulette Wheel? Maximum? 22 IEEE WCCI 2008

What is Colonial Competitive Algorithm? A big picture 23 IEEE WCCI 2008

What is Colonial Competitive Algorithm? Pseudo Code ¡ ¡ ¡ 24 ¡ ¡ Select some random points on the function and initialize the empires. Move the colonies toward their relevant imperialist (Assimilating). If there is a colony in an empire which has lower cost than that of imperialist, exchange the positions of that colony and the imperialist. Compute the total cost of all empires (Related to the power of both imperialist and its colonies). Pick the weakest colony (colonies) from the weakest empire and give it (them) to the empire that has the most likelihood to possess it (Imperialistic competition). Eliminate the powerless empires. If there is just one empire, stop, if not go to 2. IEEE WCCI 2008

Simulation Results 2*2 MIMO Distillation Column 25 IEEE WCCI 2008

Simulation Results § Wang, Q. G. , Zou, B. , Lee, T. H. , & Qiang, B. (1997). Autotuning of multivariable PID controllers from decentralized relay feedback. Automatica, 33(3), pp 319– 330. 26 IEEE WCCI 2008

Simulation Results Schematics 27 IEEE WCCI 2008

Simulation Results Convergence the steady state convergence value of CCA is 12. 8549, which is smaller than that of GA, 14. 9334. 28 IEEE WCCI 2008

Simulation Results Resulting Controllers 29 IEEE WCCI 2008

Simulation Results Step Responses Output 1 Output 2 30 IEEE WCCI 2008

Simulation Results Step Responses (Cont. ) Error Output 2 Error Output 1 31 IEEE WCCI 2008

Simulation Results Comparing § The controlller obtained by CCA has generally better performance than the others. 32 IEEE WCCI 2008

Conclusion ¡ Colonial Competitive Algorithm is a novel evolutionary optimization algorithm. ¡ It has successfully been used to solve some optimization problems. ¡ It is based on the sociopolitical evolution of human. ¡ It was able to properly tune the PID parameters for a MIMO ¡ It has a lot to do with. 33 IEEE WCCI 2008

The end Thanks for your attention! 34 IEEE WCCI 2008

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