As Cristiano Ronaldo left the Principality Stadium in Cardiff last June, a couple of hours after helping Real Madrid win its third Champions League trophy in four years - and La Duodecima, the 12th in its history - he walked past a black town car, idling by an exit.

Ronaldo peered into its tinted window, smiled and rapped his knuckles on the glass. A moment later, a door opened, and out stepped Florentino Perez, Real Madrid's president.

The two had seen each other only minutes earlier, in Real's locker room, where Perez had introduced King Juan Carlos of Spain to his jubilant players. Ronaldo, though, clearly wanted to exult just a little more in victory. "How do you like winning Champions Leagues?" he asked his president.

Perez, buttoning his jacket, smiled back. "I could say the same to you," he said. As the men embraced, Perez spoke again. He sounded almost solemn.

"What we are achieving," he whispered, "is not normal, you know."

Real Madrid's last four years have been anything but normal: not just because of those three Champions League triumphs, in Lisbon, Milan and Cardiff, but because of the manner in which they were achieved. Real was a club - and Perez a president - that seemed to defy too many of football's accepted wisdoms to succeed.

The team was too unbalanced and the squad, loaded up on attacking talent, too thin; managers came and went too frequently, and the latest incumbent, Zinedine Zidane, was regarded cruelly by some of his contemporaries as an "entrenador de palmas": a coach who did nothing more than clap.

And yet it all worked, spectacularly. That night in Cardiff, Real completed what Perez would later describe as "the best season, in terms of title triumphs, in our 115-year history." To the European Super Cup, the World Club Championship and the Spanish title was added a second consecutive Champions League crown. Real Madrid became the first team in the modern era to retain the trophy. To Perez, it was "the latest symbol of our legendary status: achieving something that had previously seemed impossible."

Quite how abnormal that season was has been laid bare in the months since. When Real Madrid returned to Champions League action on Wednesday, it did so with its season in ruins: Zidane's team sits fourth in La Liga, 17 points adrift of Barcelona. A spokesman for the Asociación de Socios de Real Madrid (SRM) - an advocacy group representing the 100,000 member-owners of the club - described it as "possibly the worst season in the club's history, an absolute failure of monumental proportions."

This time, Europe, as it so often has under Perez, provides no balm. At Real Madrid, that would mean only one thing: change. In Perez's two spells as president - from 2000 to 2006 and from 2009 onward - he has transformed his club into a sort of sporting Disneyland, a Panglossian paradise where everything is for the best, an endless victory parade. The image has to be maintained at all costs. "Any voice that is critical of his thinking is crossed out immediately as 'anti-Madridista,'" SRM said of Perez in an email. It is a mentality that also applies to fans and journalists.

Defeat, meanwhile, simply does not exist. Real Madrid TV, available for free to viewers throughout Spain, covers every Real game but does not hold live broadcast rights. It shows games Real has won in the days that follow. Footage of defeats - and sometimes ties, too - is quietly forgotten.

Perez's view of Real simply does not countenance the idea that it might lose games, at least not deservedly. When he first met Aleksander Ceferin, the then-recently installed president of UEFA, Perez's opening gambit was to ask why Real Madrid endured so many injustices at the hands of referees. Any setback, in Perez's eyes, could only be attributed to officials' incompetence or to dark conspiracy.

Of course, fostering this ruthless, relentless culture has brought Real - and by extension its president - no little reward: the European trophies; the title, bestowed by Forbes, of the most valuable sports brand on the planet; more than 200 million followers on social media.

But it all comes at a cost. Failure is not tolerated. Players who do not perform are replaced. Managers who do not deliver are fired. The question that lingers, ahead of the game against PSG, is whether the same goes for presidents.

Even within his Disneyland, there are those who feel that would not be a bad thing. Throughout Perez's reign, there has been a constant murmur of dissent from a small but significant section of Real's socios, who look beyond the glistening trophies to see a disturbing future ahead.

"There is a perception that Florentino's cycle has come to an end," said Eugenio Martinez Bravo, a leader of Plataforma Blanca, one of a number of groups that has sprung up in recent years to defend the interests of the socios.

"The members feel that the club is losing its identity," he added. "They do not feel close to Real Madrid. There is a lack of democracy and of transparency. Florentino has been in power for nearly 10 years, and nobody has ever voted for him."

When Perez returned as president in 2009, he did so unopposed (and to widespread popular acclaim). He has since called elections in 2013 and 2017, but again, has not had to face a rival candidate.

Some socios argue that was by design; Real's statutes have been tightened under Perez's aegis, and now dictate that any candidate for president has to have been a member of the club for more than 20 years - Perez is socio 2486 - and must provide a bank guarantee for personal wealth of 75 million euros (more than $92 million).

In theory, the changes were designed to protect Real from being taken over by a foreign owner; in reality, Martinez Bravo joked, the effect has been that now "to be president of Real Madrid, you have to be called Florentino."

"If you ask outside Madrid who owns Real, probably 70 percent would say Florentino, and not its members," said a spokesman for another socios group, Movimiento Ambar, which was formed in 2015 to press for Perez's resignation and new elections.

The fear, though, is that Perez is now so firmly ensconced that Real Madrid is no longer, in any real sense, a club owned by its own fans. "In practice, that has been completely forgotten," a spokesman for SRM said. Movimiento Ambar's spokesman was even more emotive. "We have gone from being members to being customers and viewers," he said.

"We have spoken to big businesses, to banks, to see if they would back a candidate to run against him," Martinez Bravo said. "But they all said the same thing: he is too powerful."

A glance at the directors' box at the Bernabeu at almost any game bears that out: the seats are filled by owners and editors of news media outlets and television stations, politicians, captains of industry. One newspaper has described it as "the Court of King Florentino."

Just how widespread the disaffection actually is may be hard to assess. Movimiento Ambar claims to speak for "thousands" of fans, but Martinez Bravo, for one, admits that the pressure for change has eased in recent years, thanks to all those Champions League victories.

"This year may be a turning point," he said. Perez has retained his power by achieving things that are simply not normal. Whether he can do so when Real looks very ordinary is a different question.